feat(poly): interpolating polynomial to find polytrope surface

Instead of treating the polytrope as a free boundary problem I have defined an interpolating polynominal, accurate to within 0.01 percent over n=[0,5) which is used to set the size of the domain for a given n

src/poly/solver/private/polySolver.cpp

@@ -1,16 +1,7 @@
 #include "mfem.hpp"
 
 #include <string>
-#include <iostream>
-#include <memory>
-#include <stdexcept>
-#include <csignal>
-#include <filesystem>
-#include <vector>
-#include <array>
-#include <utility>
 
-#include "meshIO.h"
 #include "polySolver.h"
 #include "polyMFEMUtils.h"
 #include "polyCoeff.h"
@@ -19,7 +10,6 @@
 
 #include "quill/LogMacros.h"
 
-#include "warning_control.h"
 
 namespace laneEmden {
 
@@ -122,7 +112,7 @@ void PolySolver::solve(){
     nonlinearForm->SetEssentialTrueDofs(ess_tdof_list);
     // Set the center elemID to be the Dirichlet boundary
 
-    double alpha = config.get<double>("Poly:Solver:Newton:Alpha", 1e2);
+    // double alpha = config.get<double>("Poly:Solver:Newton:Alpha", 1e2);
     double newtonRelTol = config.get<double>("Poly:Solver:Newton:RelTol", 1e-7);
     double newtonAbsTol = config.get<double>("Poly:Solver:Newton:AbsTol", 1e-7);
     int newtonMaxIter = config.get<int>("Poly:Solver:Newton:MaxIter", 200);
@@ -137,7 +127,8 @@ void PolySolver::solve(){
     LOG_INFO(logger, "GMRES Solver (relTol: {:0.2E}, absTol: {:0.2E}, maxIter: {}, printLevel: {})", gmresRelTol, gmresAbsTol, gmresMaxIter, gmresPrintLevel);
 
     std::vector<double> zeroSlopeCoordinate = {0.0, 0.0, 0.0};
-    polyMFEMUtils::ZeroSlopeNewtonSolver newtonSolver(alpha, zeroSlopeCoordinate);
+    // polyMFEMUtils::ZeroSlopeNewtonSolver newtonSolver(alpha, zeroSlopeCoordinate);
+    mfem::NewtonSolver newtonSolver;
     newtonSolver.SetRelTol(newtonRelTol);
     newtonSolver.SetAbsTol(newtonAbsTol);
     newtonSolver.SetMaxIter(newtonMaxIter);