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mfem/miniapps/electromagnetics/joule.cpp
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// Copyright (c) 2010-2020, 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.
//
// -----------------------------------------------------
// Joule Miniapp: Transient Magnetics and Joule Heating
// -----------------------------------------------------
//
// This miniapp solves a time dependent eddy current problem, resulting in Joule
// heating.
//
// This version has electrostatic potential, Phi, which is a source term in the
// EM diffusion equation. The potential itself is driven by essential BC's
//
// Div sigma Grad Phi = 0
// sigma E = Curl B/mu - sigma grad Phi
// dB/dt = - Curl E
// F = -k Grad T
// c dT/dt = -Div(F) + sigma E.E,
//
// where B is the magnetic flux, E is the electric field, T is the temperature,
// F is the thermal flux, sigma is electrical conductivity, mu is the magnetic
// permeability, and alpha is the thermal diffusivity. The geometry of the
// domain is assumed to be as follows:
//
// boundary attribute 3
// +---------------------+
// boundary --->| | boundary
// attribute 1 | | attribute 2
// (driven) +---------------------+
//
// The voltage BC condition is essential BC on attribute 1 (front) and 2 (rear)
// given by function p_bc() at bottom of this file.
//
// The E-field boundary condition specifies the essential BC (n cross E) on
// attribute 1 (front) and 2 (rear) given by function edot_bc at bottom of this
// file. The E-field can be set on attribute 3 also.
//
// The thermal boundary condition for the flux F is the natural BC on attribute 1
// (front) and 2 (rear). This means that dT/dt = 0 on the boundaries, and the
// initial T = 0.
//
// See Section 3 for how the material propertied are assigned to mesh
// attributes, this needs to be changed for different applications.
//
// See Section 5 for how the boundary conditions are assigned to mesh
// attributes, this needs to be changed for different applications.
//
// This code supports a simple version of AMR, all elements containing material
// attribute 1 are (optionally) refined.
//
// Compile with: make joule
//
// Sample runs:
//
// mpirun -np 8 joule -m cylinder-hex.mesh -p rod
// mpirun -np 8 joule -m cylinder-tet.mesh -sc 1 -amr 1 -p rod
// mpirun -np 8 joule -m cylinder-hex-q2.gen -s 22 -dt 0.1 -tf 240.0 -p rod
//
// Options:
//
// -m [string] the mesh file name
// -o [int] the order of the basis
// -rs [int] number of times to serially refine the mesh
// -rp [int] number of times to refine the mesh in parallel
// -s [int] time integrator 1=Backward Euler, 2=SDIRK2, 3=SDIRK3,
// 22=Midpoint, 23=SDIRK23, 34=SDIRK34
// -tf [double] the final time
// -dt [double] time step
// -mu [double] the magnetic permeability
// -cnd [double] the electrical conductivity
// -f [double] the frequency of the applied EM BC
// -vis [int] GLVis -vis = true -no-vis = false
// -vs [int] visualization step
// -k [string] base file name for output file
// -print [int] print solution (gridfunctions) to disk 0 = no, 1 = yes
// -amr [int] 0 = no amr, 1 = amr
// -sc [int] 0 = no static condensation, 1 = use static condensation
// -p [string] specify the problem to run, "rod", "coil", or "test"
//
//
// NOTE: Example meshes for this miniapp are the included cylinder/rod meshes:
// cylinder-hex.mesh, cylinder-tet.mesh, cylinder-hex-q2.gen,
// cylinder-tet-q2.gen, as well as the coil.gen mesh which can be
// downloaded from github.com/mfem/data (its size is 21MB). Note that the
// meshes with the "gen" extension require MFEM to be built with NetCDF.
//
// NOTE: This code is set up to solve two example problems, 1) a straight metal
// rod surrounded by air, 2) a metal rod surrounded by a metal coil all
// surrounded by air. To specify problem (1) use the command line options
// "-p rod -m cylinder-hex-q2.gen", to specify problem (2) use the
// command line options "-p coil -m coil.gen". Problem (1) has two
// materials and problem (2) has three materials, and the BC's are
// different.
//
// NOTE: We write out, optionally, grid functions for P, E, B, W, F, and
// T. These can be visualized using "glvis -np 4 -m mesh.mesh -g E",
// assuming we used 4 processors.
#include "joule_solver.hpp"
#include <memory>
#include <iostream>
#include <fstream>
using namespace std;
using namespace mfem;
using namespace mfem::common;
using namespace mfem::electromagnetics;
void display_banner(ostream & os);
static double mj_ = 0.0;
static double sj_ = 0.0;
static double wj_ = 0.0;
// Initialize variables used in joule_solver.cpp
int electromagnetics::SOLVER_PRINT_LEVEL = 0;
int electromagnetics::STATIC_COND = 0;
int main(int argc, char *argv[])
{
// 1. Initialize MPI.
MPI_Session mpi(argc, argv);
int myid = mpi.WorldRank();
// print the cool banner
if (mpi.Root()) { display_banner(cout); }
// 2. Parse command-line options.
const char *mesh_file = "cylinder-hex.mesh";
int ser_ref_levels = 0;
int par_ref_levels = 0;
int order = 2;
int ode_solver_type = 1;
double t_final = 100.0;
double dt = 0.5;
double mu = 1.0;
double sigma = 2.0*M_PI*10;
double Tcapacity = 1.0;
double Tconductivity = 0.01;
double freq = 1.0/60.0;
bool visualization = true;
bool visit = true;
int vis_steps = 1;
int gfprint = 0;
const char *basename = "Joule";
int amr = 0;
int debug = 0;
const char *problem = "rod";
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Order (degree) of the finite elements.");
args.AddOption(&ode_solver_type, "-s", "--ode-solver",
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3\n\t."
"\t 22 - Mid-Point, 23 - SDIRK23, 34 - SDIRK34.");
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&mu, "-mu", "--permeability",
"Magnetic permeability coefficient.");
args.AddOption(&sigma, "-cnd", "--sigma",
"Conductivity coefficient.");
args.AddOption(&freq, "-f", "--frequency",
"Frequency of oscillation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&visit, "-visit", "--visit", "-no-visit", "--no-visit",
"Enable or disable VisIt visualization.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
args.AddOption(&basename, "-k", "--outputfilename",
"Name of the visit dump files");
args.AddOption(&gfprint, "-print", "--print",
"Print results (grid functions) to disk.");
args.AddOption(&amr, "-amr", "--amr",
"Enable AMR");
args.AddOption(&STATIC_COND, "-sc", "--static-condensation",
"Enable static condensation");
args.AddOption(&debug, "-debug", "--debug",
"Print matrices and vectors to disk");
args.AddOption(&SOLVER_PRINT_LEVEL, "-hl", "--hypre-print-level",
"Hypre print level");
args.AddOption(&problem, "-p", "--problem",
"Name of problem to run");
args.Parse();
if (!args.Good())
{
if (mpi.Root())
{
args.PrintUsage(cout);
}
return 1;
}
if (mpi.Root())
{
args.PrintOptions(cout);
}
mj_ = mu;
sj_ = sigma;
wj_ = 2.0*M_PI*freq;
if (mpi.Root())
{
cout << "\nSkin depth sqrt(2.0/(wj*mj*sj)) = " << sqrt(2.0/(wj_*mj_*sj_))
<< "\nSkin depth sqrt(2.0*dt/(mj*sj)) = " << sqrt(2.0*dt/(mj_*sj_))
<< endl;
}
// 3. Here material properties are assigned to mesh attributes. This code is
// not general, it is assumed the mesh has 3 regions each with a different
// integer attribute: 1, 2 or 3.
//
// The coil problem has three regions: 1) coil, 2) air, 3) the rod.
// The rod problem has two regions: 1) rod, 2) air.
//
// We can use the same material maps for both problems.
std::map<int, double> sigmaMap, InvTcondMap, TcapMap, InvTcapMap;
double sigmaAir;
double TcondAir;
double TcapAir;
if (strcmp(problem,"rod")==0 || strcmp(problem,"coil")==0)
{
sigmaAir = 1.0e-6 * sigma;
TcondAir = 1.0e6 * Tconductivity;
TcapAir = 1.0 * Tcapacity;
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
if (strcmp(problem,"rod")==0 || strcmp(problem,"coil")==0)
{
sigmaMap.insert(pair<int, double>(1, sigma));
sigmaMap.insert(pair<int, double>(2, sigmaAir));
sigmaMap.insert(pair<int, double>(3, sigmaAir));
InvTcondMap.insert(pair<int, double>(1, 1.0/Tconductivity));
InvTcondMap.insert(pair<int, double>(2, 1.0/TcondAir));
InvTcondMap.insert(pair<int, double>(3, 1.0/TcondAir));
TcapMap.insert(pair<int, double>(1, Tcapacity));
TcapMap.insert(pair<int, double>(2, TcapAir));
TcapMap.insert(pair<int, double>(3, TcapAir));
InvTcapMap.insert(pair<int, double>(1, 1.0/Tcapacity));
InvTcapMap.insert(pair<int, double>(2, 1.0/TcapAir));
InvTcapMap.insert(pair<int, double>(3, 1.0/TcapAir));
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
// 4. Read the serial mesh from the given mesh file on all processors. We can
// handle triangular, quadrilateral, tetrahedral and hexahedral meshes
// with the same code.
Mesh *mesh;
mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
// 5. Assign the boundary conditions
Array<int> ess_bdr(mesh->bdr_attributes.Max());
Array<int> thermal_ess_bdr(mesh->bdr_attributes.Max());
Array<int> poisson_ess_bdr(mesh->bdr_attributes.Max());
if (strcmp(problem,"coil")==0)
{
// BEGIN CODE FOR THE COIL PROBLEM
// For the coil in a box problem we have surfaces 1) coil end (+),
// 2) coil end (-), 3) five sides of box, 4) side of box with coil BC
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[1] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[2] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[3] = 1; // boundary attribute 4 (index 3) is fixed
// Same as above, but this is for the thermal operator for HDiv
// formulation the essential BC is the flux
thermal_ess_bdr = 0;
thermal_ess_bdr[2] = 1; // boundary attribute 4 (index 3) is fixed
// Same as above, but this is for the poisson eq for H1 formulation the
// essential BC is the value of Phi
poisson_ess_bdr = 0;
poisson_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
poisson_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed
// END CODE FOR THE COIL PROBLEM
}
else if (strcmp(problem,"rod")==0)
{
// BEGIN CODE FOR THE STRAIGHT ROD PROBLEM
// the boundary conditions below are for the straight rod problem
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (rear)
ess_bdr[2] = 1; // boundary attribute 3 (index 2) is fixed (outer)
// Same as above, but this is for the thermal operator. For HDiv
// formulation the essential BC is the flux, which is zero on the front
// and sides. Note the Natural BC is T = 0 on the outer surface.
thermal_ess_bdr = 0;
thermal_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
thermal_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (rear)
// Same as above, but this is for the poisson eq for H1 formulation the
// essential BC is the value of Phi
poisson_ess_bdr = 0;
poisson_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
poisson_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (back)
// END CODE FOR THE STRAIGHT ROD PROBLEM
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
// The following is required for mesh refinement
mesh->EnsureNCMesh();
// 6. Define the ODE solver used for time integration. Several implicit
// methods are available, including singly diagonal implicit Runge-Kutta
// (SDIRK).
ODESolver *ode_solver;
switch (ode_solver_type)
{
// Implicit L-stable methods
case 1: ode_solver = new BackwardEulerSolver; break;
case 2: ode_solver = new SDIRK23Solver(2); break;
case 3: ode_solver = new SDIRK33Solver; break;
// Implicit A-stable methods (not L-stable)
case 22: ode_solver = new ImplicitMidpointSolver; break;
case 23: ode_solver = new SDIRK23Solver; break;
case 34: ode_solver = new SDIRK34Solver; break;
default:
if (mpi.Root())
{
cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
}
delete mesh;
return 3;
}
// 7. Refine the mesh in serial to increase the resolution. In this example
// we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
// a command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++)
{
mesh->UniformRefinement();
}
// 8. Define a parallel mesh by a partitioning of the serial mesh. Refine
// this mesh further in parallel to increase the resolution. Once the
// parallel mesh is defined, the serial mesh can be deleted.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < par_ref_levels; lev++)
{
pmesh->UniformRefinement();
}
// Make sure tet-only meshes are marked for local refinement.
pmesh->Finalize(true);
// 9. Apply non-uniform non-conforming mesh refinement to the mesh. The
// whole metal region is refined once, before the start of the time loop,
// i.e. this is not based on any error estimator.
if (amr == 1)
{
Array<int> ref_list;
int numElems = pmesh->GetNE();
for (int ielem = 0; ielem < numElems; ielem++)
{
int thisAtt = pmesh->GetAttribute(ielem);
if (thisAtt == 1)
{
ref_list.Append(ielem);
}
}
pmesh->GeneralRefinement(ref_list);
ref_list.DeleteAll();
}
// 10. Reorient the mesh. Must be done after refinement but before definition
// of higher order Nedelec spaces
pmesh->ReorientTetMesh();
// 11. Rebalance the mesh. Since the mesh was adaptively refined in a
// non-uniform way it will be computationally unbalanced.
if (pmesh->Nonconforming())
{
pmesh->Rebalance();
}
// 12. Define the parallel finite element spaces. We use:
//
// H(curl) for electric field,
// H(div) for magnetic flux,
// H(div) for thermal flux,
// H(grad)/H1 for electrostatic potential,
// L2 for temperature
// L2 contains discontinuous "cell-center" finite elements, type 2 is
// "positive"
L2_FECollection L2FEC(order-1, dim);
// ND contains Nedelec "edge-centered" vector finite elements with continuous
// tangential component.
ND_FECollection HCurlFEC(order, dim);
// RT contains Raviart-Thomas "face-centered" vector finite elements with
// continuous normal component.
RT_FECollection HDivFEC(order-1, dim);
// H1 contains continuous "node-centered" Lagrange finite elements.
H1_FECollection HGradFEC(order, dim);
ParFiniteElementSpace L2FESpace(pmesh, &L2FEC);
ParFiniteElementSpace HCurlFESpace(pmesh, &HCurlFEC);
ParFiniteElementSpace HDivFESpace(pmesh, &HDivFEC);
ParFiniteElementSpace HGradFESpace(pmesh, &HGradFEC);
// The terminology is TrueVSize is the unique (non-redundant) number of dofs
HYPRE_Int glob_size_l2 = L2FESpace.GlobalTrueVSize();
HYPRE_Int glob_size_nd = HCurlFESpace.GlobalTrueVSize();
HYPRE_Int glob_size_rt = HDivFESpace.GlobalTrueVSize();
HYPRE_Int glob_size_h1 = HGradFESpace.GlobalTrueVSize();
if (mpi.Root())
{
cout << "Number of Temperature Flux unknowns: " << glob_size_rt << endl;
cout << "Number of Temperature unknowns: " << glob_size_l2 << endl;
cout << "Number of Electric Field unknowns: " << glob_size_nd << endl;
cout << "Number of Magnetic Field unknowns: " << glob_size_rt << endl;
cout << "Number of Electrostatic unknowns: " << glob_size_h1 << endl;
}
int Vsize_l2 = L2FESpace.GetVSize();
int Vsize_nd = HCurlFESpace.GetVSize();
int Vsize_rt = HDivFESpace.GetVSize();
int Vsize_h1 = HGradFESpace.GetVSize();
// the big BlockVector stores the fields as
// 0 Temperature
// 1 Temperature Flux
// 2 P field
// 3 E field
// 4 B field
// 5 Joule Heating
Array<int> true_offset(7);
true_offset[0] = 0;
true_offset[1] = true_offset[0] + Vsize_l2;
true_offset[2] = true_offset[1] + Vsize_rt;
true_offset[3] = true_offset[2] + Vsize_h1;
true_offset[4] = true_offset[3] + Vsize_nd;
true_offset[5] = true_offset[4] + Vsize_rt;
true_offset[6] = true_offset[5] + Vsize_l2;
// The BlockVector is a large contiguous chunk of memory for storing required
// data for the hypre vectors, in this case: the temperature L2, the T-flux
// HDiv, the E-field HCurl, and the B-field HDiv, and scalar potential P.
BlockVector F(true_offset);
// grid functions E, B, T, F, P, and w which is the Joule heating
ParGridFunction E_gf, B_gf, T_gf, F_gf, w_gf, P_gf;
T_gf.MakeRef(&L2FESpace,F, true_offset[0]);
F_gf.MakeRef(&HDivFESpace,F, true_offset[1]);
P_gf.MakeRef(&HGradFESpace,F,true_offset[2]);
E_gf.MakeRef(&HCurlFESpace,F,true_offset[3]);
B_gf.MakeRef(&HDivFESpace,F, true_offset[4]);
w_gf.MakeRef(&L2FESpace,F, true_offset[5]);
// 13. Get the boundary conditions, set up the exact solution grid functions
// These VectorCoefficients have an Eval function. Note that e_exact and
// b_exact in this case are exact analytical solutions, taking a 3-vector
// point as input and returning a 3-vector field
VectorFunctionCoefficient E_exact(3, e_exact);
VectorFunctionCoefficient B_exact(3, b_exact);
FunctionCoefficient T_exact(t_exact);
E_exact.SetTime(0.0);
B_exact.SetTime(0.0);
// 14. Initialize the Diffusion operator, the GLVis visualization and print
// the initial energies.
MagneticDiffusionEOperator oper(true_offset[6], L2FESpace, HCurlFESpace,
HDivFESpace, HGradFESpace,
ess_bdr, thermal_ess_bdr, poisson_ess_bdr,
mu, sigmaMap, TcapMap, InvTcapMap,
InvTcondMap);
// This function initializes all the fields to zero or some provided IC
oper.Init(F);
socketstream vis_T, vis_E, vis_B, vis_w, vis_P;
char vishost[] = "localhost";
int visport = 19916;
if (visualization)
{
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
vis_T.precision(8);
vis_E.precision(8);
vis_B.precision(8);
vis_P.precision(8);
vis_w.precision(8);
int Wx = 0, Wy = 0; // window position
int Ww = 350, Wh = 350; // window size
int offx = Ww+10, offy = Wh+45; // window offsets
VisualizeField(vis_P, vishost, visport,
P_gf, "Electric Potential (Phi)", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_E, vishost, visport,
E_gf, "Electric Field (E)", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_B, vishost, visport,
B_gf, "Magnetic Field (B)", Wx, Wy, Ww, Wh);
Wx = 0;
Wy += offy;
VisualizeField(vis_w, vishost, visport,
w_gf, "Joule Heating", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_T, vishost, visport,
T_gf, "Temperature", Wx, Wy, Ww, Wh);
}
// VisIt visualization
VisItDataCollection visit_dc(basename, pmesh);
if ( visit )
{
visit_dc.RegisterField("E", &E_gf);
visit_dc.RegisterField("B", &B_gf);
visit_dc.RegisterField("T", &T_gf);
visit_dc.RegisterField("w", &w_gf);
visit_dc.RegisterField("Phi", &P_gf);
visit_dc.RegisterField("F", &F_gf);
visit_dc.SetCycle(0);
visit_dc.SetTime(0.0);
visit_dc.Save();
}
E_exact.SetTime(0.0);
B_exact.SetTime(0.0);
// 15. Perform time-integration (looping over the time iterations, ti, with a
// time-step dt). The object oper is the MagneticDiffusionOperator which
// has a Mult() method and an ImplicitSolve() method which are used by
// the time integrators.
ode_solver->Init(oper);
double t = 0.0;
bool last_step = false;
for (int ti = 1; !last_step; ti++)
{
if (t + dt >= t_final - dt/2)
{
last_step = true;
}
// F is the vector of dofs, t is the current time, and dt is the time step
// to advance.
ode_solver->Step(F, t, dt);
if (debug == 1)
{
oper.Debug(basename,t);
}
if (gfprint == 1)
{
ostringstream T_name, E_name, B_name, F_name, w_name, P_name, mesh_name;
T_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "T." << setfill('0') << setw(6) << myid;
E_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "E." << setfill('0') << setw(6) << myid;
B_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "B." << setfill('0') << setw(6) << myid;
F_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "F." << setfill('0') << setw(6) << myid;
w_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "w." << setfill('0') << setw(6) << myid;
P_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "P." << setfill('0') << setw(6) << myid;
mesh_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "mesh." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
mesh_ofs.close();
ofstream T_ofs(T_name.str().c_str());
T_ofs.precision(8);
T_gf.Save(T_ofs);
T_ofs.close();
ofstream E_ofs(E_name.str().c_str());
E_ofs.precision(8);
E_gf.Save(E_ofs);
E_ofs.close();
ofstream B_ofs(B_name.str().c_str());
B_ofs.precision(8);
B_gf.Save(B_ofs);
B_ofs.close();
ofstream F_ofs(F_name.str().c_str());
F_ofs.precision(8);
F_gf.Save(B_ofs);
F_ofs.close();
ofstream P_ofs(P_name.str().c_str());
P_ofs.precision(8);
P_gf.Save(P_ofs);
P_ofs.close();
ofstream w_ofs(w_name.str().c_str());
w_ofs.precision(8);
w_gf.Save(w_ofs);
w_ofs.close();
}
if (last_step || (ti % vis_steps) == 0)
{
double el = oper.ElectricLosses(E_gf);
if (mpi.Root())
{
cout << fixed;
cout << "step " << setw(6) << ti << ",\tt = " << setw(6)
<< setprecision(3) << t
<< ",\tdot(E, J) = " << setprecision(8) << el << endl;
}
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
if (visualization)
{
int Wx = 0, Wy = 0; // window position
int Ww = 350, Wh = 350; // window size
int offx = Ww+10, offy = Wh+45; // window offsets
VisualizeField(vis_P, vishost, visport,
P_gf, "Electric Potential (Phi)", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_E, vishost, visport,
E_gf, "Electric Field (E)", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_B, vishost, visport,
B_gf, "Magnetic Field (B)", Wx, Wy, Ww, Wh);
Wx = 0;
Wy += offy;
VisualizeField(vis_w, vishost, visport,
w_gf, "Joule Heating", Wx, Wy, Ww, Wh);
Wx += offx;
VisualizeField(vis_T, vishost, visport,
T_gf, "Temperature", Wx, Wy, Ww, Wh);
}
if (visit)
{
visit_dc.SetCycle(ti);
visit_dc.SetTime(t);
visit_dc.Save();
}
}
}
if (visualization)
{
vis_T.close();
vis_E.close();
vis_B.close();
vis_w.close();
vis_P.close();
}
// 16. Free the used memory.
delete ode_solver;
delete pmesh;
return 0;
}
namespace mfem
{
namespace electromagnetics
{
void edot_bc(const Vector &x, Vector &E)
{
E = 0.0;
}
void e_exact(const Vector &x, double t, Vector &E)
{
E[0] = 0.0;
E[1] = 0.0;
E[2] = 0.0;
}
void b_exact(const Vector &x, double t, Vector &B)
{
B[0] = 0.0;
B[1] = 0.0;
B[2] = 0.0;
}
double t_exact(const Vector &x)
{
double T = 0.0;
return T;
}
double p_bc(const Vector &x, double t)
{
// the value
double T;
if (x[2] < 0.0)
{
T = 1.0;
}
else
{
T = -1.0;
}
return T*cos(wj_ * t);
}
} // namespace electromagnetics
} // namespace mfem
void display_banner(ostream & os)
{
os << " ____. .__ " << endl
<< " | | ____ __ __| | ____ " << endl
<< " | |/ _ \\| | \\ | _/ __ \\ " << endl
<< "/\\__| ( <_> ) | / |_\\ ___/ " << endl
<< "\\________|\\____/|____/|____/\\___ >" << endl
<< " \\/ " << endl
<< flush;
}
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