maxwell_solver.cpp

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// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
 
#include "maxwell_solver.hpp"
 
#ifdef MFEM_USE_MPI
 
using namespace std;
 
namespace mfem
{
 
using namespace common;
 
namespace electromagnetics
{
 
// Used for combining scalar coefficients
real_t prodFunc(real_t a, real_t b) { return a * b; }
 
MaxwellSolver::MaxwellSolver(ParMesh & pmesh, int order,
                             real_t (*eps     )(const Vector&),
                             real_t (*muInv   )(const Vector&),
                             real_t (*sigma   )(const Vector&),
                             void   (*j_src   )(const Vector&, real_t, Vector&),
                             Array<int> & abcs,
                             Array<int> & dbcs,
                             void   (*dEdt_bc )(const Vector&, real_t, Vector&))
   : myid_(0),
     num_procs_(1),
     order_(order),
     logging_(1),
     dtMax_(-1.0),
     dtScale_(1.0e6),
     pmesh_(&pmesh),
     HCurlFESpace_(NULL),
     HDivFESpace_(NULL),
     hDivMassMuInv_(NULL),
     hCurlLosses_(NULL),
     weakCurlMuInv_(NULL),
     Curl_(NULL),
     e_(NULL),
     b_(NULL),
     j_(NULL),
     dedt_(NULL),
     rhs_(NULL),
     jd_(NULL),
     M1Losses_(NULL),
     M2MuInv_(NULL),
     NegCurl_(NULL),
     WeakCurlMuInv_(NULL),
     E_(NULL),
     B_(NULL),
     HD_(NULL),
     RHS_(NULL),
     epsCoef_(NULL),
     muInvCoef_(NULL),
     sigmaCoef_(NULL),
     etaInvCoef_(NULL),
     eCoef_(NULL),
     bCoef_(NULL),
     jCoef_(NULL),
     dEdtBCCoef_(NULL),
     eps_(eps),
     muInv_(muInv),
     sigma_(sigma),
     j_src_(j_src),
     dEdt_bc_(dEdt_bc),
     visit_dc_(NULL)
{
   // Initialize MPI variables
   MPI_Comm_size(pmesh_->GetComm(), &num_procs_);
   MPI_Comm_rank(pmesh_->GetComm(), &myid_);
 
   // Define compatible parallel finite element spaces on the parallel
   // mesh. Here we use arbitrary order H1, Nedelec, and Raviart-Thomas finite
   // elements.
   HCurlFESpace_ = new ND_ParFESpace(pmesh_,order_,pmesh_->Dimension());
   HDivFESpace_  = new RT_ParFESpace(pmesh_,order_,pmesh_->Dimension());
 
   this->height = HCurlFESpace_->GlobalTrueVSize();
   this->width  = HDivFESpace_->GlobalTrueVSize();
 
   // Check for absorbing materials or boundaries
   lossy_ = abcs.Size() > 0 || sigma_ != NULL;
 
   // Require implicit handling of loss terms
   type = lossy_ ? IMPLICIT : EXPLICIT;
 
   // Electric permittivity
   if ( eps_ == NULL )
   {
      epsCoef_ = new ConstantCoefficient(epsilon0_);
   }
   else
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating Permittivity Coefficient" << endl;
      }
      epsCoef_ = new FunctionCoefficient(eps_);
   }
 
   // Inverse of the magnetic permeability
   if ( muInv_ == NULL )
   {
      muInvCoef_ = new ConstantCoefficient(1.0/mu0_);
   }
   else
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating Permeability Coefficient" << endl;
      }
      muInvCoef_ = new FunctionCoefficient(muInv_);
   }
 
   // Electric conductivity
   if ( sigma_ != NULL )
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating Conductivity Coefficient" << endl;
      }
      sigmaCoef_ = new FunctionCoefficient(sigma_);
   }
 
   // Impedance of free space
   if ( abcs.Size() > 0 )
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating Admittance Coefficient" << endl;
      }
 
      AttrToMarker(pmesh.bdr_attributes.Max(), abcs, abc_marker_);
      etaInvCoef_ = new ConstantCoefficient(sqrt(epsilon0_/mu0_));
   }
 
   // Electric Field Boundary Condition
   if ( dbcs.Size() > 0 )
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Configuring Dirichlet BC" << endl;
      }
 
      AttrToMarker(pmesh.bdr_attributes.Max(), dbcs, dbc_marker_);
      HCurlFESpace_->GetEssentialTrueDofs(dbc_marker_, dbc_dofs_);
 
      if ( dEdt_bc_ != NULL )
      {
         dEdtBCCoef_ = new VectorFunctionCoefficient(3,dEdt_bc_);
      }
      else
      {
         Vector ebc(3); ebc = 0.0;
         dEdtBCCoef_ = new VectorConstantCoefficient(ebc);
      }
   }
 
   // Bilinear Forms
   if ( myid_ == 0 && logging_ > 0 )
   {
      cout << "Creating H(Div) Mass Operator" << endl;
   }
   hDivMassMuInv_ = new ParBilinearForm(HDivFESpace_);
   hDivMassMuInv_->AddDomainIntegrator(new VectorFEMassIntegrator(*muInvCoef_));
 
   if ( myid_ == 0 && logging_ > 0 )
   {
      cout << "Creating Weak Curl Operator" << endl;
   }
   weakCurlMuInv_ = new ParMixedBilinearForm(HDivFESpace_,HCurlFESpace_);
   weakCurlMuInv_->AddDomainIntegrator(
      new MixedVectorWeakCurlIntegrator(*muInvCoef_));
 
   // Assemble Matrices
   hDivMassMuInv_->Assemble();
   weakCurlMuInv_->Assemble();
 
   hDivMassMuInv_->Finalize();
   weakCurlMuInv_->Finalize();
 
   if ( sigmaCoef_ || etaInvCoef_ )
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating H(Curl) Loss Operator" << endl;
      }
      hCurlLosses_  = new ParBilinearForm(HCurlFESpace_);
      if ( sigmaCoef_ )
      {
         if ( myid_ == 0 && logging_ > 0 )
         {
            cout << "Adding domain integrator for conductive regions" << endl;
         }
         hCurlLosses_->AddDomainIntegrator(
            new VectorFEMassIntegrator(*sigmaCoef_));
      }
      if ( etaInvCoef_ )
      {
         if ( myid_ == 0 && logging_ > 0 )
         {
            cout << "Adding boundary integrator for absorbing boundary" << endl;
         }
         hCurlLosses_->AddBoundaryIntegrator(
            new VectorFEMassIntegrator(*etaInvCoef_), abc_marker_);
      }
      hCurlLosses_->Assemble();
      hCurlLosses_->Finalize();
      M1Losses_ = hCurlLosses_->ParallelAssemble();
   }
 
   // Create Linear Algebra Matrices
   M2MuInv_ = hDivMassMuInv_->ParallelAssemble();
   WeakCurlMuInv_ = weakCurlMuInv_->ParallelAssemble();
 
   if ( myid_ == 0 && logging_ > 0 )
   {
      cout << "Creating discrete curl operator" << endl;
   }
   Curl_ = new ParDiscreteCurlOperator(HCurlFESpace_, HDivFESpace_);
   Curl_->Assemble();
   Curl_->Finalize();
   NegCurl_ = Curl_->ParallelAssemble();
   // Beware this modifies the matrix stored within the Curl_ object.
   *NegCurl_ *= -1.0;
 
   // Build grid functions
   e_    = new ParGridFunction(HCurlFESpace_);
   dedt_ = new ParGridFunction(HCurlFESpace_);
   rhs_  = new ParGridFunction(HCurlFESpace_);
   b_    = new ParGridFunction(HDivFESpace_);
 
   E_ = e_->ParallelProject();
   B_ = b_->ParallelProject();
 
   HD_  = new HypreParVector(HDivFESpace_);
   RHS_ = new HypreParVector(HCurlFESpace_);
 
   // Initialize dedt to zero
   *dedt_ = 0.0;
 
   if ( j_src_)
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating Current Source" << endl;
      }
      jCoef_ = new VectorFunctionCoefficient(3,j_src_);
 
      j_  = new ParGridFunction(HCurlFESpace_);
      j_->ProjectCoefficient(*jCoef_);
 
      jd_ = new ParLinearForm(HCurlFESpace_);
      jd_->AddDomainIntegrator(new VectorFEDomainLFIntegrator(*jCoef_));
      jd_->Assemble();
   }
 
   dtMax_ = GetMaximumTimeStep();
}
 
MaxwellSolver::~MaxwellSolver()
{
   delete epsCoef_;
   delete muInvCoef_;
   delete etaInvCoef_;
   delete jCoef_;
   delete dEdtBCCoef_;
 
   delete E_;
   delete B_;
   delete HD_;
   delete RHS_;
 
   delete e_;
   delete b_;
   delete j_;
   delete dedt_;
   delete rhs_;
   delete jd_;
 
   delete Curl_;
 
   delete M1Losses_;
   delete M2MuInv_;
   delete NegCurl_;
   delete WeakCurlMuInv_;
 
   delete hDivMassMuInv_;
   delete hCurlLosses_;
   delete weakCurlMuInv_;
 
   delete HCurlFESpace_;
   delete HDivFESpace_;
 
   map<int, ParBilinearForm*>::iterator mit1;
   for (mit1=a1_.begin(); mit1!=a1_.end(); mit1++)
   {
      int i = mit1->first;
      delete pcg_[i];
      delete diagScale_[i];
      delete A1_[i];
      delete a1_[i];
   }
 
   map<int, Coefficient*>::iterator mit2;
   for (mit2=dtCoef_.begin(); mit2!=dtCoef_.end(); mit2++)
   {
      delete mit2->second;
   }
   for (mit2=dtSigmaCoef_.begin(); mit2!=dtSigmaCoef_.end(); mit2++)
   {
      delete mit2->second;
   }
   for (mit2=dtEtaInvCoef_.begin(); mit2!=dtEtaInvCoef_.end(); mit2++)
   {
      delete mit2->second;
   }
 
   map<string, socketstream*>::iterator mit3;
   for (mit3=socks_.begin(); mit3!=socks_.end(); mit3++)
   {
      delete mit3->second;
   }
}
 
HYPRE_BigInt
MaxwellSolver::GetProblemSize()
{
   return HCurlFESpace_->GlobalTrueVSize();
}
 
void
MaxwellSolver::PrintSizes()
{
   HYPRE_BigInt size_nd = HCurlFESpace_->GlobalTrueVSize();
   HYPRE_BigInt size_rt = HDivFESpace_->GlobalTrueVSize();
   if ( myid_ == 0 )
   {
      cout << "Number of H(Curl) unknowns: " << size_nd << endl;
      cout << "Number of H(Div)  unknowns: " << size_rt << endl << flush;
   }
}
 
void
MaxwellSolver::SetInitialEField(VectorCoefficient & EFieldCoef)
{
   eCoef_ = &EFieldCoef;
   e_->ProjectCoefficient(EFieldCoef);
   e_->ParallelProject(*E_);
}
 
void
MaxwellSolver::SetInitialBField(VectorCoefficient & BFieldCoef)
{
   bCoef_ = &BFieldCoef;
   b_->ProjectCoefficient(BFieldCoef);
   b_->ParallelProject(*B_);
}
 
void
MaxwellSolver::Mult(const Vector &B, Vector &dEdt) const
{
   implicitSolve(0.0, B, dEdt);
}
 
void
MaxwellSolver::ImplicitSolve(real_t dt, const Vector &B, Vector &dEdt)
{
   implicitSolve(dt, B, dEdt);
}
 
void
MaxwellSolver::setupSolver(const int idt, const real_t dt) const
{
   if ( pcg_.find(idt) == pcg_.end() )
   {
      if ( myid_ == 0 && logging_ > 0 )
      {
         cout << "Creating implicit operator for dt = " << dt << endl;
      }
 
      a1_[idt] = new ParBilinearForm(HCurlFESpace_);
      a1_[idt]->AddDomainIntegrator(
         new VectorFEMassIntegrator(epsCoef_));
 
      if ( idt != 0 )
      {
         dtCoef_[idt] = new ConstantCoefficient(0.5 * dt);
         if ( sigmaCoef_ )
         {
            dtSigmaCoef_[idt] = new TransformedCoefficient(dtCoef_[idt],
                                                           sigmaCoef_,
                                                           prodFunc);
            a1_[idt]->AddDomainIntegrator(
               new VectorFEMassIntegrator(dtSigmaCoef_[idt]));
         }
         if ( etaInvCoef_ )
         {
            dtEtaInvCoef_[idt] = new TransformedCoefficient(dtCoef_[idt],
                                                            etaInvCoef_,
                                                            prodFunc);
            a1_[idt]->AddBoundaryIntegrator(
               new VectorFEMassIntegrator(dtEtaInvCoef_[idt]),
               const_cast<Array<int>&>(abc_marker_));
         }
      }
 
      a1_[idt]->Assemble();
      a1_[idt]->Finalize();
      A1_[idt] = a1_[idt]->ParallelAssemble();
 
      diagScale_[idt] = new HypreDiagScale(*A1_[idt]);
      pcg_[idt] = new HyprePCG(*A1_[idt]);
      pcg_[idt]->SetTol(1.0e-12);
      pcg_[idt]->SetMaxIter(200);
      pcg_[idt]->SetPrintLevel(0);
      pcg_[idt]->SetPreconditioner(*diagScale_[idt]);
   }
}
 
void
MaxwellSolver::implicitSolve(real_t dt, const Vector &B, Vector &dEdt) const
{
   int idt = hCurlLosses_ ? ((int)(dtScale_ * dt / dtMax_)) : 0;
 
   b_->Distribute(B);
   weakCurlMuInv_->Mult(*b_, *rhs_);
 
   if ( hCurlLosses_ )
   {
      e_->Distribute(*E_);
      hCurlLosses_->AddMult(*e_, *rhs_, -1.0);
   }
 
   if ( jd_ )
   {
      jCoef_->SetTime(t); // 't' is member data from mfem::TimeDependentOperator
      jd_->Assemble();
      *rhs_ -= *jd_;
   }
 
   if ( dEdtBCCoef_ )
   {
      dEdtBCCoef_->SetTime(t);
      dedt_->ProjectBdrCoefficientTangent(*dEdtBCCoef_,
                                          const_cast<Array<int>&>(dbc_marker_));
   }
 
   // Create objects and matrices for solving with the given time step
   setupSolver(idt, dt);
 
   // Apply essential BCs and determine true DoFs for the right hand side
   a1_[idt]->FormLinearSystem(dbc_dofs_, *dedt_, *rhs_, *A1_[idt], dEdt, *RHS_);
 
   // Solve for the time derivative of the electric field (true DoFs)
   pcg_[idt]->Mult(*RHS_, dEdt);
 
   // Distribute shared DoFs to relevant processors
   a1_[idt]->RecoverFEMSolution(dEdt, *rhs_, *dedt_);
}
 
void
MaxwellSolver::SyncGridFuncs()
{
   e_->Distribute(*E_);
   b_->Distribute(*B_);
}
 
real_t
MaxwellSolver::GetMaximumTimeStep() const
{
   if ( dtMax_ > 0.0 )
   {
      return dtMax_;
   }
 
   HypreParVector * v0 = new HypreParVector(HCurlFESpace_);
   HypreParVector * v1 = new HypreParVector(HCurlFESpace_);
   HypreParVector * u0 = new HypreParVector(HDivFESpace_);
 
   v0->Randomize(1234);
 
   int iter = 0, nstep = 20;
   real_t dt0 = 1.0, dt1 = 1.0, change = 1.0, ptol = 0.001;
 
   // Create Solver assuming no loss operators
   setupSolver(0, 0.0);
 
   // Use power method to approximate the largest eigenvalue of the update
   // operator.
   while ( iter < nstep && change > ptol )
   {
      real_t normV0 = InnerProduct(*v0,*v0);
      *v0 /= sqrt(normV0);
 
      NegCurl_->Mult(*v0,*u0);
      M2MuInv_->Mult(*u0,*HD_);
      NegCurl_->MultTranspose(*HD_,*RHS_);
 
      pcg_[0]->Mult(*RHS_,*v1);
 
      real_t lambda = InnerProduct(*v0,*v1);
      dt1 = 2.0/sqrt(lambda);
      change = fabs((dt1-dt0)/dt0);
      dt0 = dt1;
 
      if ( myid_ == 0 && logging_ > 1 )
      {
         cout << iter << ":  " << dt0 << " " << change << endl;
      }
 
      std::swap(v0, v1);
 
      iter++;
   }
 
   delete v0;
   delete v1;
   delete u0;
 
   return dt0;
}
 
real_t
MaxwellSolver::GetEnergy() const
{
   real_t energy = 0.0;
 
   A1_[0]->Mult(*E_,*RHS_);
   M2MuInv_->Mult(*B_,*HD_);
 
   energy = InnerProduct(*E_,*RHS_) + InnerProduct(*B_,*HD_);
 
   return 0.5 * energy;
}
 
void
MaxwellSolver::RegisterVisItFields(VisItDataCollection & visit_dc)
{
   visit_dc_ = &visit_dc;
 
   visit_dc.RegisterField("E", e_);
   visit_dc.RegisterField("B", b_);
   if ( j_ )
   {
      visit_dc.RegisterField("J", j_);
   }
}
 
void
MaxwellSolver::WriteVisItFields(int it)
{
   if ( visit_dc_ )
   {
      if ( myid_ == 0 && logging_ > 1 )
      { cout << "Writing VisIt files ..." << flush; }
 
      if ( j_ )
      {
         jCoef_->SetTime(t);
         j_->ProjectCoefficient(*jCoef_);
      }
 
      visit_dc_->SetCycle(it);
      visit_dc_->SetTime(t);
      visit_dc_->Save();
 
      if ( myid_ == 0 && logging_ > 1 ) { cout << " " << endl << flush; }
   }
}
 
void
MaxwellSolver::InitializeGLVis()
{
   if ( myid_ == 0 && logging_ > 0 )
   { cout << "Opening GLVis sockets." << endl << flush; }
 
   socks_["E"] = new socketstream;
   socks_["E"]->precision(8);
 
   socks_["B"] = new socketstream;
   socks_["B"]->precision(8);
 
   if ( j_ )
   {
      socks_["J"] = new socketstream;
      socks_["J"]->precision(8);
   }
 
   if ( myid_ == 0 && logging_ > 0 )
   { cout << "GLVis sockets open." << endl << flush; }
}
 
void
MaxwellSolver::DisplayToGLVis(int visport)
{
   if ( myid_ == 0 && logging_ > 1 )
   { cout << "Sending data to GLVis ..." << flush; }
 
   char vishost[] = "localhost";
 
   int Wx = 0, Wy = 0; // window position
   int Ww = 350, Wh = 350; // window size
   int offx = Ww+10, offy = Wh+45; // window offsets
 
   VisualizeField(*socks_["E"], vishost, visport,
                  *e_, "Electric Field (E)", Wx, Wy, Ww, Wh);
   Wx += offx;
 
   VisualizeField(*socks_["B"], vishost, visport,
                  *b_, "Magnetic Flux Density (B)", Wx, Wy, Ww, Wh);
 
   if ( j_ )
   {
      Wx = 0;
      Wy += offy;
 
      jCoef_->SetTime(t); // Is member data from mfem::TimeDependentOperator
      j_->ProjectCoefficient(*jCoef_);
 
      VisualizeField(*socks_["J"], vishost, visport,
                     *j_, "Current Density (J)", Wx, Wy, Ww, Wh);
   }
   if ( myid_ == 0 && logging_ > 1 ) { cout << " " << flush; }
}
 
} // namespace electromagnetics
 
} // namespace mfem
 
#endif // MFEM_USE_MPI