tboudreaux/RBPoly
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
61fe4d8ae80ed5a0f813065e5f28ec66e598ae6a
RBPoly/mapping.cpp

3172 lines
108 KiB
C++
Raw Blame History

//region Includes
#include <memory>
#include <mfem.hpp>
#include <print>
#include <format>
#include <string>
#include <functional>
#include <utility>
#include <vector>
#include <cmath>
#include <expected>
#include <CLI/CLI.hpp>
#include <XAD/XAD.hpp>
#include <chrono>
#include <umfpack.h>
//endregion
static size_t s_total_num_tests = 0;
#define LOG_POINT std::println("Log Point: {}", __COUNTER__)
#define CONCAT_INNER(a, b) a##b
#define CONCAT(a, b) CONCAT_INNER(a, b)
constexpr std::string_view ANSI_GREEN = "\033[32m";
constexpr std::string_view ANSI_RED = "\033[31m";
constexpr std::string_view ANSI_YELLOW = "\033[33m";
constexpr std::string_view ANSI_BLUE = "\033[34m";
constexpr std::string_view ANSI_MAGENTA = "\033[35m";
constexpr std::string_view ANSI_CYAN = "\033[36m";
constexpr std::string_view ANSI_RESET = "\033[0m";
#define MAKE_UNIQUE_VAR_NAME(prefix) CONCAT(prefix, __COUNTER__)
#define START_TIMER(timer_name) \
auto start_##timer_name = std::chrono::steady_clock::now()
#define REPORT_TIMER(timer_name) \
std::println("Timer '{}': {}", #timer_name, elapsed_##timer_name)
#define END_TIMER(timer_name) \
auto end_##timer_name = std::chrono::steady_clock::now(); \
std::chrono::duration<double, std::milli> elapsed_##timer_name = end_##timer_name - start_##timer_name; \
REPORT_TIMER(timer_name)
#define RUN_TEST_IMPL(test_name, test_func_w_args, id) \
const int CONCAT(mpi_world_rank_, id) = mfem::Mpi::WorldRank(); \
auto CONCAT(start_var_, id) = std::chrono::steady_clock::now(); \
if (CONCAT(mpi_world_rank_, id) == 0) { \
std::println("{}===== TEST: {} ====={}", ANSI_MAGENTA, test_name, ANSI_RESET); \
} \
test_func_w_args; \
if (CONCAT(mpi_world_rank_, id) == 0) { \
auto CONCAT(end_var_, id) = std::chrono::steady_clock::now(); \
std::chrono::duration<double, std::milli> CONCAT(elapsed_var_, id) = \
CONCAT(end_var_, id) - CONCAT(start_var_, id); \
std::println("{}===== END TEST: {} ({}runtime: {:+0.2f}ms{}) ====={}", ANSI_MAGENTA, \
test_name, \
ANSI_YELLOW, \
CONCAT(elapsed_var_, id).count(), \
ANSI_MAGENTA, \
ANSI_RESET); \
}
#define RANK_GUARD(proc) \
if (mfem::Mpi::WorldRank() == 0) { \
proc \
}
#define RUN_TEST(test_name, test_func_w_args) \
RUN_TEST_IMPL(test_name, test_func_w_args, __COUNTER__)
//region Test Utilities
enum class TEST_RESULT_TYPE : uint8_t {
SUCCESS,
FAILURE,
PARTIAL
};
std::string fmt_test_msg(const std::string_view test_name, const TEST_RESULT_TYPE type, size_t num_fails, size_t total) {
std::string_view color;
switch (type) {
case TEST_RESULT_TYPE::SUCCESS:
color = ANSI_GREEN;
break;
case TEST_RESULT_TYPE::FAILURE:
color = ANSI_RED;
break;
case TEST_RESULT_TYPE::PARTIAL:
color = ANSI_YELLOW;
break;
default:
color = ANSI_RESET;
}
return std::format("{}[TEST: {}] {}/{}{}", color, test_name, total-num_fails, total, ANSI_RESET);
}
//endregion
//region Constants
/********************
* Constants
*********************/
constexpr double G = 1.0;
constexpr double MASS = 1.0;
constexpr double RADIUS = 1.0;
constexpr double CENTRAL_DENSITY = 1.0;
constexpr char HOST[10] = "localhost";
constexpr int PORT = 19916;
//endregion
//region Concepts and Typedefs
/********************
* Concepts
*********************/
template <typename T>
concept is_xad =
std::is_same_v<T, xad::AReal<long double>>
|| std::is_same_v<T, xad::AReal<double>>
|| std::is_same_v<T, xad::AReal<float>>;
template <typename T>
concept is_real = std::is_floating_point_v<T> || is_xad<T>;
/********************
* Type Defs
*********************/
template <is_real T>
using EOS_P = std::function<T(T rho, T temp)>;
//endregion
//region User Argument Structs
/********************
* User Args
*********************/
struct potential {
double rtol;
double atol;
int max_iters;
};
struct rot {
bool enabled;
double omega;
};
struct Args {
std::string mesh_file;
potential p{};
rot r{};
bool verbose{};
double index{};
double mass{};
double c{};
int quad_boost{0};
int max_iters{};
double tol{};
};
//endregion
//region Misc Structs
struct OblatePotential {
bool use{false};
double a{1};
double c{1};
double rho_0{1};
};
struct Bounds {
double r_star_ref;
double r_inf_ref;
};
enum BoundsError : uint8_t {
CANNOT_FIND_VACUUM
};
//endregion
//region Domain Enums
enum class Domains : uint8_t {
CORE = 1 << 0,
ENVELOPE = 1 << 1,
VACUUM = 1 << 2,
STELLAR = CORE | ENVELOPE,
ALL = CORE | ENVELOPE | VACUUM
};
inline Domains operator|(Domains lhs, Domains rhs) {
return static_cast<Domains>(static_cast<uint8_t>(lhs) | static_cast<uint8_t>(rhs));
}
inline Domains operator&(Domains lhs, Domains rhs) {
return static_cast<Domains>(static_cast<uint8_t>(lhs) & static_cast<uint8_t>(rhs));
}
enum class Boundaries : uint8_t {
STELLAR_SURFACE = 1,
INF_SURFACE = 2
};
inline int operator-(Boundaries b, const int a) {
return static_cast<int>(static_cast<uint8_t>(b) - static_cast<uint8_t>(a));
}
//endregion
//region Domain Mapper
/********************
* Mappers
*********************/
class DomainMapper {
public:
DomainMapper(
const double r_star_ref,
const double r_inf_ref
) :
m_d(nullptr),
m_r_star_ref(r_star_ref),
m_r_inf_ref(r_inf_ref) {
InitAllScratchSpaces();
}
explicit DomainMapper(
const mfem::GridFunction &d,
const double r_star_ref,
const double r_inf_ref
) :
m_d(&d),
m_dim(d.FESpace()->GetMesh()->Dimension()),
m_r_star_ref(r_star_ref),
m_r_inf_ref(r_inf_ref) {
InitAllScratchSpaces();
};
[[nodiscard]] bool is_vacuum(const mfem::ElementTransformation &T) const {
if (T.ElementType == mfem::ElementTransformation::ELEMENT) {
return T.Attribute == m_vacuum_attr;
} else if (T.ElementType == mfem::ElementTransformation::BDR_ELEMENT) {
return T.Attribute == m_vacuum_attr - 1; // TODO: In a more robust code this should really be read from the stroid API to ensure that the vacuum boundary is really 1 - the vacuum material attribute
}
return false;
}
void SetDisplacement(const mfem::GridFunction &d) {
if (m_dim != d.FESpace()->GetMesh()->Dimension()) {
const std::string err_msg = std::format("Dimension mismatch: DomainMapper is initialized for dimension {}, but provided displacement field has dimension {}.", m_dim, d.FESpace()->GetMesh()->Dimension());
throw std::invalid_argument(err_msg);
}
m_d = &d;
InvalidateCache();
}
[[nodiscard]] bool IsIdentity() const {
return (m_d == nullptr);
}
void ResetDisplacement() {
m_d = nullptr;
InvalidateCache();
}
void ComputeJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &J) const {
J.SetSize(m_dim, m_dim);
J = 0.0;
m_J_D = 0.0;
if (IsIdentity()) {
for (int i = 0; i < m_dim; ++i) {
m_J_D(i, i) = 1.0; // Identity mapping
}
} else {
UpdateElementCache(T);
m_dshape.SetSize(m_fe->GetDof(), m_dim);
m_fe->CalcPhysDShape(T, m_dshape);
mfem::MultAtB(m_dof_mat, m_dshape, m_J_D);
for (int i = 0; i < m_dim; ++i) {
m_J_D(i, i) += 1.0;
}
}
if (is_vacuum(T)) {
T.Transform(T.GetIntPoint(), m_x_ref);
if (IsIdentity()) {
m_x_disp = m_x_ref;
} else {
m_shape.SetSize(m_fe->GetDof());
m_fe->CalcShape(T.GetIntPoint(), m_shape);
m_dof_mat.MultTranspose(m_shape, m_d_val);
add(m_x_ref, m_d_val, m_x_disp);
}
ComputeKelvinJacobian(m_x_ref, m_x_disp, m_J_D, J);
} else {
J = m_J_D;
}
}
double ComputeDetJ(mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) const {
if (IsIdentity() && !is_vacuum(T)) return 1.0; // If no mapping, the determinant of the Jacobian is 1
T.SetIntPoint(&ip);
mfem::DenseMatrix J;
ComputeJacobian(T, J);
return J.Det();
}
void ComputeMappedDiffusionTensor(mfem::ElementTransformation &T, mfem::DenseMatrix &D) const {
ComputeJacobian(T, m_J_temp);
const double detJ = m_J_temp.Det();
mfem::CalcInverse(m_J_temp, m_JInv_temp);
D.SetSize(m_dim, m_dim);
mfem::MultABt(m_JInv_temp, m_JInv_temp, D);
D *= fabs(detJ);
}
void ComputeInverseJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &JInv) const {
ComputeJacobian(T, m_J_temp);
JInv.SetSize(m_dim, m_dim);
mfem::CalcInverse(m_J_temp, JInv);
}
void GetPhysicalPoint(mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip, mfem::Vector& x_phys) const {
x_phys.SetSize(m_dim);
T.Transform(ip, m_x_ref);
if (IsIdentity()) {
x_phys = m_x_ref;
} else {
UpdateElementCache(T);
m_shape.SetSize(m_fe->GetDof());
m_fe->CalcShape(ip, m_shape);
m_dof_mat.MultTranspose(m_shape, m_d_val);
add(m_x_ref, m_d_val, x_phys);
}
if (is_vacuum(T)) {
ApplyKelvinMapping(m_x_ref, x_phys);
}
}
[[nodiscard]] const mfem::GridFunction* GetDisplacement() const { return m_d; }
[[nodiscard]] double GetPhysInfRadius() const {
return 1.0 / (1.0 - m_xi_clamp);
}
[[nodiscard]] size_t GetCacheHits() const {
return m_cache_hits;
}
[[nodiscard]] size_t GetCacheMisses() const {
return m_cache_misses;
}
[[nodiscard]] double GetCacheHitRate() const {
return (static_cast<double>(m_cache_hits)) / static_cast<double>(m_cache_misses + m_cache_hits);
}
void ResetCacheStats() const {
m_cache_hits = 0;
m_cache_misses = 0;
}
private:
void InitAllScratchSpaces() const {
m_J_D.SetSize(m_dim, m_dim);
m_J_temp.SetSize(m_dim, m_dim);
m_JInv_temp.SetSize(m_dim, m_dim);
m_x_ref.SetSize(m_dim);
m_x_disp.SetSize(m_dim);
m_d_val.SetSize(m_dim);
}
void ApplyKelvinMapping(const mfem::Vector& x_ref, mfem::Vector& x_phys) const {
const double r_ref = x_ref.Norml2();
double xi = (r_ref - m_r_star_ref) / (m_r_inf_ref - m_r_star_ref);
xi = std::clamp(xi, 0.0, m_xi_clamp);
const double factor = m_r_star_ref / (r_ref * (1 - xi));
x_phys *= factor;
}
void ComputeKelvinJacobian(const mfem::Vector& x_ref, const mfem::Vector &x_disp, const mfem::DenseMatrix &J_D, mfem::DenseMatrix& J) const {
const double r_ref = x_ref.Norml2();
const double delta_R = m_r_inf_ref - m_r_star_ref;
double xi = (r_ref - m_r_star_ref) / delta_R;
xi = std::clamp(xi, 0.0, m_xi_clamp);
const double denom = 1.0 - xi;
const double k = m_r_star_ref / (r_ref * denom);
const double dk_dr = m_r_star_ref * (( 1.0 / (delta_R* r_ref * denom * denom)) - ( 1.0 / (r_ref * r_ref * denom)));
J.SetSize(m_dim, m_dim);
const double outer_factor = dk_dr / r_ref;
for (int i = 0; i < m_dim; ++i) {
for (int j = 0; j < m_dim; ++j) {
J(i, j) = outer_factor * x_disp(i) * x_ref(j) + k * J_D(i, j);
}
}
}
void InvalidateCache() const {
m_cached_elem_id = -1;
}
void UpdateElementCache(const mfem::ElementTransformation& T) const {
if (IsIdentity()) return;
if (T.ElementNo != m_cached_elem_id || T.ElementType != m_cached_elem_type) {
m_cache_misses++;
m_cached_elem_id = T.ElementNo;
m_cached_elem_type = T.ElementType;
const mfem::FiniteElementSpace *fes = m_d->FESpace();
mfem::Array<int> vdofs;
if (T.ElementType == mfem::ElementTransformation::ELEMENT) {
m_fe = fes->GetFE(m_cached_elem_id);
fes->GetElementVDofs(m_cached_elem_id, vdofs);
} else {
m_fe = fes->GetBE(m_cached_elem_id);
fes->GetBdrElementVDofs(m_cached_elem_id, vdofs);
}
m_d->GetSubVector(vdofs, m_elem_dofs);
const int nd = m_fe->GetDof();
const int vd = fes->GetVDim();
m_dof_mat.UseExternalData(m_elem_dofs.GetData(), nd, vd);
} else {
m_cache_hits++;
}
}
private:
const mfem::GridFunction *m_d;
std::unique_ptr<mfem::GridFunction> m_internal_d;
const int m_dim{3};
const int m_vacuum_attr{3};
const double m_r_star_ref{1.0};
const double m_r_inf_ref{2.0};
const double m_xi_clamp{0.99999999};
mutable int m_cached_elem_id{-1};
mutable int m_cached_elem_type{mfem::ElementTransformation::ELEMENT};
mutable const mfem::FiniteElement* m_fe{nullptr};
mutable mfem::Vector m_elem_dofs;
mutable mfem::DenseMatrix m_dof_mat;
mutable mfem::DenseMatrix m_dshape;
mutable mfem::Vector m_shape;
mutable size_t m_cache_hits{0};
mutable size_t m_cache_misses{0};
mutable mfem::DenseMatrix m_J_D;
mutable mfem::DenseMatrix m_J_temp;
mutable mfem::DenseMatrix m_JInv_temp;
mutable mfem::Vector m_x_ref;
mutable mfem::Vector m_x_disp;
mutable mfem::Vector m_d_val;
};
//endregion
/********************
* Cache Types
*********************/
//region State Types
class MappedScalarCoefficient;
/********************
* State Types
*********************/
struct LORPrecWrapper : public mfem::Solver {
mfem::Solver& m_amg;
explicit LORPrecWrapper(mfem::Solver& amg) : mfem::Solver(amg.Height(), amg.Width()), m_amg(amg) {}
void SetOperator(const Operator &op) override {};
void Mult(const mfem::Vector &x, mfem::Vector &y) const override { m_amg.Mult(x, y); }
};
struct GravityContext {
std::unique_ptr<mfem::ParBilinearForm> ho_laplacian;
std::unique_ptr<mfem::ParBilinearForm> lor_laplacian;
std::unique_ptr<mfem::ParGridFunction> phi;
mfem::Array<int> ho_ess_tdof_list;
mfem::Array<int> lor_ess_tdof_list;
mfem::Array<int> stellar_mask;
std::unique_ptr<mfem::MatrixCoefficient> diff_coeff;
std::unique_ptr<mfem::ParLinearForm> b;
std::unique_ptr<mfem::GridFunctionCoefficient> rho_coeff;
std::unique_ptr<mfem::ConstantCoefficient> four_pi_G_coeff;
std::unique_ptr<mfem::ProductCoefficient> rhs_coeff;
std::unique_ptr<MappedScalarCoefficient> mapped_rhs_coeff;
std::unique_ptr<mfem::ConstantCoefficient> unit_coeff;
std::unique_ptr<mfem::HypreBoomerAMG> amg_prec;
std::unique_ptr<LORPrecWrapper> amg_wrapper;
std::unique_ptr<mfem::GMRESSolver> solver;
mfem::OperatorPtr A_ho;
mfem::OperatorPtr A_lor;
mfem::Vector B_true;
mfem::Vector X_true;
};
struct BoundaryContext {
mfem::Array<int> inf_bounds;
mfem::Array<int> stellar_bounds;
};
struct FEM {
std::unique_ptr<mfem::ParMesh> mesh;
std::unique_ptr<mfem::FiniteElementCollection> H1_fec;
std::unique_ptr<mfem::ParFiniteElementSpace> H1_fes;
std::unique_ptr<mfem::ParFiniteElementSpace> Vec_H1_fes;
std::unique_ptr<mfem::ParLORDiscretization> H1_lor_disc;
const mfem::ParFiniteElementSpace* H1_lor_fes{nullptr};
std::unique_ptr<DomainMapper> mapping;
mfem::Array<int> block_true_offsets;
std::unique_ptr<mfem::ParGridFunction> reference_x;
mfem::Vector com;
mfem::DenseMatrix Q;
mfem::Array<int> ess_tdof_x;
int int_order{3};
std::unique_ptr<mfem::IntegrationRule> int_rule;
GravityContext gravity_context;
BoundaryContext boundary_context;
[[nodiscard]] bool okay() const { return (mesh != nullptr) && (H1_fec != nullptr) && (H1_fes != nullptr) && (Vec_H1_fes != nullptr); }
[[nodiscard]] bool has_mapping() const { return mapping != nullptr; }
};
struct CoupledState {
std::unique_ptr<mfem::BlockVector> U;
mfem::GridFunction rho;
mfem::GridFunction d; // Stability depends on solving for the displacement vector not the nodal position vector, those live on a reference domain.
explicit CoupledState(const FEM& fem) {
U = std::make_unique<mfem::BlockVector>(fem.block_true_offsets);
rho.MakeRef(fem.H1_fes.get(), U->GetBlock(0), 0);
d.MakeRef(fem.Vec_H1_fes.get(), U->GetBlock(1), 0);
*U = 0.0;
U->GetBlock(2) = 1.0;
}
};
//endregion
//region Function Definitions
/********************
* Core Setup Functions
*********************/
FEM setup_fem(const std::string& filename, const Args &args);
/********************
* Utility Functions
*********************/
void view_mesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title);
double domain_integrate_grid_function(const FEM& fem, const mfem::GridFunction& gf, Domains domain = Domains::ALL);
mfem::Vector get_com(const FEM& fem, const mfem::GridFunction &rho);
void get_physical_coordinates(const mfem::GridFunction& reference_pos, const mfem::GridFunction& displacement, mfem::GridFunction& physical_pos);
void populate_element_mask(const FEM& fem, Domains domain, mfem::Array<int>& mask);
std::expected<Bounds, BoundsError> DiscoverBounds(const mfem::Mesh *mesh, int vacuum_attr);
int get_mesh_order(const mfem::Mesh &mesh);
void conserve_mass(const FEM& fem, mfem::GridFunction& rho, double target_mass);
/********************
* Physics Functions
*********************/
double centrifugal_potential(const mfem::Vector& phys_x, double omega);
double get_moment_of_inertia(const FEM& fem, const mfem::GridFunction& rho);
double oblate_spheroid_surface_potential(const mfem::Vector& x, double a, double c, double total_mass);
const mfem::GridFunction &grav_potential(FEM &fem, const Args &args, const mfem::GridFunction &rho,
bool phi_warm = false);
mfem::GridFunction get_potential(FEM &fem, const Args &args, const mfem::GridFunction &rho);
mfem::DenseMatrix compute_quadrupole_moment_tensor(const FEM& fem, const mfem::GridFunction& rho, const mfem::Vector& com);
double l2_multipole_potential(const FEM& fem, double total_mass, const mfem::Vector& phys_x);
//endregion
//region Mapping Coefficients
class MappedScalarCoefficient : public mfem::Coefficient {
public:
enum class EVAL_POINTS : uint8_t {
PHYSICAL,
REFERENCE
};
MappedScalarCoefficient(
const DomainMapper& map,
mfem::Coefficient& coeff,
const EVAL_POINTS eval_point=EVAL_POINTS::PHYSICAL
) :
m_map(map),
m_coeff(coeff),
m_eval_point(eval_point) {};
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
T.SetIntPoint(&ip);
double detJ = m_map.ComputeDetJ(T, ip);
double f_val = 0.0;
switch (m_eval_point) {
case EVAL_POINTS::PHYSICAL: {
f_val = eval_at_point(m_coeff, T, ip);
break;
}
case EVAL_POINTS::REFERENCE: {
f_val = m_coeff.Eval(T, ip);
break;
}
}
return f_val * fabs(detJ);
}
private:
static double eval_at_point(mfem::Coefficient& c, mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) {
return c.Eval(T, ip);
}
private:
const DomainMapper& m_map;
mfem::Coefficient& m_coeff;
EVAL_POINTS m_eval_point;
};
class MappedDiffusionCoefficient : public mfem::MatrixCoefficient {
public:
MappedDiffusionCoefficient(
const DomainMapper& map,
mfem::Coefficient& sigma,
const int dim
) :
mfem::MatrixCoefficient(dim),
m_map(map),
m_scalar(&sigma),
m_tensor(nullptr) {};
MappedDiffusionCoefficient(
const DomainMapper& map,
mfem::MatrixCoefficient& sigma
) :
mfem::MatrixCoefficient(sigma.GetHeight()),
m_map(map),
m_scalar(nullptr),
m_tensor(&sigma) {};
void Eval(mfem::DenseMatrix &K, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
const int dim = height;
T.SetIntPoint(&ip);
mfem::DenseMatrix J(dim, dim), JInv(dim, dim);
m_map.ComputeJacobian(T, J);
const double detJ = J.Det();
mfem::CalcInverse(J, JInv);
if (m_scalar) {
const double sig_val = m_scalar->Eval(T, ip);
mfem::MultABt(JInv, JInv, K);
K *= sig_val * fabs(detJ);
} else {
mfem::DenseMatrix sig_mat(dim, dim);
m_tensor->Eval(sig_mat, T, ip);
mfem::DenseMatrix temp(dim, dim);
Mult(JInv, sig_mat, temp);
MultABt(temp, JInv, K);
K *= fabs(detJ);
}
}
private:
const DomainMapper& m_map;
mfem::Coefficient* m_scalar;
mfem::MatrixCoefficient* m_tensor;
};
class MappedVectorCoefficient : public mfem::VectorCoefficient {
public:
MappedVectorCoefficient(
const DomainMapper& map,
mfem::VectorCoefficient& coeff
) :
mfem::VectorCoefficient(coeff.GetVDim()),
m_map(map),
m_coeff(coeff) {};
void Eval(mfem::Vector& V, mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) override {
const int dim = vdim;
T.SetIntPoint(&ip);
mfem::DenseMatrix JInv(dim, dim);
m_map.ComputeInverseJacobian(T, JInv);
double detJ = m_map.ComputeDetJ(T, ip);
mfem::Vector C_phys(dim);
m_coeff.Eval(C_phys, T, ip);
V.SetSize(dim);
JInv.Mult(C_phys, V);
V *= fabs(detJ);
}
private:
const DomainMapper& m_map;
mfem::VectorCoefficient& m_coeff;
};
class PhysicalPositionFunctionCoefficient : public mfem::Coefficient {
public:
using Func = std::function<double(const mfem::Vector& x)>;
PhysicalPositionFunctionCoefficient(
const DomainMapper& map,
Func f
) :
m_f(std::move(f)),
m_map(map) {};
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
T.SetIntPoint(&ip);
mfem::Vector x;
m_map.GetPhysicalPoint(T, ip, x);
return m_f(x);
}
private:
Func m_f;
const DomainMapper& m_map;
};
//endregion
//region Integrators
/********************
* Integrators
*********************/
template <is_xad EOS_T>
class FluidIntegrator : public mfem::NonlinearFormIntegrator {
using Scalar = EOS_T::value_type;
public:
explicit FluidIntegrator(
const FEM& fem,
EOS_P<EOS_T> eos,
const DomainMapper* map = nullptr
) :
m_fem(fem),
m_eos(std::move(eos)),
m_map(map)
{};
void AssembleElementVector(
const mfem::FiniteElement &el,
mfem::ElementTransformation &Tr,
const mfem::Vector &elfun,
mfem::Vector &elvect
) override {
const int dof = el.GetDof();
elvect.SetSize(dof);
elvect = 0.0;
const mfem::IntegrationRule *ir = m_fem.int_rule.get();
mfem::Vector shape(dof);
for (int i = 0; i < ir->GetNPoints(); i++) {
const mfem::IntegrationPoint& ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
el.CalcShape(ip, shape);
double u = shape * elfun;
EOS_T rho = u;
const double val = m_eos(rho, 0.0).value();
double weight = ip.weight * Tr.Weight() * val;
if (m_map) weight *= fabs(m_map->ComputeDetJ(Tr, ip));
elvect.Add(weight, shape);
}
}
void AssembleElementGrad(
const mfem::FiniteElement &el,
mfem::ElementTransformation &Tr,
const mfem::Vector &elfun,
mfem::DenseMatrix &elmat
) override {
const int dof = el.GetDof();
elmat.SetSize(dof);
elmat = 0.0;
const mfem::IntegrationRule *ir = m_fem.int_rule.get();
mfem::Vector shape(dof);
for (int i = 0; i < ir->GetNPoints(); i++) {
const mfem::IntegrationPoint& ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
el.CalcShape(ip, shape);
double u = shape * elfun;
double d_val_d_rho = 0.0;
if (u > 1e-15) {
xad::Tape<Scalar> tape;
EOS_T x_r = u;
EOS_T x_t = 0.0; // In future this is one area where we introduce a temp dependency
tape.registerInput(x_r);
EOS_T result = m_eos(x_r, x_t);
tape.registerOutput(result);
result.setAdjoint(1.0);
tape.computeAdjoints();
d_val_d_rho = x_r.getAdjoint();
}
double weight = ip.weight * Tr.Weight() * d_val_d_rho;
if (m_map) weight *= fabs(m_map->ComputeDetJ(Tr, ip));
mfem::AddMult_a_VVt(weight, shape, elmat);
}
}
[[nodiscard]] bool has_mapping() const { return m_map != nullptr; }
void set_mapping(const DomainMapper* map) { m_map = map; }
void clear_mapping() { m_map = nullptr; }
private:
const FEM& m_fem;
EOS_P<EOS_T> m_eos;
const DomainMapper* m_map{nullptr};
};
//endregion
//region Coefficients
/********************
* Coefficient Defs
*********************/
template <is_xad EOS_T>
class PressureBoundaryForce : public mfem::VectorCoefficient {
public:
PressureBoundaryForce(
const int dim,
const FEM& fem,
const mfem::GridFunction& rho,
const EOS_P<EOS_T>& eos,
const double P_fit
) : VectorCoefficient(dim), m_fem(fem), m_rho(rho), m_eos(eos), m_P_fit(P_fit) {};
void Eval(mfem::Vector &V, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
V.SetSize(vdim);
V = 0.0;
double rho = m_rho.GetValue(T, ip);
EOS_T x_rho = rho;
const double P_curr = m_eos(x_rho, 0.0).value();
const double delta_P = P_curr - m_P_fit;
mfem::Vector phys(vdim);
T.Transform(ip, phys);
mfem::Vector normal(vdim);
mfem::CalcOrtho(T.Jacobian(), normal);
for (int i = 0; i < vdim; ++i) {
V(i) = delta_P * normal(i);
}
}
private:
const FEM& m_fem;
const mfem::GridFunction& m_rho;
const EOS_P<EOS_T>& m_eos;
double m_P_fit;
};
template <is_xad EOS_T>
class MappingDetJacobianCoefficient : public mfem::Coefficient {
public:
MappingDetJacobianCoefficient(
const mfem::GridFunction& d,
const mfem::FiniteElementSpace& fes
) :
m_d(d),
m_fes(fes) {}
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
const int dim = T.GetSpaceDim();
mfem::DenseMatrix grad_d(dim, dim);
m_d.GetVectorGradient(T, grad_d);
for (int i = 0; i < dim; ++i) {
grad_d(i, i) += 1.0;
}
return grad_d.Det();
}
private:
const mfem::GridFunction& m_d; // Displacement vector
const mfem::FiniteElementSpace &m_fes;
};
//endregion
//region Operators
/********************
* Operator Defs
*********************/
template <is_xad EOS_T>
class VectorOperator : public mfem::Operator {
public:
VectorOperator() = default;
VectorOperator(
const mfem::Vector& v,
const bool is_col
) :
Operator(is_col ? v.Size() : 1, is_col ? 1 : v.Size()),
m_v(v),
m_is_col(is_col),
m_is_initialized(true) {}
void SetVector(const mfem::Vector& v, const bool is_col) {
if (v.Size() != m_v.Size()) {
m_v.SetSize(v.Size());
}
m_v = v;
m_is_col = is_col;
height = is_col ? v.Size() : 1;
width = is_col ? 1 : v.Size();
m_is_initialized = true;
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
if (!m_is_initialized) throw std::runtime_error("VectorOperator Not initialized");
if (m_is_col) {
y.SetSize(m_v.Size());
y = 0.0;
y.Add(x(0), m_v);
} else {
y.SetSize(1);
y(0) = m_v * x;
}
}
private:
mfem::Vector m_v;
bool m_is_col{false};
bool m_is_initialized{false};
};
template <is_xad EOS_T>
class PressureDensityCoupling : public mfem::Operator {
public:
PressureDensityCoupling(
FEM& fem,
const mfem::GridFunction& rho,
const EOS_P<EOS_T>& eos_pressure)
: Operator(fem.Vec_H1_fes->GetTrueVSize(), fem.H1_fes->GetTrueVSize()),
m_fem(fem),
m_rho(rho),
m_eos(eos_pressure) {
Assemble();
}
void Assemble() {
const int dim = m_fem.mesh->Dimension();
const int scalar_size = m_fem.H1_fes->GetTrueVSize();
const int vector_size = m_fem.Vec_H1_fes->GetTrueVSize();
m_mat = std::make_unique<mfem::SparseMatrix>(vector_size, scalar_size);
for (int be = 0; be < m_fem.mesh->GetNBE(); ++be) {
auto* ftr = m_fem.mesh->GetBdrFaceTransformations(be);
if (!ftr) continue;
const int elem = ftr->Elem1No;
const auto& scalar_fe = *m_fem.H1_fes->GetFE(elem);
const int sdof = scalar_fe.GetDof();
mfem::Array<int> scalar_dofs, vector_dofs;
m_fem.H1_fes->GetElementDofs(elem, scalar_dofs);
m_fem.Vec_H1_fes->GetElementDofs(elem, vector_dofs);
mfem::DenseMatrix elmat(vector_dofs.Size(), scalar_dofs.Size());
elmat = 0.0;
const auto& face_ir = mfem::IntRules.Get(ftr->GetGeometryType(), 2 * scalar_fe.GetOrder() + 2);
mfem::Vector shape(sdof);
mfem::Vector normal(dim);
for (int q = 0; q < face_ir.GetNPoints(); ++q) {
const auto& face_ip = face_ir.IntPoint(q);
ftr->SetAllIntPoints(&face_ip);
const mfem::IntegrationPoint& vol_ip = ftr->GetElement1IntPoint();
scalar_fe.CalcShape(vol_ip, shape);
mfem::CalcOrtho(ftr->Face->Jacobian(), normal);
mfem::ElementTransformation& vol_trans = ftr->GetElement1Transformation();
vol_trans.SetIntPoint(&vol_ip);
double rho_val = m_rho.GetValue(vol_trans, vol_ip);
double dPdrho = 0.0;
if (rho_val > 1e-15) {
using Scalar = EOS_T::value_type;
xad::Tape<Scalar> tape;
EOS_T x_rho = rho_val;
tape.registerInput(x_rho);
EOS_T P = m_eos(x_rho, EOS_T(0.0));
tape.registerOutput(P);
P.setAdjoint(1.0);
tape.computeAdjoints();
dPdrho = x_rho.getAdjoint();
}
const double w = face_ip.weight;
for (int k = 0; k < sdof; ++k) {
for (int j = 0; j < sdof; ++j) {
double base = -dPdrho * shape(j) * shape(k) * w;
for (int c = 0; c < dim; ++c) {
elmat(k + c * sdof, j) += base * normal(c);
}
}
}
}
m_mat->AddSubMatrix(vector_dofs, scalar_dofs, elmat);
}
m_mat->Finalize();
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
m_mat->Mult(x, y);
}
[[nodiscard]] mfem::SparseMatrix& SpMat() const { return *m_mat; }
private:
FEM& m_fem;
const mfem::GridFunction& m_rho;
const EOS_P<EOS_T>& m_eos;
std::unique_ptr<mfem::SparseMatrix> m_mat;
};
template <is_xad EOS_T>
class MassDisplacementCoupling : public mfem::Operator {
public:
MassDisplacementCoupling(
FEM& fem,
const mfem::GridFunction& rho,
const bool is_col
) :
Operator(
is_col ? fem.Vec_H1_fes->GetTrueVSize() : 1,
is_col ? 1 : fem.Vec_H1_fes->GetTrueVSize()
),
m_fem(fem),
m_rho(rho),
m_is_col(is_col){
m_D.SetSize(m_fem.Vec_H1_fes->GetTrueVSize());
Assemble();
}
void Assemble() const {
const int dim = m_fem.mesh->Dimension();
m_D = 0.0;
for (int elemID = 0; elemID < m_fem.mesh->GetNE(); ++elemID) {
auto* trans = m_fem.mesh->GetElementTransformation(elemID);
const auto& fe = *m_fem.Vec_H1_fes->GetFE(elemID);
const int dof = fe.GetDof();
mfem::Array<int> vdofs;
m_fem.Vec_H1_fes->GetElementDofs(elemID, vdofs);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2 * fe.GetOrder() + 1);
mfem::DenseMatrix dshape(dof, dim);
mfem::Vector elvec(dof * dim);
elvec = 0.0;
for (int q = 0; q < ir.GetNPoints(); ++q) {
const auto& ip = ir.IntPoint(q);
trans->SetIntPoint(&ip);
fe.CalcPhysDShape(*trans, dshape);
double rho_val = m_rho.GetValue(elemID, ip);
double ref_weight = trans->Weight() * ip.weight;
mfem::DenseMatrix J_map(dim, dim), J_inv(dim, dim);
m_fem.mapping->ComputeJacobian(*trans, J_map);
double detJ = J_map.Det();
mfem::CalcInverse(J_map, J_inv);
for (int k = 0; k < dof; ++k) {
for (int c = 0; c < dim; ++c) {
double trace_contrib = 0.0;
for (int j = 0; j < dim; ++j) {
trace_contrib += J_inv(j, c) * dshape(k, j);
}
elvec(k + c * dof) += rho_val * fabs(detJ) * trace_contrib * ref_weight;
}
}
}
m_D.AddElementVector(vdofs, elvec);
}
}
[[nodiscard]] mfem::Vector& GetVec() const {
return m_D;
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
if (m_is_col) {
y.SetSize(m_D.Size());
y = 0.0;
y.Add(x(0), m_D);
} else {
y.SetSize(1);
y(0) = m_D * x;
}
}
private:
const FEM& m_fem;
const mfem::GridFunction& m_rho;
const bool m_is_col;
mutable mfem::Vector m_D;
};
template <is_xad EOS_T>
class ResidualOperator : public mfem::Operator {
public:
ResidualOperator(
FEM& fem,
const Args& args,
const EOS_P<EOS_T>& eos_enthalpy,
const EOS_P<EOS_T>& eos_pressure,
const double alpha
) :
Operator(fem.block_true_offsets.Last()),
m_fem(fem),
m_args(args),
m_eos_enthalpy(eos_enthalpy),
m_eos_pressure(eos_pressure),
m_alpha(std::make_unique<mfem::ConstantCoefficient>(alpha)),
m_fluid_nlf(m_fem.H1_fes.get()),
m_reference_stiffness(m_fem.Vec_H1_fes.get())
{
auto* fluid_integrator = new FluidIntegrator<EOS_T>(m_fem, m_eos_enthalpy, m_fem.has_mapping() ? m_fem.mapping.get() : nullptr);
fluid_integrator->SetIntRule(fem.int_rule.get());
populate_element_mask(m_fem, Domains::STELLAR, m_stellar_mask);
m_bdr_mask.SetSize(m_fem.mesh->bdr_attributes.Max());
m_bdr_mask = 0;
m_bdr_mask[0] = 1;
m_fluid_nlf.AddDomainIntegrator(fluid_integrator, m_stellar_mask);
auto* alpha_integrator = new mfem::VectorMassIntegrator(*m_alpha);
alpha_integrator->SetIntRule(fem.int_rule.get());
auto* diff_integrator = new mfem::VectorDiffusionIntegrator();
diff_integrator->SetIntRule(fem.int_rule.get());
m_reference_stiffness.AddDomainIntegrator(alpha_integrator, m_stellar_mask);
m_reference_stiffness.AddDomainIntegrator(diff_integrator, m_stellar_mask);
m_reference_stiffness.Assemble();
m_reference_stiffness.Finalize();
};
void Mult(const mfem::Vector &u, mfem::Vector &r) const override {
mfem::GridFunction rho, d;
rho.MakeRef(m_fem.H1_fes.get(), u.GetData() + m_fem.block_true_offsets[0]);
d.MakeRef(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_true_offsets[1]);
double lambda = u(m_fem.block_true_offsets[2]);
m_fem.mapping->SetDisplacement(d);
m_fem.com = get_com(m_fem, rho);
m_fem.Q = compute_quadrupole_moment_tensor(m_fem, rho, m_fem.com);
mfem::GridFunction r_rho, r_d;
r_rho.MakeRef(m_fem.H1_fes.get(), r.GetData() + m_fem.block_true_offsets[0]);
r_d.MakeRef(m_fem.Vec_H1_fes.get(), r.GetData() + m_fem.block_true_offsets[1]);
double &r_lambda = r(m_fem.block_true_offsets[2]);
m_fluid_nlf.Mult(rho, r_rho);
auto phi = get_potential(m_fem, m_args, rho);
mfem::GridFunctionCoefficient phi_c(&phi);
MappedScalarCoefficient mapped_phi_c(*m_fem.mapping, phi_c);
mfem::LinearForm phi_lf(m_fem.H1_fes.get());
auto* potential_lf_integrator = new mfem::DomainLFIntegrator(mapped_phi_c);
potential_lf_integrator -> SetIntRule(m_fem.int_rule.get());
phi_lf.AddDomainIntegrator(potential_lf_integrator, m_stellar_mask);
phi_lf.Assemble();
r_rho += phi_lf;
mfem::ConstantCoefficient lambda_c(lambda);
MappedScalarCoefficient mapped_lambda_c(*m_fem.mapping, lambda_c);
mfem::LinearForm mass_grad_lf(m_fem.H1_fes.get());
auto* lambda_lf_integrator = new mfem::DomainLFIntegrator(mapped_lambda_c);
lambda_lf_integrator->SetIntRule(m_fem.int_rule.get());
mass_grad_lf.AddDomainIntegrator(lambda_lf_integrator, m_stellar_mask);
mass_grad_lf.Assemble();
// ReSharper disable once CppDFAUnusedValue
r_rho -= mass_grad_lf;
m_reference_stiffness.Mult(d, r_d);
PressureBoundaryForce<EOS_T> pbf(
m_fem.H1_fes->GetMesh()->Dimension(),
m_fem,
rho,
m_eos_pressure,
m_args.c
);
mfem::LinearForm pbf_lf(m_fem.Vec_H1_fes.get());
auto* vec_bdr_integrator = new mfem::VectorBoundaryLFIntegrator(pbf);
vec_bdr_integrator->SetIntRule(m_fem.int_rule.get());
pbf_lf.AddBoundaryIntegrator(vec_bdr_integrator, m_bdr_mask);
pbf_lf.Assemble();
r_d -= pbf_lf;
for (int i = 0; i < m_fem.ess_tdof_x.Size(); ++i) {
r_d(m_fem.ess_tdof_x[i]) = 0.0;
}
double current_mass = domain_integrate_grid_function(m_fem, rho, Domains::STELLAR);
r_lambda = current_mass - m_args.mass;
auto com = get_com(m_fem, rho);
std::cout << std::flush;
}
[[nodiscard]] Operator& GetGradient(const mfem::Vector &u) const override {
mfem::Array<int> stellar_mask;
populate_element_mask(m_fem, Domains::STELLAR, stellar_mask);
mfem::GridFunction rho, d;
rho.MakeRef(m_fem.H1_fes.get(), u.GetData() + m_fem.block_true_offsets[0]);
d.MakeRef(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_true_offsets[1]);
m_fem.mapping->SetDisplacement(d);
m_approx_jacobian = std::make_unique<mfem::BlockOperator>(m_fem.block_true_offsets);
const mfem::GridFunction grad(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_true_offsets[1]);
m_approx_jacobian->SetBlock(0, 0, &m_fluid_nlf.GetGradient(rho));
m_approx_jacobian->SetBlock(1, 1, &m_reference_stiffness);
B_vec.SetSize(m_fem.H1_fes->GetTrueVSize());
B_vec = 0.0;
mfem::ConstantCoefficient one(1.0);
MappedScalarCoefficient mapped_b_vec(*m_fem.mapping, one);
mfem::LinearForm b_lf(m_fem.H1_fes.get());
auto* lf_integrator = new mfem::DomainLFIntegrator(mapped_b_vec);
lf_integrator->SetIntRule(m_fem.int_rule.get());
b_lf.AddDomainIntegrator(lf_integrator, stellar_mask);
b_lf.Assemble();
B_vec += b_lf;
m_B_vec_op_row.SetVector(B_vec, false);
B_vec *= -1.0;
m_B_vec_op_col.SetVector(B_vec, true);
m_approx_jacobian->SetBlock(0, 2, &m_B_vec_op_col);
m_approx_jacobian->SetBlock(2, 0, &m_B_vec_op_row);
m_C = std::make_unique<PressureDensityCoupling<EOS_T>>(m_fem, rho, m_eos_pressure);
m_D = std::make_unique<MassDisplacementCoupling<EOS_T>>(m_fem, rho, false);
m_approx_jacobian->SetBlock(1, 0, m_C.get());
m_approx_jacobian->SetBlock(2, 1, m_D.get());
return *m_approx_jacobian;
}
private:
FEM& m_fem;
const Args& m_args;
const EOS_P<EOS_T>& m_eos_enthalpy;
const EOS_P<EOS_T>& m_eos_pressure;
const std::unique_ptr<mfem::ConstantCoefficient> m_alpha;
mutable mfem::Array<int> m_stellar_mask;
mutable mfem::Array<int> m_bdr_mask;
mutable mfem::NonlinearForm m_fluid_nlf;
mutable mfem::BilinearForm m_reference_stiffness;
mutable std::unique_ptr<mfem::BlockOperator> m_approx_jacobian = nullptr;
mutable mfem::Vector B_vec;
mutable VectorOperator<EOS_T> m_B_vec_op_col;
mutable VectorOperator<EOS_T> m_B_vec_op_row;
mutable std::unique_ptr<PressureDensityCoupling<EOS_T>> m_C;
mutable std::unique_ptr<MassDisplacementCoupling<EOS_T>> m_D;
};
class JFNKOperator : public mfem::Operator {
public:
JFNKOperator(const Operator& F, const mfem::Vector& u0, const mfem::Vector& F_u0) :
Operator(F.Width()), m_F(F), m_u0(u0), m_F_u0(F_u0), m_w(u0.Size()), m_eps(1e-8) {}
void Mult(const mfem::Vector &dx, mfem::Vector &Jdx) const override {
add(m_u0, m_eps, dx, m_w);
m_F.Mult(m_w, Jdx);
Jdx.Add(-1.0, m_F_u0);
Jdx /= m_eps;
}
private:
const Operator& m_F;
const mfem::Vector& m_u0;
const mfem::Vector& m_F_u0;
mutable mfem::Vector m_w;
double m_eps;
};
//endregion
//region Utility Functions
FEM setup_fem(const std::string& filename, const Args &args) {
FEM fem;
//==================================================================
// Section 1: Mesh and FE Space Setup
//==================================================================
mfem::Mesh serial_mesh(filename, 0, 0);
fem.mesh = std::make_unique<mfem::ParMesh>(MPI_COMM_WORLD, serial_mesh);
fem.mesh->EnsureNodes();
const int geom_order = get_mesh_order(*fem.mesh);
int dim = fem.mesh->Dimension();
// Assume solution space order == geometrical order
fem.H1_fec = std::make_unique<mfem::H1_FECollection>(geom_order, dim);
fem.H1_fes = std::make_unique<mfem::ParFiniteElementSpace>(fem.mesh.get(), fem.H1_fec.get());
fem.Vec_H1_fes = std::make_unique<mfem::ParFiniteElementSpace>(fem.mesh.get(), fem.H1_fec.get(), dim, mfem::Ordering::byNODES);
// LOR discretization for fast preconditioning
fem.H1_lor_disc = std::make_unique<mfem::ParLORDiscretization>(*fem.H1_fes);
fem.H1_lor_fes = &fem.H1_lor_disc->GetParFESpace();
//==================================================================
// Section 2: Domain Mapping
//==================================================================
auto [r_star_ref, r_inf_ref] = DiscoverBounds(fem.mesh.get(), 3)
.or_else([](const BoundsError& err)->std::expected<Bounds, BoundsError> {
throw std::runtime_error("Unable to determine vacuum domain reference boundary...");
}).value();
fem.mapping = std::make_unique<DomainMapper>(r_star_ref, r_inf_ref);
//==================================================================
// Section 3: Multi-physics Block-offsets
// Layout: [rho (scalar H1) | d (vector H1) | λ (scalar)]
//==================================================================
fem.block_true_offsets.SetSize(4);
fem.block_true_offsets[0] = 0;
fem.block_true_offsets[1] = fem.H1_fes->GetTrueVSize();
fem.block_true_offsets[2] = fem.block_true_offsets[1] + fem.Vec_H1_fes->GetTrueVSize();
fem.block_true_offsets[3] = fem.block_true_offsets[2] + 1;
//==================================================================
// Section 4: Multipole BC setup.
// Assumes:
// - COM starts at origin
// - Geometry starts out as a spherically symmetric
//==================================================================
fem.com.SetSize(dim); fem.com = 0.0;
fem.Q.SetSize(dim, dim); fem.Q = 0.0;
fem.reference_x = std::make_unique<mfem::ParGridFunction>(fem.Vec_H1_fes.get());
fem.mesh->GetNodes(*fem.reference_x);
//==================================================================
// Section 5: Integration Rules
// Assumes:
// - Mesh is composed of hex elements (CUBE)
//==================================================================
MFEM_ASSERT(fem.mesh->GetElementGeometry(0) == mfem::Geometry::CUBE, "Currently only hexahedral meshes are supported");
const int element_order = fem.H1_fes->GetMaxElementOrder();
fem.int_order = 2 * element_order + geom_order - 2 + args.quad_boost;
fem.int_rule = std::make_unique<mfem::IntegrationRule>(mfem::IntRules.Get(mfem::Geometry::CUBE, fem.int_order));
//==================================================================
// Section 6: Essential Degrees of Freedom and Boundary Markers
//==================================================================
fem.ess_tdof_x.SetSize(0); // No essential boundary conditions for the displacement, the null space here is handled with a weak penalty term
populate_element_mask(fem, Domains::STELLAR, fem.gravity_context.stellar_mask);
const int n_bdr_attrs = fem.mesh->bdr_attributes.Max();
fem.boundary_context.inf_bounds.SetSize(n_bdr_attrs);
fem.boundary_context.stellar_bounds.SetSize(n_bdr_attrs);
fem.boundary_context.inf_bounds = 0;
fem.boundary_context.stellar_bounds = 0;
fem.boundary_context.inf_bounds[Boundaries::INF_SURFACE - 1] = 1; // Vacuum boundary
fem.boundary_context.stellar_bounds[Boundaries::STELLAR_SURFACE - 1] = 1; // Stellar boundary
fem.H1_fes->GetEssentialTrueDofs(fem.boundary_context.inf_bounds, fem.gravity_context.ho_ess_tdof_list);
fem.H1_lor_fes->GetEssentialTrueDofs(fem.boundary_context.inf_bounds, fem.gravity_context.lor_ess_tdof_list);
//==================================================================
// Section 7: Gravity Solution Field
//==================================================================
fem.gravity_context.phi = std::make_unique<mfem::ParGridFunction>(fem.H1_fes.get());
*fem.gravity_context.phi = 0.0;
//==================================================================
// Section 8: Laplacian Coefficients
//==================================================================
fem.gravity_context.unit_coeff = std::make_unique<mfem::ConstantCoefficient>(1.0);
if (fem.has_mapping()) {
fem.gravity_context.diff_coeff = std::make_unique<MappedDiffusionCoefficient>(*fem.mapping, *fem.gravity_context.unit_coeff, fem.mesh->Dimension());
} else {
throw std::runtime_error("Unable to determine domain reference boundary or mapping...");
}
//==================================================================
// Section 9: High order Laplacian (Partial Assembly)
//==================================================================
fem.gravity_context.ho_laplacian = std::make_unique<mfem::ParBilinearForm>(fem.H1_fes.get());
{
auto* ho_di = new mfem::DiffusionIntegrator(*fem.gravity_context.diff_coeff);
ho_di->SetIntRule(fem.int_rule.get());
fem.gravity_context.ho_laplacian->AddDomainIntegrator(ho_di);
}
fem.gravity_context.ho_laplacian->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL);
fem.gravity_context.ho_laplacian->Assemble();
//==================================================================
// Section 10: Low order Laplacian (preconditioning)
//==================================================================
fem.gravity_context.lor_laplacian = std::make_unique<mfem::ParBilinearForm>(&fem.H1_lor_disc->GetParFESpace());
{
auto* lo_di = new mfem::DiffusionIntegrator(*fem.gravity_context.diff_coeff);
fem.gravity_context.lor_laplacian->AddDomainIntegrator(lo_di);
}
fem.gravity_context.lor_laplacian->Assemble();
fem.gravity_context.lor_laplacian->Finalize();
//==================================================================
// Section 11: Constrained System Operators
//==================================================================
fem.gravity_context.ho_laplacian->FormSystemMatrix(
fem.gravity_context.ho_ess_tdof_list,
fem.gravity_context.A_ho
);
fem.gravity_context.lor_laplacian->FormSystemMatrix(
fem.gravity_context.lor_ess_tdof_list,
fem.gravity_context.A_lor
);
//==================================================================
// Section 12: AMG Preconditioners and CG Solver
//==================================================================
fem.gravity_context.amg_prec = std::make_unique<mfem::HypreBoomerAMG>(*fem.gravity_context.A_lor.As<mfem::HypreParMatrix>());
fem.gravity_context.amg_prec->SetPrintLevel(0);
fem.gravity_context.amg_wrapper = std::make_unique<LORPrecWrapper>(*fem.gravity_context.amg_prec);
fem.gravity_context.solver = std::make_unique<mfem::GMRESSolver>(MPI_COMM_WORLD);
fem.gravity_context.solver->SetOperator(*fem.gravity_context.A_ho.Ptr());
fem.gravity_context.solver->SetPreconditioner(*fem.gravity_context.amg_wrapper);
fem.gravity_context.solver->SetRelTol(args.p.rtol);
fem.gravity_context.solver->SetAbsTol(args.p.atol);
fem.gravity_context.solver->SetMaxIter(1000);
fem.gravity_context.solver->SetKDim(50);
fem.gravity_context.solver->SetPrintLevel(0);
//==================================================================
// Section 13: RHS Coefficient Chain
// Assumes:
// - fem.gravity_context.rho_coeff->SetGridFunction(&rho)
// must be called before each assembly of the RHS
//==================================================================
fem.gravity_context.four_pi_G_coeff = std::make_unique<mfem::ConstantCoefficient>(-4.0 * M_PI * G);
fem.gravity_context.rho_coeff = std::make_unique<mfem::GridFunctionCoefficient>();
fem.gravity_context.rhs_coeff = std::make_unique<mfem::ProductCoefficient>(*fem.gravity_context.four_pi_G_coeff, *fem.gravity_context.rho_coeff);
fem.gravity_context.mapped_rhs_coeff = std::make_unique<MappedScalarCoefficient>(*fem.mapping, *fem.gravity_context.rhs_coeff, MappedScalarCoefficient::EVAL_POINTS::REFERENCE);
//==================================================================
// Section 14: RHS Linear Form
//==================================================================
fem.gravity_context.b = std::make_unique<mfem::ParLinearForm>(fem.H1_fes.get());
{
auto* grav_rhs_integrator = new mfem::DomainLFIntegrator(*fem.gravity_context.mapped_rhs_coeff);
grav_rhs_integrator->SetIntRule(fem.int_rule.get());
fem.gravity_context.b->AddDomainIntegrator(grav_rhs_integrator, fem.gravity_context.stellar_mask);
}
//=========================================================
// Section 15: Diagnostic Output
//=========================================================
std::println(
"{}Setup (rank: {}): element_order={}, geom_order={}, int_order={}, dim={}, "
"r_star={:.3f}, r_inf={:.3f}, HO_ndofs={}, LOR_ndofs={}{}",
ANSI_BLUE,
mfem::Mpi::WorldRank(),
element_order, geom_order, fem.int_order, dim,
r_star_ref, r_inf_ref,
fem.H1_fes->GlobalTrueVSize(), // Global DOF count for HO space
fem.H1_lor_fes->GlobalTrueVSize(), // Global DOF count for LOR space
ANSI_RESET);
return fem;
}
void update_stiffness_matrix(FEM& fem) {
auto& ctx = fem.gravity_context;
const mfem::GridFunction* saved_d = fem.mapping->GetDisplacement();
fem.mapping->ResetDisplacement();
ctx.lor_laplacian = std::make_unique<mfem::ParBilinearForm>(&fem.H1_lor_disc->GetParFESpace());
ctx.lor_laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator(*ctx.diff_coeff));
ctx.lor_laplacian->Assemble();
ctx.lor_laplacian->Finalize();
ctx.A_lor.Clear();
ctx.lor_laplacian->FormSystemMatrix(ctx.lor_ess_tdof_list, ctx.A_lor);
ctx.amg_prec = std::make_unique<mfem::HypreBoomerAMG>(*ctx.A_lor.As<mfem::HypreParMatrix>());
ctx.amg_prec->SetPrintLevel(0);
ctx.amg_wrapper = std::make_unique<LORPrecWrapper>(*ctx.amg_prec);
ctx.solver->SetPreconditioner(*ctx.amg_wrapper);
if (saved_d) {
fem.mapping->SetDisplacement(*saved_d);
}
ctx.ho_laplacian = std::make_unique<mfem::ParBilinearForm>(fem.H1_fes.get());
auto* ho_di = new mfem::DiffusionIntegrator(*ctx.diff_coeff);
ho_di->SetIntRule(fem.int_rule.get());
ctx.ho_laplacian->AddDomainIntegrator(ho_di);
ctx.ho_laplacian->SetAssemblyLevel(mfem::AssemblyLevel::PARTIAL);
ctx.ho_laplacian->Assemble();
ctx.A_ho.Clear();
ctx.ho_laplacian->FormSystemMatrix(ctx.ho_ess_tdof_list, ctx.A_ho);
ctx.solver->SetOperator(*ctx.A_ho.Ptr());}
void view_mesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title) {
mfem::socketstream sol_sock(host.c_str(), port);
if (!sol_sock.is_open()) return;
sol_sock << "solution\n" << mesh << gf;
sol_sock << "window_title '" << title << "\n" << std::flush;
}
double domain_integrate_grid_function(const FEM& fem, const mfem::GridFunction& gf, Domains domain) {
mfem::LinearForm lf(fem.H1_fes.get());
mfem::GridFunctionCoefficient gf_c(&gf);
double local_integral;
mfem::Array<int> elem_markers;
populate_element_mask(fem, domain, elem_markers);
if (fem.has_mapping()) {
MappedScalarCoefficient mapped_gf_c(*fem.mapping, gf_c);
// ReSharper disable once CppDFAMemoryLeak // Disabled because MFEM takes ownership so memory is not leaked
auto* lf_integrator = new mfem::DomainLFIntegrator(mapped_gf_c);
lf_integrator->SetIntRule(fem.int_rule.get());
lf.AddDomainIntegrator(lf_integrator, elem_markers);
lf.Assemble();
local_integral = lf.Sum();
} else {
lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(gf_c), elem_markers);
lf.Assemble();
local_integral = lf.Sum();
}
double global_integral = 0.0;
MPI_Allreduce(&local_integral, &global_integral, 1, MPI_DOUBLE, MPI_SUM, fem.H1_fes->GetComm());
return global_integral;
}
mfem::Vector get_com(const FEM& fem, const mfem::GridFunction &rho) {
const int dim = fem.mesh->Dimension();
mfem::Vector local_com(dim);
local_com = 0.0;
double local_mass = 0.0;
for (int i = 0; i < fem.H1_fes->GetNE(); ++i) {
if (fem.mesh->GetAttribute(i) == 3) continue;
mfem::ElementTransformation *trans = fem.H1_fes->GetElementTransformation(i);
const mfem::IntegrationRule &ir = *fem.int_rule;
for (int j = 0; j < ir.GetNPoints(); ++j) {
const mfem::IntegrationPoint &ip = ir.IntPoint(j);
trans->SetIntPoint(&ip);
double weight = trans->Weight() * ip.weight;
if (fem.has_mapping()) {
weight *= fem.mapping->ComputeDetJ(*trans, ip);
}
double rho_val = rho.GetValue(i, ip);
mfem::Vector phys_point(dim);
if (fem.has_mapping()) {
fem.mapping->GetPhysicalPoint(*trans, ip, phys_point);
} else {
trans->Transform(ip, phys_point);
}
const double mass_term = rho_val * weight;
local_mass += mass_term;
for (int d = 0; d < dim; ++d) {
local_com(d) += phys_point(d) * mass_term;
}
}
}
double global_mass = 0.0;
mfem::Vector global_com(dim);
MPI_Comm comm = fem.H1_fes->GetComm();
MPI_Allreduce(&local_mass, &global_mass, 1, MPI_DOUBLE, MPI_SUM, comm);
MPI_Allreduce(local_com.GetData(), global_com.GetData(), dim, MPI_DOUBLE, MPI_SUM, comm);
if (global_mass > 1e-18) {
global_com /= global_mass;
} else {
global_com = 0.0;
}
return global_com;
}
void get_physical_coordinates(const mfem::GridFunction& reference_pos, const mfem::GridFunction& displacement, mfem::GridFunction& physical_pos) {
add(reference_pos, displacement, physical_pos);
}
void populate_element_mask(const FEM &fem, Domains domain, mfem::Array<int> &mask) {
mask.SetSize(fem.mesh->attributes.Max());
mask = 0;
if ((domain & Domains::CORE) == Domains::CORE) {
mask[0] = 1;
}
if ((domain & Domains::ENVELOPE) == Domains::ENVELOPE) {
mask[1] = 1;
}
if ((domain & Domains::VACUUM) == Domains::VACUUM) {
mask[2] = 1;
}
}
std::expected<Bounds, BoundsError> DiscoverBounds(const mfem::Mesh *mesh, const int vacuum_attr) {
double local_min_r = std::numeric_limits<double>::max();
double local_max_r = -std::numeric_limits<double>::max();
bool found_vacuum = false;
for (int i = 0; i < mesh->GetNE(); ++i) {
if (mesh->GetAttribute(i) == vacuum_attr) {
found_vacuum = true;
mfem::Array<int> vertices;
mesh->GetElementVertices(i, vertices);
for (const int v : vertices) {
const double* coords = mesh->GetVertex(v);
double r = std::sqrt(coords[0]*coords[0] + coords[1]*coords[1] + coords[2]*coords[2]);
local_min_r = std::min(local_min_r, r);
local_max_r = std::max(local_max_r, r);
}
}
}
double global_min_r, global_max_r;
int global_found_vacuum;
int l_found = found_vacuum ? 1 : 0;
MPI_Comm comm = MPI_COMM_WORLD;
if (const auto* pmesh = dynamic_cast<const mfem::ParMesh*>(mesh)) {
comm = pmesh->GetComm();
}
MPI_Allreduce(&local_min_r, &global_min_r, 1, MPI_DOUBLE, MPI_MIN, comm);
MPI_Allreduce(&local_max_r, &global_max_r, 1, MPI_DOUBLE, MPI_MAX, comm);
MPI_Allreduce(&l_found, &global_found_vacuum, 1, MPI_INT, MPI_MAX, comm);
if (global_found_vacuum) {
return Bounds(global_min_r, global_max_r);
}
return std::unexpected(CANNOT_FIND_VACUUM);
}
int get_mesh_order(const mfem::Mesh &mesh) {
if (mesh.GetNodes() != nullptr) {
return mesh.GetNodes() -> FESpace() -> GetMaxElementOrder();
}
return 1;
}
void conserve_mass(const FEM& fem, mfem::GridFunction& rho, const double target_mass) {
if (const double current_mass = domain_integrate_grid_function(fem, rho, Domains::STELLAR); current_mass > 1e-15) rho *= (target_mass / current_mass);
}
//endregion
//region Physics Functions
double centrifugal_potential(const mfem::Vector& phys_x, const double omega) {
const double s2 = std::pow(phys_x(0), 2) + std::pow(phys_x(1), 2);
return -0.5 * s2 * std::pow(omega, 2);
}
double get_moment_of_inertia(const FEM& fem, const mfem::GridFunction& rho) {
auto s2_func = [](const mfem::Vector& x) {
return std::pow(x(0), 2) + std::pow(x(1), 2);
};
std::unique_ptr<mfem::Coefficient> s2_coeff;
if (fem.has_mapping()) {
s2_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, s2_func);
} else {
s2_coeff = std::make_unique<mfem::FunctionCoefficient>(s2_func);
}
mfem::GridFunctionCoefficient rho_coeff(&rho);
mfem::ProductCoefficient I_integrand(rho_coeff, *s2_coeff);
mfem::LinearForm I_lf(fem.H1_fes.get());
double I = 0.0;
// TODO: Need to filter here to just the stellar domain and also update the IntRule
if (fem.has_mapping()) {
MappedScalarCoefficient mapped_integrand(*fem.mapping, I_integrand);
I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_integrand));
I_lf.Assemble();
I = I_lf.Sum();
} else {
I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(I_integrand));
I_lf.Assemble();
I = I_lf.Sum();
}
return I;
}
//endregion
//region potentials
const mfem::GridFunction &grav_potential(FEM &fem, const Args &args, const mfem::GridFunction &rho, const bool phi_warm) {
auto& ctx = fem.gravity_context;
if (!phi_warm) {
*ctx.phi = 0.0;
}
double total_mass = domain_integrate_grid_function(fem, rho, Domains::STELLAR);
auto bdr_func = [&fem, total_mass](const mfem::Vector& x) {
return l2_multipole_potential(fem, total_mass, x);
};
PhysicalPositionFunctionCoefficient phi_bdr_coeff(*fem.mapping, bdr_func);
ctx.phi->ProjectBdrCoefficient(phi_bdr_coeff, fem.boundary_context.inf_bounds);
ctx.rho_coeff->SetGridFunction(&rho);
ctx.b->Assemble();
ctx.ho_laplacian->FormLinearSystem(
ctx.ho_ess_tdof_list,
*ctx.phi,
*ctx.b,
ctx.A_ho,
ctx.X_true,
ctx.B_true
);
ctx.solver->SetOperator(*ctx.A_ho.Ptr());
ctx.solver->Mult(ctx.B_true, ctx.X_true);
ctx.ho_laplacian->RecoverFEMSolution(ctx.X_true, *ctx.b, *ctx.phi);
return *ctx.phi;
}
mfem::GridFunction get_potential(FEM &fem, const Args &args, const mfem::GridFunction &rho) {
auto phi = grav_potential(fem, args, rho);
if (args.r.enabled) {
auto rot = [&args](const mfem::Vector& x) {
return centrifugal_potential(x, args.r.omega);
};
std::unique_ptr<mfem::Coefficient> centrifugal_coeff;
if (fem.has_mapping()) {
centrifugal_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, rot);
} else {
centrifugal_coeff = std::make_unique<mfem::FunctionCoefficient>(rot);
}
mfem::GridFunction centrifugal_gf(fem.H1_fes.get());
centrifugal_gf.ProjectCoefficient(*centrifugal_coeff);
phi += centrifugal_gf;
}
return phi;
}
mfem::DenseMatrix compute_quadrupole_moment_tensor(const FEM& fem, const mfem::GridFunction& rho, const mfem::Vector& com) {
const int dim = fem.mesh->Dimension();
mfem::DenseMatrix local_Q(dim, dim);
local_Q = 0.0;
for (int i = 0; i < fem.H1_fes->GetNE(); ++i) {
if (fem.mesh->GetAttribute(i) == 3) continue;
mfem::ElementTransformation *trans = fem.mesh->GetElementTransformation(i);
const mfem::IntegrationRule &ir = *fem.int_rule;
for (int j = 0; j < ir.GetNPoints(); ++j) {
const mfem::IntegrationPoint &ip = ir.IntPoint(j);
trans->SetIntPoint(&ip);
double weight = trans->Weight() * ip.weight;
if (fem.has_mapping()) {
weight *= fem.mapping->ComputeDetJ(*trans, ip);
}
const double rho_val = rho.GetValue(i, ip);
mfem::Vector phys_point(dim);
if (fem.has_mapping()) {
fem.mapping->GetPhysicalPoint(*trans, ip, phys_point);
} else {
trans->Transform(ip, phys_point);
}
mfem::Vector x_prime(dim);
double r_sq = 0.0;
for (int d = 0; d < dim; ++d) {
x_prime(d) = phys_point(d) - com(d);
r_sq += x_prime(d) * x_prime(d);
}
for (int m = 0; m < dim; ++m) {
for (int n = 0; n < dim; ++n) {
const double delta = (m == n) ? 1.0 : 0.0;
const double contrib = 3.0 * x_prime(m) * x_prime(n) - delta * r_sq;
local_Q(m, n) += rho_val * contrib * weight;
}
}
}
}
mfem::DenseMatrix global_Q(dim, dim);
MPI_Allreduce(local_Q.GetData(), global_Q.GetData(), dim * dim, MPI_DOUBLE, MPI_SUM, fem.H1_fes->GetComm());
return global_Q;
}
double l2_multipole_potential(const FEM &fem, const double total_mass, const mfem::Vector &phys_x) {
const double r = phys_x.Norml2();
if (r < 1e-12) return 0.0;
const int dim = fem.mesh->Dimension();
mfem::Vector n(phys_x);
n /= r;
double l2_mult_factor = 0.0;
for (int i = 0; i < dim; ++i) {
for (int j = 0; j < dim; ++j) {
l2_mult_factor += fem.Q(i, j) * n(i) * n(j);
}
}
const double l2_contrib = - (G / (2.0 * std::pow(r, 3))) * l2_mult_factor;
const double l0_contrib = -G * total_mass / r;
// l1 contribution is zero for a system centered on its COM
return l0_contrib + l2_contrib;
}
//endregion
//region Tests
void test_mesh_load(const FEM& fem) {
size_t failed = 0;
if (not fem.okay()) ++failed;
const int dim = fem.mesh->Dimension();
if (dim != 3) ++failed;
const int n_scalar = fem.H1_fes->GetTrueVSize();
const int n_vector = fem.Vec_H1_fes->GetTrueVSize();
if (n_vector != dim * n_scalar) ++failed;
if (fem.block_true_offsets[0] != 0) ++failed;
if (fem.block_true_offsets[1] != n_scalar) ++failed;
if (fem.block_true_offsets[2] != n_scalar + n_vector) ++failed;
if (fem.block_true_offsets[3] != n_scalar + n_vector + 1) ++failed;
constexpr size_t num_tests = 6;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::string test_msg = fmt_test_msg("Mesh Load Test", result_type, failed, num_tests);
std::println("{}", test_msg);
)
assert(dim == 3);
assert(n_vector == (n_scalar * dim));
assert (fem.block_true_offsets[0] == 0);
assert (fem.block_true_offsets[1] == n_scalar);
assert (fem.block_true_offsets[2] == n_scalar + n_vector);
assert (fem.block_true_offsets[3] == n_scalar + n_vector + 1);
}
void test_ref_coord_storage(const FEM& fem) {
size_t failed = 0;
if (not fem.mapping->IsIdentity()) ++failed;
const size_t num_elemIDs = std::min(30, fem.mesh->GetNE());
for (int elemID = 0; elemID < num_elemIDs; ++elemID) {
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2);
const auto& ip = ir.IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_ref, x_phys;
trans->Transform(ip, x_ref);
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
x_ref -= x_phys;
if (not (x_ref.Norml2() < 1e-12)) ++failed;
}
const size_t num_tests = num_elemIDs + 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::string test_msg = fmt_test_msg("Mesh Ref Coord", result_type, failed, num_tests);
std::println("{}", test_msg);
)
}
void test_reference_volume_integral(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
double vol = domain_integrate_grid_function(fem, ones, Domains::STELLAR);
double expected = (4.0/3.0) * M_PI * std::pow(RADIUS, 3.0);
double rel_err = std::abs(vol - expected) / expected;
if (rel_err > 1e-2) ++failed;
constexpr size_t num_tests = 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Reference Volume Integral", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Volume: {}, Expected: {}, Error (rel): {}", vol, expected, rel_err);
}
)
}
void test_spherically_symmetric_com(const FEM& fem) {
mfem::GridFunction rho(fem.H1_fes.get());
rho = 1.0;
mfem::Vector com = get_com(fem, rho);
size_t failed = 0;
const size_t dim = fem.mesh->Dimension();
const size_t num_tests = dim;
for (int dimID = 0; dimID < num_tests; ++dimID) {
if (std::abs(com(dimID)) > 1e-12) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Uniform COM", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\t COM=<{:+0.3E}, {:+0.3E}, {:+0.3E}>", com(0), com(1), com(2));
}
)
}
void test_com_variance_to_displacement(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction linear_displacement(fem.Vec_H1_fes.get());
linear_displacement = 10.0; // This will linearly displace the domain by 10 unit along all axes
fem.mapping->SetDisplacement(linear_displacement);
mfem::GridFunction rho(fem.H1_fes.get());
rho = 1.0;
mfem::Vector mapped_com = get_com(fem, rho);
const size_t dim = fem.mesh->Dimension();
const size_t num_tests = dim;
for (int dimID = 0; dimID < num_tests; ++dimID) {
if (10 - std::abs(mapped_com(dimID)) > 1e-12) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("COM variance to displacement", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE COM=<{:+0.2E}, {:+0.2E}, {:+0.2E}>", mapped_com(0), mapped_com(1), mapped_com(2));
}
)
fem.mapping->ResetDisplacement();
}
void test_volume_invariance_to_displacement(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction linear_displacement(fem.Vec_H1_fes.get());
linear_displacement = 10.0; // This will linearly displace the domain by 10 unit along all axes
fem.mapping->SetDisplacement(linear_displacement);
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
double mapped_vol = domain_integrate_grid_function(fem, ones, Domains::STELLAR);
double expected = (4.0/3.0) * M_PI * std::pow(RADIUS, 3.0);
double rel_err = std::abs(mapped_vol - expected) / expected;
if (rel_err > 1e-2) ++failed;
constexpr size_t num_tests = 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Invariance of volume against translation", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Volume: {}, Expected: {}", mapped_vol, expected);
}
)
fem.mapping->ResetDisplacement();
}
void test_volume_ellipsoid_deformation(const FEM& fem) {
size_t failed = 0;
size_t num_tests = 0;
constexpr double a = 2.0; // x-axis
constexpr double b = 0.5; // y-axis
constexpr double c = 1.5; // z-axis
constexpr double expected_vol = (4.0 / 3.0) * M_PI * a * b * c;
mfem::GridFunction ellipsoid_displacement(fem.Vec_H1_fes.get());
{
const int dim = fem.mesh->Dimension();
mfem::VectorFunctionCoefficient disp_coeff(dim, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(x.Size());
d(0) = (a - 1.0) * x(0);
d(1) = (b - 1.0) * x(1);
d(2) = (c - 1.0) * x(2);
});
ellipsoid_displacement.ProjectCoefficient(disp_coeff);
}
fem.mapping->SetDisplacement(ellipsoid_displacement);
{
++num_tests;
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
const double mapped_vol = domain_integrate_grid_function(fem, ones, Domains::STELLAR);
const double rel_err = std::abs(mapped_vol - expected_vol) / expected_vol;
if (rel_err > 1e-3) {
++failed;
RANK_GUARD(
std::println("\tFAILURE Test 1: Mapped volume = {:.6f}, expected = {:.6f}, rel_err = {:.2e}",
mapped_vol, expected_vol, rel_err);
)
}
}
{
++num_tests;
const double expected_x2_integral = std::pow(a, 3) * b * c * (4.0 * M_PI / 15.0);
mfem::GridFunction x_ref_sq(fem.H1_fes.get());
mfem::FunctionCoefficient x_sq_coeff([](const mfem::Vector& x) {
return x(0) * x(0);
});
x_ref_sq.ProjectCoefficient(x_sq_coeff);
mfem::GridFunction x_phys_sq(fem.H1_fes.get());
PhysicalPositionFunctionCoefficient x_phys_sq_coeff(*fem.mapping,
[](const mfem::Vector& x_phys) {
return x_phys(0) * x_phys(0);
}
);
x_phys_sq.ProjectCoefficient(x_phys_sq_coeff);
const double mapped_x2_integral = domain_integrate_grid_function(fem, x_phys_sq, Domains::STELLAR);
if (const double rel_err = std::abs(mapped_x2_integral - expected_x2_integral) / expected_x2_integral; rel_err > 1e-3) {
++failed;
RANK_GUARD(std::println("\tFAILURE Test 2: integral x_phys^2 = {:.6f}, expected = {:.6f}, rel_err = {:.2e}",
mapped_x2_integral, expected_x2_integral, rel_err);)
}
}
{
++num_tests;
constexpr double expected_detJ = a * b * c;
double max_detJ_err = 0.0;
for (int e = 0; e < std::min(5, fem.mesh->GetNE()); ++e) {
if (fem.mesh->GetAttribute(e) == 3) { // We want to ignore vacuum elements for this test
e--;
continue;
}
auto* trans = fem.mesh->GetElementTransformation(e);
const auto& ir = *fem.int_rule;
for (int q = 0; q < ir.GetNPoints(); ++q) {
const auto& ip = ir.IntPoint(q);
trans->SetIntPoint(&ip);
const double detJ = fem.mapping->ComputeDetJ(*trans, ip);
max_detJ_err = std::max(max_detJ_err, std::abs(detJ - expected_detJ));
}
}
if (max_detJ_err > 1e-10) {
++failed;
RANK_GUARD(std::println("\tFAILURE Test 3: max pointwise |det(J) - a*b*c| = {:.2e}", max_detJ_err);)
}
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(std::println("{}", fmt_test_msg("Volume under ellipsoidal deformation", result_type, failed, num_tests));)
fem.mapping->ResetDisplacement();
}
void test_uniform_potential(FEM& fem, const Args& args) {
fem.mapping->ResetDisplacement();
update_stiffness_matrix(fem);
const double analytic_vol = (4.0/3.0) * M_PI * std::pow(RADIUS, 3);
const double rho0 = MASS / analytic_vol;
mfem::GridFunction rho_uniform(fem.H1_fes.get());
rho_uniform = rho0;
fem.com = get_com(fem, rho_uniform);
fem.Q = compute_quadrupole_moment_tensor(fem, rho_uniform, fem.com);
const auto phi = grav_potential(fem, args, rho_uniform);
double local_max_abs_err = 0.0;
double local_max_rel_err = 0.0;
constexpr double tol = 1e-3;
size_t local_failed = 0;
size_t local_num_tests = 0;
const size_t num_elemIDs = std::min(30, fem.mesh->GetNE());
for (int elemID = 0; elemID < num_elemIDs; ++elemID) {
local_num_tests++;
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2);
const auto& ip = ir.IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_phys;
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
const double r = x_phys.Norml2();
if (r < 1e-9) continue;
const double phi_analytic = (-G * MASS / (2.0 * std::pow(RADIUS, 3.0))) * (3.0*RADIUS*RADIUS - r*r);
const double phi_fem = phi.GetValue(elemID, ip); // Evaluates local ParGridFunction part
const double abs_err = std::abs(phi_fem - phi_analytic);
const double rel_err = abs_err / std::abs(phi_analytic);
local_max_abs_err = std::max(local_max_abs_err, abs_err);
local_max_rel_err = std::max(local_max_rel_err, rel_err);
if (rel_err > tol) ++local_failed;
}
double global_max_abs_err = 0.0;
double global_max_rel_err = 0.0;
long global_failed = 0;
long global_num_tests = 0;
MPI_Comm comm = fem.H1_fes->GetComm();
MPI_Allreduce(&local_max_abs_err, &global_max_abs_err, 1, MPI_DOUBLE, MPI_MAX, comm);
MPI_Allreduce(&local_max_rel_err, &global_max_rel_err, 1, MPI_DOUBLE, MPI_MAX, comm);
long l_failed = static_cast<long>(local_failed);
long l_tests = static_cast<long>(local_num_tests);
MPI_Allreduce(&l_failed, &global_failed, 1, MPI_LONG, MPI_SUM, comm);
MPI_Allreduce(&l_tests, &global_num_tests, 1, MPI_LONG, MPI_SUM, comm);
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (global_failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (global_failed < global_num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Test Uniform Potential", result_type, global_failed, global_num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE || result_type == TEST_RESULT_TYPE::PARTIAL) {
std::println("\tFAILURE: global max abs error: {:+0.2E}, global max rel error: {:+0.2E}",
global_max_abs_err, global_max_rel_err);
}
)
}
void test_ellipsoidal_potential(FEM& fem, const Args& args) {
constexpr double a = 1.0 * RADIUS;
constexpr double b = a; // oblate
constexpr double c = 0.99 * RADIUS;
constexpr double expected_vol = (4.0 / 3.0) * M_PI * a * b * c;
constexpr double rho0 = MASS / expected_vol;
mfem::GridFunction ellipsoidal_disp(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient disp_coeff(3, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(3);
d(0) = (a/RADIUS - 1.0) * x(0);
d(1) = (b/RADIUS - 1.0) * x(1);
d(2) = (c/RADIUS - 1.0) * x(2);
});
ellipsoidal_disp.ProjectCoefficient(disp_coeff);
fem.mapping->SetDisplacement(ellipsoidal_disp);
update_stiffness_matrix(fem);
mfem::GridFunction rho(fem.H1_fes.get());
rho = rho0;
fem.com = get_com(fem, rho);
fem.Q = compute_quadrupole_moment_tensor(fem, rho, fem.com);
// OblatePotential oblate{.use=true, .a=a, .c=c,.rho_0=rho0};
const auto phi = grav_potential(fem, args, rho);
constexpr double e_sq = 1.0 - (c * c)/(a*a);
const double e = std::sqrt(e_sq);
const double I_const = (2.0 * std::sqrt(1.0 - e_sq) / e) * std::asin(e);
const double A_R = (std::sqrt(1.0-e_sq) / std::pow(e, 3.0)) * std::asin(e) - (1.0 - e_sq)/e_sq;
const double A_z = (2.0 / e_sq) * (1.0 - (std::sqrt(1.0-e_sq) / e) * std::asin(e));
size_t failed = 0;
size_t num_tests = 0;
double max_rel_err = 0.0;
double total_err = 0.0;
const size_t check_count = std::min(50, fem.mesh->GetNE());
for (int elemID = 0; elemID < check_count; ++elemID) {
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ip = mfem::IntRules.Get(trans->GetGeometryType(), 2).IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_phys;
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
const double R2 = x_phys(0)*x_phys(0) + x_phys(1)*x_phys(1);
const double z2 = x_phys(2)*x_phys(2);
const double phi_analytic = -M_PI * G * rho0 * (a*a*I_const - A_R * R2 - A_z * z2);
const double phi_fem = phi.GetValue(elemID, ip);
const double rel_err = std::abs(phi_fem - phi_analytic) / std::abs(phi_analytic);
max_rel_err = std::max(max_rel_err, rel_err);
total_err += rel_err;
num_tests++;
if (rel_err > 1e-3) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Test Ellipsoidal Potential", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: max rel error: {:+0.2E}, mean rel error: {:+0.2E}", max_rel_err, total_err/static_cast<double>(num_tests));
}
)
}
void test_ferrers_sphere_potential(FEM& fem, const Args& args) {
constexpr double R = RADIUS;
constexpr double rho0 = 1.0;
[[maybe_unused]] const double expected_mass = (8.0 / 15.0) * M_PI * rho0 * std::pow(R, 3.0);
fem.mapping->ResetDisplacement();
update_stiffness_matrix(fem);
mfem::FunctionCoefficient rho_coeff([&](const mfem::Vector& x) {
double r = x.Norml2();
if (r > R) return 0.0;
return rho0 * (1.0 - std::pow(r / R, 2.0));
});
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
fem.com = get_com(fem, rho);
fem.Q = compute_quadrupole_moment_tensor(fem, rho, fem.com);
const auto phi = grav_potential(fem, args, rho);
size_t failed = 0;
size_t num_tests = 0;
double max_rel_err = 0.0;
// Phi(r) = 4*pi*G*rho0 * (r^2/6 - r^4/(20*R^2)) - pi*G*rho0*R^2
const size_t check_count = std::min(50, fem.mesh->GetNE());
for (int elemID = 0; elemID < check_count; ++elemID) {
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ip = mfem::IntRules.Get(trans->GetGeometryType(), 2).IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_phys;
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
const double r = x_phys.Norml2();
if (r < R) {
num_tests++;
const double term1 = 4.0 * M_PI * G * rho0 * ((r*r / 6.0) - (std::pow(r, 4.0) / (20.0 * R*R)));
constexpr double term2 = M_PI * G * rho0 * R*R;
const double phi_analytic = term1 - term2;
const double phi_fem = phi.GetValue(elemID, ip);
const double rel_err = std::abs(phi_fem - phi_analytic) / std::abs(phi_analytic);
max_rel_err = std::max(max_rel_err, rel_err);
if (rel_err > 1e-4) ++failed;
}
}
RANK_GUARD(
auto result_type = (failed == 0) ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE;
std::println("{}", fmt_test_msg("Test Ferrers Inhomogeneous Potential", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: max rel error: {:+0.2E}", max_rel_err);
}
)
}
void test_force_continuity(FEM& fem, const Args& args) {
constexpr double rho0 = 1.0;
constexpr double R = RADIUS;
mfem::GridFunction rho(fem.H1_fes.get());
rho = rho0;
fem.mapping->ResetDisplacement();
update_stiffness_matrix(fem);
const auto phi = grav_potential(fem, args, rho);
size_t failed = 0;
size_t num_tests = 0;
double max_jump = 0.0;
for (int i = 0; i < fem.mesh->GetNE(); i++) {
mfem::ElementTransformation *T = fem.mesh->GetElementTransformation(i);
const mfem::IntegrationRule &ir = mfem::IntRules.Get(T->GetGeometryType(), 2);
for (int j = 0; j < ir.GetNPoints(); j++) {
const mfem::IntegrationPoint &ip = ir.IntPoint(j);
T->SetIntPoint(&ip);
mfem::Vector x;
fem.mapping->GetPhysicalPoint(*T, ip, x);
const double r = x.Norml2();
// Check very close to the surface R
if (std::abs(r - R) < 0.05) {
num_tests++;
mfem::Vector grad_phi;
phi.GetGradient(*T, grad_phi);
const double g_mag_fem = grad_phi.Norml2();
const double total_mass = (4.0/3.0) * M_PI * std::pow(R, 3.0) * rho0;
const double g_mag_analytic = (r <= R) ? (4.0/3.0)*M_PI*G*rho0*r : (G*total_mass)/(r*r);
const double rel_err = std::abs(g_mag_fem - g_mag_analytic) / g_mag_analytic;
max_jump = std::max(max_jump, rel_err);
if (rel_err > 5e-3) ++failed; // Gradients are usually 1 order less accurate than the solution
}
}
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Test Force Continuity",
(failed == 0) ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE, failed, num_tests));
)
}
void test_ferrers_ellipsoid_potential(FEM& fem, const Args& args) {
constexpr double a = 1.1 * RADIUS;
constexpr double b = 1.0 * RADIUS;
constexpr double c = 0.9 * RADIUS;
constexpr double rho0 = 1.0;
mfem::GridFunction ferrers_disp(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient disp_coeff(3, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(3);
d(0) = (a/RADIUS - 1.0) * x(0);
d(1) = (b/RADIUS - 1.0) * x(1);
d(2) = (c/RADIUS - 1.0) * x(2);
});
ferrers_disp.ProjectCoefficient(disp_coeff);
fem.mapping->SetDisplacement(ferrers_disp);
update_stiffness_matrix(fem);
auto rho_func = [&](const mfem::Vector& x_phys) {
double m2 = std::pow(x_phys(0)/a, 2) + std::pow(x_phys(1)/b, 2) + std::pow(x_phys(2)/c, 2);
return (m2 < 1.0) ? rho0 * (1.0 - m2) : 0.0;
};
PhysicalPositionFunctionCoefficient rho_coeff(*fem.mapping, rho_func);
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
fem.com = get_com(fem, rho);
fem.Q = compute_quadrupole_moment_tensor(fem, rho, fem.com);
const auto phi = grav_potential(fem, args, rho);
auto calc_analytic_phi = [&](const mfem::Vector& x) {
auto integrand = [&](double theta) {
if (theta == 0.0) return 0.0;
if (theta >= M_PI / 2.0) return 1.0 / a;
const double tan_t = std::tan(theta);
const double sec_t = 1.0 / std::cos(theta);
const double u = a * a * tan_t * tan_t;
const double du_dtheta = 2.0 * a * a * tan_t * sec_t * sec_t;
const double a2_u = a*a + u;
const double b2_u = b*b + u;
const double c2_u = c*c + u;
const double delta = std::sqrt(a2_u * b2_u * c2_u);
const double m_u2 = (x(0)*x(0))/a2_u + (x(1)*x(1))/b2_u + (x(2)*x(2))/c2_u;
const double val = 0.5 * std::pow(1.0 - m_u2, 2) / delta;
return val * du_dtheta;
};
int n_steps = 1000;
double dtheta = (M_PI / 2.0) / n_steps;
double sum = integrand(0.0) + integrand(M_PI / 2.0);
for (int i = 1; i < n_steps; ++i) {
const double theta = i * dtheta;
sum += (i % 2 == 0 ? 2.0 : 4.0) * integrand(theta);
}
sum *= dtheta / 3.0;
return -M_PI * G * a * b * c * rho0 * sum;
};
size_t failed = 0;
size_t num_tests = 0;
double max_rel_err = 0.0;
double total_rel_err = 0.0;
const size_t check_count = std::min(50, fem.mesh->GetNE());
for (int elemID = 0; elemID < check_count; ++elemID) {
if (fem.mesh->GetAttribute(elemID) != 1) continue;
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ip = mfem::IntRules.Get(trans->GetGeometryType(), 2).IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_phys;
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
double phi_fem = phi.GetValue(elemID, ip);
double phi_analytic = calc_analytic_phi(x_phys);
double rel_err = std::abs(phi_fem - phi_analytic) / std::abs(phi_analytic);
max_rel_err = std::max(max_rel_err, rel_err);
total_rel_err += rel_err;
num_tests++;
if (rel_err > 1e-4) ++failed;
}
RANK_GUARD(
auto result_type = (failed == 0) ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE;
std::println("{}", fmt_test_msg("Test Ferrers Ellipsoid (n=1)", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Max Rel Error: {:+0.2E}, Mean Rel Error: {:+0.2E}", max_rel_err, total_rel_err/static_cast<double>(num_tests));
}
)
}
void test_mass_conservation_constraint(const FEM& fem, const Args& args) {
constexpr double target_mass = MASS;
constexpr double R = RADIUS;
fem.mapping->ResetDisplacement();
mfem::FunctionCoefficient rho_coeff([&](const mfem::Vector& x) {
double r = x.Norml2();
return (r < R) ? (1.0 - (r/R)*(r/R)) : 0.0;
});
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
auto enforce_mass = [&](mfem::GridFunction& gf) {
double current_m = domain_integrate_grid_function(fem, gf, Domains::STELLAR);
if (current_m > 0.0) {
gf *= (target_mass / current_m);
}
};
size_t failed = 0;
size_t num_tests = 0;
enforce_mass(rho);
double mass_undeformed = domain_integrate_grid_function(fem, rho, Domains::STELLAR);
num_tests++;
if (std::abs(mass_undeformed - target_mass) / target_mass > 1e-12) {
failed++;
RANK_GUARD(
std::println("\tFAILURE (Undeformed Conservation):");
std::println("\t\tExpected Mass: {:.6e}", target_mass);
std::println("\t\tActual Mass: {:.6e}", mass_undeformed);
std::println("\t\tRel Error: {:+0.2E}", std::abs(mass_undeformed - target_mass) / target_mass);
)
}
constexpr double a = 1.5 * RADIUS;
constexpr double b = 0.8 * RADIUS;
constexpr double c = 0.5 * RADIUS;
mfem::GridFunction disp(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient disp_coeff(3, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(3);
d(0) = (a/R - 1.0) * x(0);
d(1) = (b/R - 1.0) * x(1);
d(2) = (c/R - 1.0) * x(2);
});
disp.ProjectCoefficient(disp_coeff);
fem.mapping->SetDisplacement(disp);
double expected_scaled_mass = target_mass * (a * b * c) / (R * R * R);
double mass_deformed_unscaled = domain_integrate_grid_function(fem, rho, Domains::STELLAR);
num_tests++;
if (std::abs(mass_deformed_unscaled - expected_scaled_mass) / expected_scaled_mass > 1e-10) {
failed++;
RANK_GUARD(
std::println("\tFAILURE (Geometric Scaling):");
std::println("\t\tDisplacement mapping did not correctly scale the physical mass integral.");
std::println("\t\tExpected Scaled Mass: {:.6e}", expected_scaled_mass);
std::println("\t\tActual Scaled Mass: {:.6e}", mass_deformed_unscaled);
std::println("\t\tRel Error: {:+0.2E}", std::abs(mass_deformed_unscaled - expected_scaled_mass) / expected_scaled_mass);
)
}
enforce_mass(rho);
double mass_deformed_conserved = domain_integrate_grid_function(fem, rho, Domains::STELLAR);
num_tests++;
if (std::abs(mass_deformed_conserved - target_mass) / target_mass > 1e-12) {
failed++;
RANK_GUARD(
std::println("\tFAILURE (Deformed Conservation):");
std::println("\t\tFailed to enforce mass constraint on the deformed geometry.");
std::println("\t\tExpected Mass: {:.6e}", target_mass);
std::println("\t\tActual Mass: {:.6e}", mass_deformed_conserved);
std::println("\t\tRel Error: {:+0.2E}", std::abs(mass_deformed_conserved - target_mass) / target_mass);
)
}
RANK_GUARD(
auto result_type = (failed == 0) ? TEST_RESULT_TYPE::SUCCESS : (failed < num_tests ? TEST_RESULT_TYPE::PARTIAL : TEST_RESULT_TYPE::FAILURE);
std::println("{}", fmt_test_msg("Test Mass Conservation Constraint", result_type, failed, num_tests));
)
}
void test_xad_eos_derivative(const FEM& fem, const Args& args) {
constexpr double K = 2.5;
constexpr double gamma = 5.0 / 3.0;
auto polytropic_eos = [&](const auto& rho) {
using std::pow; // Allow ADL to find xad::pow if necessary
return K * pow(rho, gamma);
};
fem.mapping->ResetDisplacement();
mfem::FunctionCoefficient rho_coeff([&](const mfem::Vector& x) {
double r = x.Norml2();
return std::max(0.1, 1.0 - (r / RADIUS));
});
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
size_t failed = 0;
size_t num_tests = 0;
double max_rel_err_p = 0.0;
double max_rel_err_dp = 0.0;
const size_t check_count = std::min(100, fem.mesh->GetNE());
for (int elemID = 0; elemID < check_count; ++elemID) {
if (fem.mesh->GetAttribute(elemID) != 1) continue; // Only Core elements
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ir = *fem.int_rule;
for (int q = 0; q < ir.GetNPoints(); ++q) {
const auto& ip = ir.IntPoint(q);
trans->SetIntPoint(&ip);
double rho_val = rho.GetValue(elemID, ip);
double p_analytic = K * std::pow(rho_val, gamma);
double dp_drho_analytic = K * gamma * std::pow(rho_val, gamma - 1.0);
xad::FReal<double> rho_ad(rho_val, 1.0);
xad::FReal<double> p_ad = polytropic_eos(rho_ad);
const double p_xad = p_ad.getValue();
const double dp_drho_xad = p_ad.getDerivative();
double rel_err_p = std::abs(p_xad - p_analytic) / std::abs(p_analytic);
double rel_err_dp = std::abs(dp_drho_xad - dp_drho_analytic) / std::abs(dp_drho_analytic);
max_rel_err_p = std::max(max_rel_err_p, rel_err_p);
max_rel_err_dp = std::max(max_rel_err_dp, rel_err_dp);
num_tests++;
if (rel_err_p > 1e-12 || rel_err_dp > 1e-12) {
failed++;
}
}
}
RANK_GUARD(
const auto result_type = (failed == 0) ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE;
std::println("{}", fmt_test_msg("Test XAD EOS Derivative", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Max Rel Error (P): {:+0.2E}, Max Rel Error (dP/drho): {:+0.2E}",
max_rel_err_p, max_rel_err_dp);
}
)
}
void test_domain_mapper_state_isolation(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction messy_disp(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient disp_coeff(3, [](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(3);
d(0) = std::sin(x(0) * M_PI);
d(1) = std::cos(x(1) * M_PI);
d(2) = x(0) * x(1);
});
messy_disp.ProjectCoefficient(disp_coeff);
fem.mapping->SetDisplacement(messy_disp);
int elem_A = 0;
int elem_B = fem.mesh->GetNE() / 2;
auto* trans_A = fem.mesh->GetElementTransformation(elem_A);
auto* trans_B = fem.mesh->GetElementTransformation(elem_B);
const auto& ip = mfem::IntRules.Get(trans_A->GetGeometryType(), 2).IntPoint(0);
mfem::DenseMatrix J_A_baseline, J_B_baseline, J_A_test, J_B_test;
trans_A->SetIntPoint(&ip);
fem.mapping->ComputeJacobian(*trans_A, J_A_baseline);
trans_B->SetIntPoint(&ip);
fem.mapping->ComputeJacobian(*trans_B, J_B_baseline);
for (int i = 0; i < 5; ++i) {
trans_A->SetIntPoint(&ip);
fem.mapping->ComputeJacobian(*trans_A, J_A_test);
trans_B->SetIntPoint(&ip);
fem.mapping->ComputeJacobian(*trans_B, J_B_test);
J_A_test.Add(-1.0, J_A_baseline);
if (J_A_test.MaxMaxNorm() > 1e-12) ++failed;
J_B_test.Add(-1.0, J_B_baseline);
if (J_B_test.MaxMaxNorm() > 1e-12) ++failed;
}
RANK_GUARD(
std::println("{}", fmt_test_msg("Test DomainMapper State Isolation",
(failed == 0) ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE,
failed, 10));
)
fem.mapping->ResetDisplacement();
}
void test_hydrostatic_zero_residual(FEM& fem, const Args& i_args) {
fem.mapping->ResetCacheStats();
Args args = i_args;
constexpr double R = RADIUS;
constexpr double k = M_PI / R;
constexpr double rho_c = 1.0;
constexpr double K_poly = (2.0 * G * R * R) / M_PI;
constexpr double exact_mass = (4.0 * R * R * R * rho_c) / M_PI;
constexpr double exact_lambda = -(4.0 * G * R * R * rho_c) / M_PI;
args.mass = exact_mass;
auto eos_pressure = [&](const auto& rho_val, const auto& temp_val) {
using std::pow;
return K_poly * pow(rho_val, 2.0);
};
auto eos_enthalpy = [&](const auto& rho_val, const auto& temp_val) {
return 2.0 * K_poly * rho_val;
};
fem.mapping->ResetDisplacement();
update_stiffness_matrix(fem);
mfem::FunctionCoefficient rho_coeff([&](const mfem::Vector& x) -> double {
double r = x.Norml2();
if (r < 1e-8) return rho_c;
if (r >= R) return 0.0;
return rho_c * std::sin(k * r) / (k * r);
});
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
mfem::BlockVector state(fem.block_true_offsets);
state = 0.0;
mfem::Vector& state_rho = state.GetBlock(0);
state_rho = rho; // TODO: How to this in a safer way which does not involve slicing a GridFunction into a vector
state(fem.block_true_offsets[2]) = exact_lambda;
mfem::BlockVector residual(fem.block_true_offsets);
residual = 0.0;
ResidualOperator<xad::AReal<double>> coupled_operator(fem, args, eos_enthalpy, eos_pressure, 1.0);
coupled_operator.Mult(state, residual);
mfem::Vector& r_rho = residual.GetBlock(0);
mfem::Vector& r_d = residual.GetBlock(1);
double r_lambda = residual(fem.block_true_offsets[2]);
double force_scale = K_poly * rho_c * rho_c * R * R;
double norm_rho = r_rho.Norml2() / force_scale;
double norm_d = r_d.Norml2();
double abs_r_lambda = std::abs(r_lambda) / exact_mass;
size_t failed = 0;
size_t num_tests = 3;
if (norm_rho > 1e-4) ++failed;
if (norm_d > 1e-4) ++failed;
if (abs_r_lambda > 1e-5) ++failed;
RANK_GUARD(
auto result_type = (failed == 0) ? TEST_RESULT_TYPE::SUCCESS :
(failed < num_tests ? TEST_RESULT_TYPE::PARTIAL : TEST_RESULT_TYPE::FAILURE);
std::println("{}", fmt_test_msg("Test Hydrostatic Zero Residual (n=1)", result_type, failed, num_tests));
if (result_type != TEST_RESULT_TYPE::SUCCESS) {
std::println("\tFAILURE: The Residual Operator did not achieve equilibrium.");
std::println("\t\tDensity Rel Residual (H + Phi - Lambda): {:+0.2E}", norm_rho);
std::println("\t\tDisplacement Abs Residual (Stiffness - PBF): {:+0.2E}", norm_d);
std::println("\t\tLambda Rel Residual (Mass Conservation): {:+0.2E}", abs_r_lambda);
}
)
mfem::BlockVector perturbed_state(state);
mfem::Vector& perturbed_rho = perturbed_state.GetBlock(0);
mfem::Vector& perturbed_d = perturbed_state.GetBlock(1);
perturbed_rho *= 1.05;
mfem::GridFunction p_d_gf(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient pd_coeff(3, [&](const mfem::Vector& x, mfem::Vector& v) {
v.SetSize(3);
v(0) = 0.01 + x(0);
v(1) = 0.01 + x(1);
v(2) = 0.01 + x(2);
});
p_d_gf.ProjectCoefficient(pd_coeff);
perturbed_d = p_d_gf;
mfem::BlockVector perturbed_residual(fem.block_true_offsets);
perturbed_residual = 0.0;
coupled_operator.Mult(perturbed_state, perturbed_residual);
mfem::Vector& p_r_rho = perturbed_residual.GetBlock(0);
mfem::Vector& p_r_d = perturbed_residual.GetBlock(1);
double p_r_lambda = perturbed_residual(fem.block_true_offsets[2]);
double p_norm_rho = p_r_rho.Norml2() / force_scale;
double p_norm_d = p_r_d.Norml2();
double p_abs_r_lambda = std::abs(p_r_lambda) / exact_mass;
size_t perturb_failed = 0;
size_t perturb_tests = 3;
if (p_norm_rho <= norm_rho) ++perturb_failed;
if (p_norm_d <= norm_d) ++perturb_failed;
if (p_abs_r_lambda <= abs_r_lambda) ++perturb_failed;
RANK_GUARD(
auto perturb_result = (perturb_failed == 0) ? TEST_RESULT_TYPE::SUCCESS :
(perturb_failed < perturb_tests ? TEST_RESULT_TYPE::PARTIAL : TEST_RESULT_TYPE::FAILURE);
std::println("{}", fmt_test_msg("Test Hydrostatic Perturbation Spike", perturb_result, perturb_failed, perturb_tests));
if (perturb_result != TEST_RESULT_TYPE::SUCCESS) {
std::println("\tFAILURE: Perturbing the state did not worsen the residual.");
std::println("\t\tDensity Res jump: {:.2e} -> {:.2e}", norm_rho, p_norm_rho);
std::println("\t\tDisp Res jump: {:.2e} -> {:.2e}", norm_d, p_norm_d);
std::println("\t\tLambda Res jump: {:.2e} -> {:.2e}", abs_r_lambda, p_abs_r_lambda);
};
)
}
void test_single_newton_step(FEM& fem, const Args& i_args) {
Args args = i_args;
constexpr double R = RADIUS;
constexpr double k = M_PI / R;
constexpr double rho_c = 1.0;
constexpr double K_poly = (2.0 * G * R * R) / M_PI;
constexpr double exact_mass = (4.0 * R * R * R * rho_c) / M_PI;
constexpr double exact_lambda = -(4.0 * G * R * R * rho_c) / M_PI;
args.mass = exact_mass;
auto eos_pressure = [&](const auto& rho_val, const auto& temp_val) {
using std::pow;
return K_poly * pow(rho_val, 2.0);
};
auto eos_enthalpy = [&](const auto& rho_val, const auto& temp_val) {
return 2.0 * K_poly * rho_val;
};
fem.mapping->ResetDisplacement();
mfem::FunctionCoefficient rho_coeff([&](const mfem::Vector& x) -> double {
double r = x.Norml2();
if (r < 1e-8) return rho_c;
if (r >= R) return 0.0;
return rho_c * std::sin(k * r) / (k * r);
});
mfem::GridFunction rho(fem.H1_fes.get());
rho.ProjectCoefficient(rho_coeff);
mfem::BlockVector state(fem.block_true_offsets);
state = 0.0;
mfem::Vector& state_rho = state.GetBlock(0);
state_rho = rho; // TODO: How to this in a safer way which does not involve slicing a GridFunction into a vector
state(fem.block_true_offsets[2]) = exact_lambda;
mfem::BlockVector residual(fem.block_true_offsets);
residual = 0.0;
ResidualOperator<xad::AReal<double>> coupled_operator(fem, args, eos_enthalpy, eos_pressure, 1.0);
mfem::BlockVector u_perturbed(state);
mfem::Vector& perturbed_rho = u_perturbed.GetBlock(0);
mfem::Vector& perturbed_d = u_perturbed.GetBlock(1);
perturbed_rho *= 1.05;
mfem::GridFunction p_d_gf(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient pd_coeff(3, [&](const mfem::Vector& x, mfem::Vector& v) {
v.SetSize(3);
v(0) = 0.01 * x(0);
v(1) = 0.01 * x(1);
v(2) = 0.01 * x(2);
});
p_d_gf.ProjectCoefficient(pd_coeff);
perturbed_d = p_d_gf;
mfem::BlockVector initial_res(fem.block_true_offsets);
coupled_operator.Mult(u_perturbed, initial_res);
double initial_norm = initial_res.Norml2();
// mfem::Operator& J = coupled_operator.GetGradient(u_perturbed);
JFNKOperator jfnk_j(coupled_operator, u_perturbed, initial_res);
mfem::BlockVector du(fem.block_true_offsets);
du = 0.0;
mfem::GMRESSolver solver;
solver.SetOperator(jfnk_j);
solver.SetAbsTol(1e-12);
solver.SetRelTol(1e-10);
solver.SetMaxIter(500);
solver.SetPrintLevel(0);
mfem::Vector neg_res = initial_res;
neg_res *= -1.0;
solver.Mult(neg_res, du);
mfem::BlockVector u_new(u_perturbed);
u_new += du;
// 5. Evaluate new residual
mfem::BlockVector final_res(fem.block_true_offsets);
coupled_operator.Mult(u_new, final_res);
double final_norm = final_res.Norml2();
bool success = (final_norm < initial_norm * 0.01);
RANK_GUARD(
std::println("{}", fmt_test_msg("Test Single Newton Step",
success ? TEST_RESULT_TYPE::SUCCESS : TEST_RESULT_TYPE::FAILURE,
success ? 1 : 0, 1));
std::println("\tInitial Residual Norm: {:.6e}", initial_norm);
std::println("\tFinal Residual Norm: {:.6e}", final_norm);
std::println("\tConvergence Factor: {:.2e}", final_norm / initial_norm);
)
}
//endregion
void run_grav_potential_timer(FEM& fem, const Args& args) {
mfem::GridFunction rho(fem.H1_fes.get());
rho = 1.0;
fem.com = get_com(fem, rho);
fem.Q = compute_quadrupole_moment_tensor(fem, rho, fem.com);
START_TIMER(grav_potential_cold_start);
auto phi_1 = grav_potential(fem, args, rho);
END_TIMER(grav_potential_cold_start);
rho *= 1.01;
START_TIMER(grav_potential_warm_start);
auto phi_2 = grav_potential(fem, args, rho, true);
END_TIMER(grav_potential_warm_start);
}
int main(int argc, char** argv) {
mfem::Mpi::Init(argc, argv);
std::string device_config = "cpu";
mfem::Device device(device_config);
const int myid = mfem::Mpi::WorldRank();
const int num_procs = mfem::Mpi::WorldSize();
if (myid == 0) {
std::println("Starting MFEM run on {} processors.", num_procs);
}
Args args;
CLI::App app{"Mapped Coordinates XAD-Enabled Non-Linear Solver"};
app.add_option("-m,--mesh", args.mesh_file)->required()->check(CLI::ExistingFile);
app.add_option("--max-iters", args.max_iters)->default_val(20);
app.add_option("--index", args.index)->default_val(1);
app.add_option("--mass", args.mass)->default_val(MASS);
app.add_option("--surface-pressure-scalar", args.c)->default_val(1e-4);
app.add_option("-q,--quad-boost", args.quad_boost)->default_val(0);
args.r.enabled = false;
args.p.rtol = 1e-8;
args.p.atol = 1e-7;
args.p.max_iters = 1000;
CLI11_PARSE(app, argc, argv);
FEM fem = setup_fem(args.mesh_file, args);
// run_grav_potential_timer(fem, args);
RUN_TEST("Mesh Loading", test_mesh_load(fem));
RUN_TEST("Test Reference Coordinates", test_ref_coord_storage(fem));
RUN_TEST("Test Reference Volume Integral", test_reference_volume_integral(fem));
RUN_TEST("Test Spherically Symmetric Center of Mass", test_spherically_symmetric_com(fem));
RUN_TEST("Test COM variance to displacement", test_com_variance_to_displacement(fem));
RUN_TEST("Test Volume Invariance to Displacement", test_volume_invariance_to_displacement(fem))
RUN_TEST("Test Volume of Ellipsoid Deformation", test_volume_ellipsoid_deformation(fem));
RUN_TEST("Test Uniform Potential", test_uniform_potential(fem, args));
RUN_TEST("Test Ellipsoidal Potential", test_ellipsoidal_potential(fem, args));
RUN_TEST("Test Ferrers Sphere Potential", test_ferrers_sphere_potential(fem, args));
RUN_TEST("Test Ferrers Ellipsoid Potential", test_ferrers_ellipsoid_potential(fem, args));
RUN_TEST("Test Mass Conservation Constraint", test_mass_conservation_constraint(fem, args));
RUN_TEST("Test XAD EOS Derivative", test_xad_eos_derivative(fem, args));
RUN_TEST("Test Force Continuity", test_force_continuity(fem, args));
RUN_TEST("Test Domain Mapper State Isolation", test_domain_mapper_state_isolation(fem));
RUN_TEST("Test Hydrostatic Zero Residuals", test_hydrostatic_zero_residual(fem, args));
// test_single_newton_step(fem, args);
// CoupledState state(fem);
// typedef xad::AReal<double> adouble;
//
// EOS_P<adouble> eos_enthalpy = [index = args.index](const adouble& rho, const adouble& temp) -> adouble {
// if (rho.value() < 1e-15) return {0.0};
// return (index + 1.0) * pow(rho, 1.0 / index);
// };
//
// EOS_P<adouble> eos_pressure = [index = args.index](const adouble& rho, const adouble& temp) -> adouble {
// if (rho.value() < 1e-15) return {0.0};
// return pow(rho, 1.0 + (1.0 / index));
// };
//
// auto init_rho_func = [&](const mfem::Vector& pt) {
// const double r = pt.Norml2();
// return (r < RADIUS) ? (1.0 - r/RADIUS) : 0.0;
// };
// mfem::FunctionCoefficient init_rho_coeff(init_rho_func);
// state.rho.ProjectCoefficient(init_rho_coeff);
// conserve_mass(fem, state.rho, args.mass);
// view_mesh(HOST, PORT, *fem.mesh, state.rho, "Initial Density Solution with XAD AD");
// view_mesh(HOST, PORT, *fem.mesh, state.d, "Initial Position Solution with XAD AD");
//
// std::println("Starting Coupled Block Solver with XAD AD...");
//
// ResidualOperator coupled_operator(fem, args, eos_enthalpy, eos_pressure);
//
// mfem::NewtonSolver newton_solver;
// newton_solver.SetOperator(coupled_operator);
// newton_solver.SetMaxIter(500);
// newton_solver.SetRelTol(1e-6);
// newton_solver.SetPrintLevel(1);
//
// mfem::GMRESSolver jfnk_solver;
// jfnk_solver.SetMaxIter(100);
// jfnk_solver.SetRelTol(1e-4);
// newton_solver.SetSolver(jfnk_solver);
// newton_solver.SetAdaptiveLinRtol(2, 0.5, 0.9, 0.9, 1.1);
//
// mfem::Vector zero_rhs(fem.block_offsets.Last());
// zero_rhs = 0.0;
// newton_solver.Mult(zero_rhs, *state.U);
//
// mfem::GridFunction rho(fem.H1_fes.get(), state.U->GetBlock(0), 0);
// mfem::GridFunction x(fem.Vec_H1_fes.get(), state.U->GetBlock(1), 0);
// view_mesh(HOST, PORT, *fem.mesh, rho, "Final Density Solution with XAD AD");
// view_mesh(HOST, PORT, *fem.mesh, x, "Final Position Solution with XAD AD");
//
// std::println("Solver finished using XAD machine-precision gradients.");
// return 0;
}
Reference in New Issue View Git Blame Copy Permalink