Scalar and vector H1 gradients share the existing value/divergence coefficient contractions. More...

#include <operand_evaluation.hpp>

Public Types
using	Term = typename OperandT::term_type

using	Value = discretization::forms::OperandValue<OperandT>

using	ReferenceValue = std::conditional_t<needs_vector_gradient, std::array<double, 9>, Value>

Static Public Member Functions
static void	sample_basis (const discretization::backend::mfem::DofMap &binding, int element, const ::mfem::IntegrationRule &rule, BasisEvaluation &basis, TensorBasisCache &cache, ContractionMode mode, ::mfem::ElementTransformation &transformation, BasisWorkspace &workspace)
	A global coefficient has basis one; spatial operands use their native element basis.

static void	sample_basis (const ::mfem::FiniteElement &element, const ::mfem::IntegrationRule &rule, BasisEvaluation &basis, TensorBasisCache &cache, ContractionMode mode, ::mfem::ElementTransformation &transformation, BasisWorkspace &workspace, const discretization::backend::mfem::ElementReconstruction *reconstruction=nullptr)
	Sample a canonical tensor/dense basis, then apply MFEM's fixed-mesh mapping.

static void	map_basis_point (int point, const mapping::MappingPointContext &context, const BasisEvaluation &reference, BasisEvaluation &result, BasisWorkspace &workspace, const mapping::MappingPointVariation *variation=nullptr)
	Apply SERiF's map to small tensor point maps, or to dense basis columns on other elements.

static void	evaluate (const BasisEvaluation &basis, const ::mfem::Vector &coefficients, ::mfem::Vector &values, BasisWorkspace &workspace)
	Apply a cached tensor or dense basis using reusable contraction scratch.

static void	integrate (const BasisEvaluation &basis, const ::mfem::Vector &values, ::mfem::Vector &result, BasisWorkspace &workspace)
	Transpose the same contraction; global scalar reductions retain compensated summation.

static ReferenceValue	reference_value (const ::mfem::Vector &values, int point)
	Read the reference data needed for one physical operand sample.

static Value	physical_value (const ReferenceValue &reference, const mapping::MappingPointContext &context)
	Apply only SERiF's additional fixed-mesh to physical map (MFEM's map is already included).

static Value	geometry_variation (const ReferenceValue &reference, const mapping::MappingPointContext &context, const mapping::MappingPointVariation &variation)
	At fixed coefficients: scalar gradients and H1 divergence vary through A^-1; values do not vary.

Static Public Attributes
static constexpr int	components = discretization::forms::component_count<Value>

static constexpr bool	global_scalar = discretization::blocks::GlobalScalarTerm<Term>

static constexpr bool	divergence = std::same_as<typename OperandT::operation_type, discretization::forms::Operation::Divergence>

static constexpr bool	vector_copies

static constexpr bool	h1_divergence = vector_copies && divergence

static constexpr bool	scalar_gradient = ScalarGradientOperand<OperandT>

static constexpr bool	vector_gradient = VectorGradientOperand<OperandT>

static constexpr bool	needs_vector_gradient = h1_divergence \|\| vector_gradient

static constexpr bool	geometry_dependent = needs_vector_gradient \|\| scalar_gradient

static constexpr int	reference_components = needs_vector_gradient ? 9 : components

Static Private Member Functions
static Value	transform_vector_gradient (const ReferenceValue &gradient, const ::mfem::DenseMatrix &inverse)
	Apply G_x = G_X A^-1; the inverse variation gives the same contraction for delta(G_x).

static Value	transform_gradient (const ReferenceValue &gradient, const ::mfem::DenseMatrix &inverse)
	grad_x(z) = A^-T grad_X(z); the inverse variation gives its geometry derivative.

static double	gradient_trace (const ReferenceValue &gradient, const ::mfem::DenseMatrix &inverse)
	div_x(u) = trace(G A^-1); replacing A^-1 by its variation gives delta(div_x(u)).

Detailed Description

template<MappedOperand OperandT>
struct serif::operators::backend::mfem::OperandEvaluator< OperandT >

Scalar and vector H1 gradients share the existing value/divergence coefficient contractions.