//                                MFEM Example 1
//
// Compile with: make exSBP
//
// Sample runs:  exSBP -sbp -o 0 -p 0 -r 1
//               exSBP -sbp -o 4 -p 3
//               
//
// Description:  This example code builds on Example 1 but adds SBP operators.
//               It demonstrates the use of MFEM to define a simple finite
//               element discretization of the Laplace problem -Delta u = 1
//               with homogeneous Dirichlet boundary conditions. Specifically,
//               we discretize using a FE or SBP space of the specified order,
//               or if order < 1 using an isoparametric/isogeometric space
//               (i.e. quadratic for quadratic curvilinear mesh, NURBS for
//               NURBS mesh, etc.)
//
//               The example highlights the use of mesh refinement, finite
//               element grid functions, as well as linear and bilinear forms
//               corresponding to the left-hand side and right-hand side of the
//               discrete linear system. We also cover the explicit elimination
//               of essential boundary conditions, static condensation, and the
//               optional connection to the GLVis tool for visualization.

#include "mfem.hpp"
#include <fstream>
#include <iostream>
#include <chrono>

using namespace std;
using namespace mfem;

int problem;

// Prescribed time-independent boundary and right-hand side functions.
double bdr_func(const Vector &pt);
double rhs_func(const Vector &pt);

int main(int argc, char *argv[])
{
   // 1. Parse command-line options.
   const char *mesh_file = "../data/unitGridTestMesh.msh";
   int order = 1;
   bool static_cond = false;
	bool visualization = 1;
	bool sbp = 1;
	problem = 1;
	int ref_levels = 0;
	bool convOut = false;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&sbp, "-sbp", "--summationbyparts", "-no-sbp",
                  "--no-summationbyparts",
                  "Enable or disable use of SBP operators.");
	args.AddOption(&problem, "-p", "--problem",
                  "Problem setup to use: 0 = transcendental manufactured solution, "
						"1 = linear displacement, "
						"2 = quadratic displacement, "
						"3 = cubic displacement, "
						"4 = quartic displacement.");
	args.AddOption(&ref_levels, "-r", "--ref-levels",
                  "Number of initial uniform refinement levels.");
   args.Parse();
   if (!args.Good())
   {
      args.PrintUsage(cout);
      return 1;
   }
   args.PrintOptions(cout);

   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

   // 3. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
   //    largest number that gives a final mesh with no more than 50,000
   //    elements.
   {
      for (int l = 0; l < ref_levels; l++)
      {
         mesh->UniformRefinement();
      }
   }

   // 4. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange finite elements of the specified order. If order < 1, we
   //    instead use an isoparametric/isogeometric space.
   FiniteElementCollection *fec;
   if (sbp)
   {
      fec = new C_SBPCollection(order, dim);
   }
   else if (order > 0)
   {
      fec = new H1_FECollection(order, dim);
   }
   else if (mesh->GetNodes())
   {
      fec = mesh->GetNodes()->OwnFEC();
      cout << "Using isoparametric FEs: " << fec->Name() << endl;
   }
   else
   {
      fec = new H1_FECollection(order = 1, dim);
   }
   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
   cout << "Number of finite element unknowns: "
        << fespace->GetTrueVSize() << endl;

   // 7. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero,
   //    which satisfies the boundary conditions.
	GridFunction x(fespace);
	x = 0.0;

	// Create function coefficient bdr which holds the exact solution and is
	// used to strongly impose boundary conditions.
	FunctionCoefficient bdr(bdr_func);

   // 5. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined by marking all
   //    the boundary attributes from the mesh as essential (Dirichlet) and
   //    converting them to a list of true dofs.
   Array<int> ess_tdof_list;
   if (mesh->bdr_attributes.Size())
   {
      Array<int> ess_bdr(mesh->bdr_attributes.Max());
      ess_bdr = 1;

		// Project boundary conditions onto grid function to strongly impose
		// boundary conditions. BC's are defined in the function `bdr_func`.
		x.ProjectBdrCoefficient(bdr, ess_bdr);

      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
   LinearForm *b = new LinearForm(fespace);
	
	FunctionCoefficient rhs(rhs_func);
	b->AddDomainIntegrator(new DomainLFIntegrator(rhs));

	if (problem < 0 || problem > 4)
	{
		mfem::out << "Invalid problem type: " << problem << "\n";
		delete mesh;
      return 3;
	}
	
   // // Start timing
   // std::chrono::time_point<std::chrono::high_resolution_clock> start = std::chrono::high_resolution_clock::now();

   b->Assemble();

   // // End timing and compute interval
   // std::chrono::time_point<std::chrono::high_resolution_clock> finish = std::chrono::high_resolution_clock::now();
   // std::chrono::duration<double> elapsed = finish - start;
   // std::cout << "\nb->Assemble() elapsed time: " << elapsed.count() << " s\n";

   // 8. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //    domain integrator.
   BilinearForm *a = new BilinearForm(fespace);
	ConstantCoefficient one(1.0);
   a->AddDomainIntegrator(new DiffusionIntegrator(one));

   // 9. Assemble the bilinear form and the corresponding linear system,
   //    applying any necessary transformations such as: eliminating boundary
   //    conditions, applying conforming constraints for non-conforming AMR,
   //    static condensation, etc.
   if (static_cond) { a->EnableStaticCondensation(); }

   // // Start timing
   // start = std::chrono::high_resolution_clock::now();

   a->Assemble();

   // // End timing and compute interval
   // finish = std::chrono::high_resolution_clock::now();
   // elapsed = finish - start;
   // std::cout << "\na->Assemble() elapsed time: " << elapsed.count() << " s\n";

   SparseMatrix A;
   Vector B, X;
   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);

   mfem::out << "Size of linear system: " << A.Height() << endl;

#ifndef MFEM_USE_SUITESPARSE
   // 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
   //     solve the system A X = B with PCG.
   GSSmoother M(A);
   PCG(A, M, B, X, 1, 1000, 1e-12, 0.0);
#else
   // 10. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
   UMFPackSolver umf_solver;
   umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
   umf_solver.SetOperator(A);
   umf_solver.Mult(B, X);
#endif

   // 11. Recover the solution as a finite element grid function.
   a->RecoverFEMSolution(X, *b, x);

	// 12. Compute and print the L^2 norm of the error.
   mfem::out << "\n|| u_h - u ||_{L^2} = " << x.ComputeL2Error(bdr) << '\n' << endl;
	// mfem::out << "h: " << 0.1 / pow(2, ref_levels) << "\n";

   // 12. Save the refined mesh and the solution. This output can be viewed later
   //     using GLVis: "glvis -m refined.mesh -g sol.gf".
   ofstream mesh_ofs("refined.mesh");
   mesh_ofs.precision(8);
   mesh->Print(mesh_ofs);
   // mesh->PrintVTK(mesh_ofs); 
   ofstream sol_ofs("sol.gf");
   sol_ofs.precision(8);
   x.Save(sol_ofs);

   // Save solution mesh in vtk file
   char solFileName[32];
   if (sbp)
   {
      snprintf(solFileName, 32, "exSBP_SBP_O%d_P%d.vtk", order, problem);
   }
   else
   {
      snprintf(solFileName, 32, "exSBP_FE_O%d_P%d.vtk", order, problem);
   }

	if (convOut)
	{
		// Save convergence study information in output file
		char outfileName[32];
		if (problem == 0)
		{
			snprintf(outfileName, 32, "convOutputP%d_manufactured.txt", order);
		}
		else if (problem == 1)
		{
			snprintf(outfileName, 32, "convOutputP%d_lin.txt", order);
		}
		else if (problem == 2)
		{
			snprintf(outfileName, 32, "convOutputP%d_quad.txt", order);
		}
		else if (problem == 3)
		{
			snprintf(outfileName, 32, "convOutputP%d_cubic.txt", order);
		}
		else if (problem == 4)
		{
			snprintf(outfileName, 32, "convOutputP%d_quartic.txt", order);
		}
		

		ofstream outputFile;
		outputFile.open(outfileName, ios::out | ios::app); 

		if (outputFile.is_open())
		{
			outputFile << x.ComputeL2Error(bdr) << ", " << 0.1 / pow(2, ref_levels) << "\n";
		}
		outputFile.close();
	}

   ofstream omesh(solFileName);
   omesh.precision(14); 
   mesh->PrintVTK(omesh, 1); 
   x.SaveVTK(omesh, "sol", 1);

   // 13. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "solution\n" << *mesh << x << flush;
   }

   // 14. Free the used memory.
   delete a;
   delete b;
   delete fespace;
   if (order > 0) { delete fec; }
   delete mesh;

   return 0;
}

// Exact solution, used for the Dirichlet BC.
double bdr_func(const Vector &pt)
{
	double x = pt(0), y = pt(1), z = 0.0;

	if (problem == 0) // manufactured solution
	{
		z = sin(M_PI*x)*sin(M_PI*y);
	}
	else if (problem == 1) // linear displacement
	{
		z = 0.5*x + 0.5*y;
	}
	else if (problem == 2) // quadratic displacement
	{
		z = 0.5*x*x + 0.5*y*y;
	}
	else if (problem == 3) // manufactured solution
	{
		z = 0.5*x*x*x + 0.5*y*y*y;
	}
	else if (problem == 4) // manufactured solution
	{
		z = 0.5*x*x*x*x + 0.5*y*y*y*y;
	}
	return z;
}

// right hand side function for manufactured solution
double rhs_func(const Vector &pt)
{
	double x = pt(0), y = pt(1), z = 0.0;
	if (problem == 0)
	{
		z = 2*M_PI*M_PI*sin(M_PI*x)*sin(M_PI*y);
	}
	else if (problem == 1)
	{
		z = 0;
	}
	else if (problem == 2)
	{
		z = -2;
	}
	else if (problem == 3)
	{
		z = -3*(x+y);
	}
	else if (problem == 4)
	{
		z = -6*(x*x + y*y);
	}
	return z;
}