feat(polytrope-operator): finished computing the preconditioner

src/poly/utils/private/operator.cpp

@@ -193,10 +193,9 @@ void PolytropeOperator::Mult(const mfem::Vector &x, mfem::Vector &y) const {
 //       Trying to understand the multimodal hump in the residuals vector.
 //       There is a jupyter notebook about this. I was thinking that this was
 //       perhapse related to the non consistent application of boundary conditions.
-void approxJacobiInvert(const mfem::SparseMatrix& mat, std::unique_ptr<mfem::SparseMatrix>& invMat, std::string name="matrix") {
+void approxJacobiInvert(const mfem::SparseMatrix& mat, std::unique_ptr<mfem::SparseMatrix>& invMat, const std::string& name="matrix") {
-    // TODO: This likely can be made much more efficient and will probably be called in tight loops, a good
+    // PERF: This likely can be made much more efficient and will probably be called in tight loops, a good
-    // place for some easy optimization might be here.
+    // PERF:   place for some easy optimization might be here.
-    // Get the diagonal of the matrix
     mfem::Vector diag;
     mat.GetDiag(diag);
 
@@ -230,23 +229,12 @@ void PolytropeOperator::updateInverseSchurCompliment() const {
     mfem::SparseMatrix* temp_QxdfInv = mfem::Mult(*m_Qmat, *m_invNonlinearJacobian); // Q * df^{-1}
     mfem::SparseMatrix* temp_QxdfInvxM = mfem::Mult(*temp_QxdfInv, *m_Mmat); // Q * df^{-1} * M
 
+    // PERF: Could potentially add some caching in here to only update the preconditioner when some condition has been met
     schurCompliment->Add(-1, *temp_QxdfInvxM); // D - Q * df^{-1} * M
+    approxJacobiInvert(*schurCompliment, m_invSchurCompliment, "Schur Compliment");
 
-    // Note: EMB (April 9, 2025) Where I left for the day, so I don't pull my hair out tomorrow:
+    m_schurPreconditioner->SetDiagonalBlock(0, m_invNonlinearJacobian.get());
-    /*
+    m_schurPreconditioner->SetDiagonalBlock(1, m_invSchurCompliment.get());
-     * Need to calculate the inverse of Schur's compliment to precondition the jacobian
-     * I think I have this close; however, when running there is a seg fault when converting to a DenseMatrix for
-     *   writing out to CSV. This bodes poorly for the underlying memory structure.
-     *
-     * Also, there is a lot of math happening in these tight loops, probably need to think about that and
-     *   make it more efficient.
-     */
-
-    // TODO Also I need to actually invert the schur compliment since so far I have just found its non inverted state
-    // Should probably add an energy check to make sure it is roughly diagonal
-
-    // I did this manually in python for the non linear jacobian and the energy along the diagonal was ~99.999 % of the
-    // total energy indicating that it is very strongly diagonal.
 }
 
 mfem::Operator& PolytropeOperator::GetGradient(const mfem::Vector &x) const {

src/poly/utils/public/operator.h

@@ -64,15 +64,14 @@ private:
     /*
      * The schur preconditioner has the form
      *
-     * | df/drtheta^-1 0    |
+     *  ⎡ḟ(θ)^-1  0 ⎤
-     * | 0             S^-1 |
+     *  ⎣ 0     S^-1 ⎦
      *
      * Where S is the Schur compliment of the system
      *
      */
 
-    // TODO: I have not combined these parts yet and they need to be combined
+    mutable std::unique_ptr<mfem::BlockDiagonalPreconditioner> m_schurPreconditioner;
-    mutable std::unique_ptr<mfem::SparseMatrix> m_schurPreconditioner;
 
     bool m_isFinalized = false;