docs(laneEmdenVariationalForm): updated to match MFEM sign convention more closley

docs/derivations/laneEmdenVariationalForm/laneEmdenVariationalBlockForm.tex

@@ -84,7 +84,7 @@ Now we exploit the linearity of summation and integration to move the sums out o
 \end{align}
 We will now define $M_{kj}$, $D_{\ell j}$, and $Q_{\ell i}$ such that
 \begin{align}
-    M_{kj} &\equiv \int_{\Omega}\nabla \psi_{k}^{\theta}\cdot \vec{N}_{j}^{\phi}dV \\
+    M_{kj} &\equiv -\int_{\Omega}\nabla \psi_{k}^{\theta}\cdot \vec{N}_{j}^{\phi}dV \\
     D_{\ell j} &\equiv \int_{\Omega}\vec{\psi}_{\ell}^{\phi}\cdot\vec{N}_{j}^{\phi}dV \\
     Q_{\ell i} &\equiv \int_{\Omega}\vec{\psi}_{\ell}^{\phi}\cdot\nabla N_{i}^{\theta} dV
 \end{align}
@@ -96,18 +96,18 @@ f(\bar{\theta}) \equiv \int_{\Omega}\psi_{k}^{\theta}\left(\theta_{h}\right)^{n}
 \end{align}
 We can write the variational form of our system of equations as
 \begin{align}
--\sum_{j=1}^{N_{dof}^{\phi}}\phi_{j}M_{kj} + f(\bar{\theta)} &= 0 \\
+\sum_{j=1}^{N_{dof}^{\phi}}\phi_{j}M_{kj} + f(\bar{\theta)} &= 0 \\
 \sum_{j=1}^{N^{\phi}_{dof}}\phi_{j}D_{\ell j} - \sum_{i=1}^{N_{dof}^{\theta}}\theta_{i}Q_{\ell i} &= 0
 \end{align}
 Or using the notation we defined
 \begin{align}
--\mathbf{M}\bar{\phi} + f(\bar{\theta}) &= 0 \\
+\mathbf{M}\bar{\phi} + f(\bar{\theta}) &= 0 \\
 \mathbf{D}\bar{\phi} - \mathbf{Q}\bar{\theta} &= 0
 \end{align}
 We can then set this up as a matrix operation
 \begin{align}
     \begin{bmatrix}
-        0 & -\mathbf{M} \\
+        0 & \mathbf{M} \\
         -\mathbf{Q} & \mathbf{D}
     \end{bmatrix}
     \begin{bmatrix}
@@ -126,7 +126,7 @@ From this form we can easily see that the residual matrix is
 
 \begin{align}
     R &= \begin{bmatrix}
-        f(\bar{\theta}) - M\bar{\phi} \\
+        f(\bar{\theta}) + M\bar{\phi} \\
         D\bar{\phi} - Q\bar{\theta}
     \end{bmatrix}
 \end{align}
@@ -144,11 +144,11 @@ in our Newton-Raphson method. Generally the Jacobian is the matrix of partial de
 So then the Jacobian is
 \begin{align}
     J &= \begin{bmatrix}
-        \frac{\partial}{\partial \theta}\left(f(\theta) - M\phi\right) & \frac{\partial}{\partial \phi}\left(f(\theta) - M\phi\right) \\
+        \frac{\partial}{\partial \theta}\left(f(\theta) + M\phi\right) & \frac{\partial}{\partial \phi}\left(f(\theta) + M\phi\right) \\
         \frac{\partial}{\partial \theta}\left(D\phi - Q\theta\right) & \frac{\partial}{\partial \phi}\left(D\phi - Q\theta\right)
     \end{bmatrix} \\
     J &= \begin{bmatrix}
-        \frac{df}{d\theta} - \phi\frac{\partial M}{\partial \theta} & -M-\phi\frac{\partial M}{\partial \phi} \\
+        \frac{df}{d\theta} + \phi\frac{\partial M}{\partial \theta} & M+\phi\frac{\partial M}{\partial \phi} \\
         -Q - \theta\frac{\partial Q}{\partial \theta} & D + \phi\frac{\partial D}{\partial \phi} - \theta\frac{\partial Q}{\partial \phi}
     \end{bmatrix}
 \end{align}
@@ -156,7 +156,7 @@ So then the Jacobian is
 Finally, we know that the matrices $M$, $D$, and $Q$ are constant with respect to $\theta$ and $\phi$. Therefore, we can drop the partial derivatives with respect to $\theta$ and $\phi$ from the Jacobian. This gives us
 \begin{align}
   \mathbf{J} &= \begin{bmatrix}
-        \frac{df}{d\theta} & -M \\
+        \frac{df}{d\theta} & M \\
         -Q & D
     \end{bmatrix}
 \end{align}
@@ -164,9 +164,9 @@ Finally, we know that the matrices $M$, $D$, and $Q$ are constant with respect t
 \noindent In a fully assembled, distritized form this will look like
 
 \begin{align}
-  \mathbf{J} = \begin{bmatrix} \frac{df}{d\theta}_{00}          & \dots  & \frac{df}{d\theta}_{0n_{\theta}}          & -M_{00}                  & \dots            & -M_{0n_{\phi}} \\
+  \mathbf{J} = \begin{bmatrix} \frac{df}{d\theta}_{00}          & \dots  & \frac{df}{d\theta}_{0n_{\theta}}          & M_{00}                  & \dots            & M_{0n_{\phi}} \\
   \vdots          & \ddots &                          & \vdots                   & \ddots           & \\
-    \frac{df}{d\theta}_{n_{\theta}0} &        & \frac{df}{d\theta}_{n_{\theta}n_{\theta}} & -M_{n_{\theta}0}         &                  & -M_{n_{\theta}n_{\phi}} \\
+    \frac{df}{d\theta}_{n_{\theta}0} &        & \frac{df}{d\theta}_{n_{\theta}n_{\theta}} & M_{n_{\theta}0}         &                  & M_{n_{\theta}n_{\phi}} \\
   -Q_{00}         & \dots  & -Q_{0n_{\theta}}         & D_{00}                   & \dots            & D_{0n_{\phi}} \\
   \vdots          & \ddots &                          & \vdots                   & \ddots           & \\
   -Q_{n_{\phi}0}  &        & -Q_{n_{\phi}n_{\theta}}  & D_{n_{\phi}0}            &                  & D_{n_{\phi}n_{\phi}}

src/poly/utils/private/polytropeOperator.cpp

@@ -58,38 +58,50 @@ void PolytropeOperator::finalize(const mfem::Vector &initTheta) {
     m_Qmat = std::make_unique<mfem::SparseMatrix>(m_Q->SpMat());
     m_Dmat = std::make_unique<mfem::SparseMatrix>(m_D->SpMat());
 
+    saveSparseMatrixBinary(*m_Mmat, "MmatRawO2.bin");
+    saveSparseMatrixBinary(*m_Qmat, "QmatRawO2.bin");
+    saveSparseMatrixBinary(*m_Dmat, "DmatRawO2.bin");
+
     // Remove the essential dofs from the constant matrices
     for (const auto& dof: m_theta_ess_tdofs.first) {
+        std::cout << "Eliminating dof: " << dof << std::endl;
         m_Mmat->EliminateRow(dof);
         m_Qmat->EliminateCol(dof);
     }
 
+    saveSparseMatrixBinary(*m_Mmat, "MmatBCThetaO2.bin");
+    saveSparseMatrixBinary(*m_Qmat, "QmatBCThetaO2.bin");
+    saveSparseMatrixBinary(*m_Dmat, "DmatBCThetaO2.bin");
+
     for (const auto& dof: m_phi_ess_tdofs.first) {
         m_Mmat->EliminateCol(dof);
         m_Qmat->EliminateRow(dof);
         m_Dmat->EliminateRowCol(dof);
     }
+    saveSparseMatrixBinary(*m_Mmat, "MmatBCO2.bin");
+    saveSparseMatrixBinary(*m_Qmat, "QmatBCO2.bin");
+    saveSparseMatrixBinary(*m_Dmat, "DmatBCO2.bin");
 
     m_negM_mat = std::make_unique<mfem::ScaledOperator>(m_Mmat.get(), -1.0);
     m_negQ_mat = std::make_unique<mfem::ScaledOperator>(m_Qmat.get(), -1.0);
 
-    m_schurCompliment = std::make_unique<SchurCompliment>(*m_Qmat, *m_Dmat, *m_Mmat);
+    // m_schurCompliment = std::make_unique<SchurCompliment>(*m_Qmat, *m_Dmat, *m_Mmat);
 
     // Set up the constant parts of the jacobian now
 
     // We use the assembled matrices with their boundary conditions already removed for the jacobian
     m_jacobian = std::make_unique<mfem::BlockOperator>(m_blockOffsets);
-    m_jacobian->SetBlock(0, 1, m_negM_mat.get()); //<- -M (constant)
+    m_jacobian->SetBlock(0, 1, m_Mmat.get());     //<- M (constant)
     m_jacobian->SetBlock(1, 0, m_negQ_mat.get()); //<- -Q (constant)
     m_jacobian->SetBlock(1, 1, m_Dmat.get());     //<-  D (constant)
 
-    m_invSchurCompliment = std::make_unique<GMRESInverter>(*m_schurCompliment);
+    // m_invSchurCompliment = std::make_unique<GMRESInverter>(*m_schurCompliment);
 
     m_isFinalized = true;
 
     // Build the initial preconditioner based on some initial guess
     const auto &grad = m_f->GetGradient(initTheta);
-    updatePreconditioner(grad);
+    // updatePreconditioner(grad);
 
 }
 
@@ -137,7 +149,7 @@ void PolytropeOperator::Mult(const mfem::Vector &x, mfem::Vector &y) const {
     mfem::Vector Qtheta_term(phi_size);
 
     // Calculate R0 and R1 terms
-    // R0 = f(θ) - Mɸ
+    // R0 = f(θ) + Mɸ
     // R1 = Dɸ - Qθ
 
     MFEM_ASSERT(m_f.get() != nullptr, "NonlinearForm m_f is null in PolytropeOperator::Mult");
@@ -147,7 +159,7 @@ void PolytropeOperator::Mult(const mfem::Vector &x, mfem::Vector &y) const {
     m_D->Mult(x_phi, Dphi_term);
     m_Q->Mult(x_theta, Qtheta_term);
 
-    subtract(f_term, Mphi_term, y_R0);
+    add(f_term, Mphi_term, y_R0);
     subtract(Dphi_term, Qtheta_term, y_R1);
 
     // -- Apply essential boundary conditions --
@@ -211,7 +223,7 @@ mfem::Operator& PolytropeOperator::GetGradient(const mfem::Vector &x) const {
     const mfem::Vector& x_theta = x_block.GetBlock(0);
 
     auto &grad = m_f->GetGradient(x_theta);
-    updatePreconditioner(grad);
+    // updatePreconditioner(grad);
 
     m_jacobian->SetBlock(0, 0, &grad);
 

src/poly/utils/private/utilities.cpp

@@ -0,0 +1,5 @@
+//
+// Created by Emily Boudreaux on 6/4/25.
+//
+
+#include "utilities.h"