feat(poly): moved to a block form for poly

essential dofs can be applied to both theta and phi (grad theta) if we move to a block form. I have done this derivation and made that change so that we can properly apply the central boundary condition to the slope

src/poly/utils/private/integrators.cpp

@@ -0,0 +1,118 @@
+/* ***********************************************************************
+//
+//   Copyright (C) 2025 -- The 4D-STAR Collaboration
+//   File Author: Emily Boudreaux
+//   Last Modified: March 19, 2025
+//
+//   4DSSE is free software; you can use it and/or modify
+//   it under the terms and restrictions the GNU General Library Public
+//   License version 3 (GPLv3) as published by the Free Software Foundation.
+//
+//   4DSSE is distributed in the hope that it will be useful,
+//   but WITHOUT ANY WARRANTY; without even the implied warranty of
+//   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+//   See the GNU Library General Public License for more details.
+//
+//   You should have received a copy of the GNU Library General Public License
+//   along with this software; if not, write to the Free Software
+//   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+//
+// *********************************************************************** */
+#include "mfem.hpp"
+#include <cmath>
+#include <vector>
+#include <limits>
+#include <stdexcept>
+
+#include "quill/LogMacros.h"
+
+#include "integrators.h"
+#include "debug.h"
+
+
+namespace polyMFEMUtils {
+  NonlinearPowerIntegrator::NonlinearPowerIntegrator(
+    mfem::Coefficient &coeff,
+    double n) : 
+    
+    m_coeff(coeff), 
+    m_polytropicIndex(n) {}
+
+  void NonlinearPowerIntegrator::AssembleElementVector(
+    const mfem::FiniteElement &el,
+    mfem::ElementTransformation &Trans,
+    const mfem::Vector &elfun,
+    mfem::Vector &elvect) {
+      
+      const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
+      int dof = el.GetDof();
+      elvect.SetSize(dof);
+      elvect = 0.0;
+  
+      mfem::Vector shape(dof);
+  
+      for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
+        mfem::IntegrationPoint ip = ir->IntPoint(iqp);
+        Trans.SetIntPoint(&ip);
+        double weight = ip.weight * Trans.Weight();
+  
+        el.CalcShape(ip, shape);
+  
+        double u_val = 0.0;
+        for (int j = 0; j < dof; j++) {
+          u_val += elfun(j) * shape(j);
+        }
+        double u_safe = std::max(u_val, 0.0);
+        double u_nl = std::pow(u_safe, m_polytropicIndex);
+  
+        double coeff_val = m_coeff.Eval(Trans, ip);
+        double x2_u_nl = coeff_val * u_nl;
+  
+        for (int i = 0; i < dof; i++){
+          elvect(i) += shape(i) * x2_u_nl * weight;
+        }
+      }
+    }
+  
+
+    void NonlinearPowerIntegrator::AssembleElementGrad (
+      const mfem::FiniteElement &el,
+      mfem::ElementTransformation &Trans,
+      const mfem::Vector &elfun,
+      mfem::DenseMatrix &elmat) {
+    
+        const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
+        int dof = el.GetDof();
+        elmat.SetSize(dof);
+        elmat = 0.0;
+        mfem::Vector shape(dof);
+    
+        for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
+          const mfem::IntegrationPoint &ip = ir->IntPoint(iqp);
+          Trans.SetIntPoint(&ip);
+          double weight = ip.weight * Trans.Weight();
+    
+          el.CalcShape(ip, shape);
+    
+          double u_val = 0.0;
+    
+          for (int j = 0; j < dof; j++) {
+            u_val += elfun(j) * shape(j);
+          }
+          double coeff_val = m_coeff.Eval(Trans, ip);
+          
+    
+          // Calculate the Jacobian
+          double u_safe = std::max(u_val, 0.0);
+          double d_u_nl = coeff_val * m_polytropicIndex * std::pow(u_safe, m_polytropicIndex - 1);
+          double x2_d_u_nl = d_u_nl;
+    
+          for (int i = 0; i < dof; i++) {
+            for (int j = 0; j < dof; j++) {
+              elmat(i, j) += shape(i) * x2_d_u_nl * shape(j) * weight;
+            }
+          }
+    
+        }
+    }
+} // namespace polyMFEMUtils