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// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
// reserved. See file COPYRIGHT for details.
//
// This file is part of the MFEM library. For more information and source code
// availability see http://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License (as published by the Free
// Software Foundation) version 2.1 dated February 1999.
//
// -----------------------------------------------------
// Tesla Miniapp: Simple Magnetostatics Simulation Code
// -----------------------------------------------------
//
// This miniapp solves a simple 3D magnetostatic problem.
//
// Curl 1/mu Curl A = J + Curl mu0/mu M
//
// The permeability function is that of the vacuum with an optional diamagnetic
// or paramagnetic spherical shell. The optional current density takes the form
// of a user defined ring of current. The optional magnetization consists of a
// cylindrical bar of constant magnetization.
//
// The boundary conditions either apply a user selected uniform magnetic flux
// density or a surface current flowing between user defined surfaces.
//
// We discretize the vector potential with H(Curl) finite elements. The magnetic
// flux B is discretized with H(Div) finite elements.
//
// Compile with: make tesla
//
// Sample runs:
//
// A cylindrical bar magnet in a metal sphere:
// mpirun -np 4 tesla -bm '0 -0.5 0 0 0.5 0 0.2 1'
//
// A spherical shell of paramagnetic material in a uniform B field:
// mpirun -np 4 tesla -ubbc '0 0 1' -ms '0 0 0 0.2 0.4 10'
//
// A ring of current in a metal sphere:
// mpirun -np 4 tesla -cr '0 0 -0.2 0 0 0.2 0.2 0.4 1'
//
// A Halbach array of permanent magnets:
// mpirun -np 4 tesla -m ../../data/beam-hex.mesh -rs 2
// -ha '1 0.1 0.3 7 0.9 0.7 0 1 12'
//
// An example demonstrating the use of surface currents:
// mpirun -np 4 tesla -m square-angled-pipe.mesh
// -kbcs '3' -vbcs '1 2' -vbcv '-0.5 0.5'
//
// An example combining the paramagnetic shell, permanent magnet,
// and current ring:
// mpirun -np 4 tesla -m ../../data/inline-hex.mesh
// -ms '0.5 0.5 0.5 0.4 0.45 20'
// -bm '0.5 0.5 0.3 0.5 0.5 0.7 0.1 1'
// -cr '0.5 0.5 0.45 0.5 0.5 0.55 0.2 0.3 1'
//
// By default the sources and fields are all zero:
// mpirun -np 4 tesla
#include "tesla_solver.hpp"
#include <fstream>
#include <iostream>
using namespace std;
using namespace mfem;
using namespace mfem::electromagnetics;
// Permeability Function
Coefficient * SetupInvPermeabilityCoefficient();
static Vector pw_mu_(0); // Piecewise permeability values
static Vector pw_mu_inv_(0); // Piecewise inverse permeability values
static Vector ms_params_(0); // Center, Inner and Outer Radii, and
// Permeability of magnetic shell
double magnetic_shell(const Vector &);
double magnetic_shell_inv(const Vector & x) { return 1.0/magnetic_shell(x); }
// Current Density Function
static Vector cr_params_(0); // Axis Start, Axis End, Inner Ring Radius,
// Outer Ring Radius, and Total Current
// of current ring (annulus)
void current_ring(const Vector &, Vector &);
// Magnetization
static Vector bm_params_(0); // Axis Start, Axis End, Bar Radius,
// and Magnetic Field Magnitude
void bar_magnet(const Vector &, Vector &);
static Vector ha_params_(0); // Bounding box,
// axis index (0->'x', 1->'y', 2->'z'),
// rotation axis index
// and number of segments
void halbach_array(const Vector &, Vector &);
// A Field Boundary Condition for B = (Bx,By,Bz)
static Vector b_uniform_(0);
void a_bc_uniform(const Vector &, Vector&);
// Phi_M Boundary Condition for H = (0,0,1)
double phi_m_bc_uniform(const Vector &x);
// Prints the program's logo to the given output stream
void display_banner(ostream & os);
int main(int argc, char *argv[])
{
MPI_Session mpi(argc, argv);
if ( mpi.Root() ) { display_banner(cout); }
// Parse command-line options.
const char *mesh_file = "../../data/ball-nurbs.mesh";
int order = 1;
int maxit = 100;
int serial_ref_levels = 0;
int parallel_ref_levels = 0;
bool visualization = true;
bool visit = true;
Array<int> kbcs;
Array<int> vbcs;
Vector vbcv;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree).");
args.AddOption(&serial_ref_levels, "-rs", "--serial-ref-levels",
"Number of serial refinement levels.");
args.AddOption(&parallel_ref_levels, "-rp", "--parallel-ref-levels",
"Number of parallel refinement levels.");
args.AddOption(&b_uniform_, "-ubbc", "--uniform-b-bc",
"Specify if the three components of the constant magnetic flux density");
args.AddOption(&pw_mu_, "-pwm", "--piecewise-mu",
"Piecewise values of Permeability");
args.AddOption(&ms_params_, "-ms", "--magnetic-shell-params",
"Center, Inner Radius, Outer Radius, and Permeability of Magnetic Shell");
args.AddOption(&cr_params_, "-cr", "--current-ring-params",
"Axis End Points, Inner Radius, Outer Radius and Total Current of Annulus");
args.AddOption(&bm_params_, "-bm", "--bar-magnet-params",
"Axis End Points, Radius, and Magnetic Field of Cylindrical Magnet");
args.AddOption(&ha_params_, "-ha", "--halbach-array-params",
"Bounding Box Corners and Number of Segments");
args.AddOption(&kbcs, "-kbcs", "--surface-current-bc",
"Surfaces for the Surface Current (K) Boundary Condition");
args.AddOption(&vbcs, "-vbcs", "--voltage-bc-surf",
"Voltage Boundary Condition Surfaces (to drive K)");
args.AddOption(&vbcv, "-vbcv", "--voltage-bc-vals",
"Voltage Boundary Condition Values (to drive K)");
args.AddOption(&maxit, "-maxit", "--max-amr-iterations",
"Max number of iterations in the main AMR loop.");
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.Parse();
if (!args.Good())
{
if (mpi.Root())
{
args.PrintUsage(cout);
}
return 1;
}
if (mpi.Root())
{
args.PrintOptions(cout);
}
// Read the (serial) mesh from the given mesh file on all processors. We
// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
// and volume meshes with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
if (mpi.Root())
{
cout << "Starting initialization." << endl;
}
// Project a NURBS mesh to a piecewise-quadratic curved mesh
if (mesh->NURBSext)
{
mesh->UniformRefinement();
if (serial_ref_levels > 0) { serial_ref_levels--; }
mesh->SetCurvature(2);
}
// Ensure that quad and hex meshes are treated as non-conforming.
mesh->EnsureNCMesh();
// Refine the serial mesh on all processors to increase the resolution. In
// this example we do 'ref_levels' of uniform refinement.
for (int l = 0; l < serial_ref_levels; l++)
{
mesh->UniformRefinement();
}
// 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(MPI_COMM_WORLD, *mesh);
delete mesh;
// Refine this mesh in parallel to increase the resolution.
int par_ref_levels = parallel_ref_levels;
for (int l = 0; l < par_ref_levels; l++)
{
pmesh.UniformRefinement();
}
// If values for Voltage BCs were not set issue a warning and exit
if ( ( vbcs.Size() > 0 && kbcs.Size() == 0 ) ||
( kbcs.Size() > 0 && vbcs.Size() == 0 ) ||
( vbcv.Size() < vbcs.Size() ) )
{
if ( mpi.Root() )
{
cout << "The surface current (K) boundary condition requires "
<< "surface current boundary condition surfaces (with -kbcs), "
<< "voltage boundary condition surface (with -vbcs), "
<< "and voltage boundary condition values (with -vbcv)."
<< endl;
}
return 3;
}
// Create a coefficient describing the magnetic permeability
Coefficient * muInvCoef = SetupInvPermeabilityCoefficient();
// Create the Magnetostatic solver
TeslaSolver Tesla(pmesh, order, kbcs, vbcs, vbcv, *muInvCoef,
(b_uniform_.Size() > 0 ) ? a_bc_uniform : NULL,
(cr_params_.Size() > 0 ) ? current_ring : NULL,
(bm_params_.Size() > 0 ) ? bar_magnet :
(ha_params_.Size() > 0 ) ? halbach_array : NULL);
// Initialize GLVis visualization
if (visualization)
{
Tesla.InitializeGLVis();
}
// Initialize VisIt visualization
VisItDataCollection visit_dc("Tesla-AMR-Parallel", &pmesh);
if ( visit )
{
Tesla.RegisterVisItFields(visit_dc);
}
if (mpi.Root()) { cout << "Initialization done." << endl; }
// The main AMR loop. In each iteration we solve the problem on the current
// mesh, visualize the solution, estimate the error on all elements, refine
// the worst elements and update all objects to work with the new mesh. We
// refine until the maximum number of dofs in the Nedelec finite element
// space reaches 10 million.
const int max_dofs = 10000000;
for (int it = 1; it <= maxit; it++)
{
if (mpi.Root())
{
cout << "\nAMR Iteration " << it << endl;
}
// Display the current number of DoFs in each finite element space
Tesla.PrintSizes();
// Assemble all forms
Tesla.Assemble();
// Solve the system and compute any auxiliary fields
Tesla.Solve();
// Determine the current size of the linear system
int prob_size = Tesla.GetProblemSize();
// Write fields to disk for VisIt
if ( visit )
{
Tesla.WriteVisItFields(it);
}
// Send the solution by socket to a GLVis server.
if (visualization)
{
Tesla.DisplayToGLVis();
}
if (mpi.Root())
{
cout << "AMR iteration " << it << " complete." << endl;
}
// Check stopping criteria
if (prob_size > max_dofs)
{
if (mpi.Root())
{
cout << "Reached maximum number of dofs, exiting..." << endl;
}
break;
}
if ( it == maxit )
{
break;
}
// Wait for user input. Ask every 10th iteration.
char c = 'c';
if (mpi.Root() && (it % 10 == 0))
{
cout << "press (q)uit or (c)ontinue --> " << flush;
cin >> c;
}
MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);
if (c != 'c')
{
break;
}
// Estimate element errors using the Zienkiewicz-Zhu error estimator.
Vector errors(pmesh.GetNE());
Tesla.GetErrorEstimates(errors);
double local_max_err = errors.Max();
double global_max_err;
MPI_Allreduce(&local_max_err, &global_max_err, 1,
MPI_DOUBLE, MPI_MAX, pmesh.GetComm());
// Refine the elements whose error is larger than a fraction of the
// maximum element error.
const double frac = 0.5;
double threshold = frac * global_max_err;
if (mpi.Root()) { cout << "Refining ..." << endl; }
pmesh.RefineByError(errors, threshold);
// Update the magnetostatic solver to reflect the new state of the mesh.
Tesla.Update();
if (pmesh.Nonconforming() && mpi.WorldSize() > 1)
{
if (mpi.Root()) { cout << "Rebalancing ..." << endl; }
pmesh.Rebalance();
// Update again after rebalancing
Tesla.Update();
}
}
delete muInvCoef;
return 0;
}
// Print the Volta ascii logo to the given ostream
void display_banner(ostream & os)
{
os << " ___________ __ " << endl
<< " \\__ ___/___ _____| | _____ " << endl
<< " | |_/ __ \\ / ___/ | \\__ \\ " << endl
<< " | |\\ ___/ \\___ \\| |__/ __ \\_ " << endl
<< " |____| \\___ >____ >____(____ / " << endl
<< " \\/ \\/ \\/ " << endl << flush;
}
// The Permeability is a required coefficient which may be defined in
// various ways so we'll determine the appropriate coefficient type here.
Coefficient *
SetupInvPermeabilityCoefficient()
{
Coefficient * coef = NULL;
if ( ms_params_.Size() > 0 )
{
coef = new FunctionCoefficient(magnetic_shell_inv);
}
else if ( pw_mu_.Size() > 0 )
{
pw_mu_inv_.SetSize(pw_mu_.Size());
for (int i = 0; i < pw_mu_.Size(); i++)
{
MFEM_ASSERT( pw_mu_[i] > 0.0, "permeability values must be positive" );
pw_mu_inv_[i] = 1.0/pw_mu_[i];
}
coef = new PWConstCoefficient(pw_mu_inv_);
}
else
{
coef = new ConstantCoefficient(1.0/mu0_);
}
return coef;
}
// A spherical shell with constant permeability. The sphere has inner
// and outer radii, center, and relative permeability specified on the
// command line and stored in ms_params_.
double magnetic_shell(const Vector &x)
{
double r2 = 0.0;
for (int i = 0; i < x.Size(); i++)
{
r2 += (x(i) - ms_params_(i))*(x(i) - ms_params_(i));
}
if ( sqrt(r2) >= ms_params_(x.Size()) &&
sqrt(r2) <= ms_params_(x.Size()+1) )
{
return mu0_*ms_params_(x.Size()+2);
}
return mu0_;
}
// An annular ring of current density. The ring has two axis end
// points, inner and outer radii, and a constant current in Amperes.
void current_ring(const Vector &x, Vector &j)
{
MFEM_ASSERT(x.Size() == 3, "current_ring source requires 3D space.");
j.SetSize(x.Size());
j = 0.0;
Vector a(x.Size()); // Normalized Axis vector
Vector xu(x.Size()); // x vector relative to the axis end-point
Vector ju(x.Size()); // Unit vector in direction of current
xu = x;
for (int i=0; i<x.Size(); i++)
{
xu[i] -= cr_params_[i];
a[i] = cr_params_[x.Size()+i] - cr_params_[i];
}
double h = a.Norml2();
if ( h == 0.0 )
{
return;
}
double ra = cr_params_[2*x.Size()+0];
double rb = cr_params_[2*x.Size()+1];
if ( ra > rb )
{
double rc = ra;
ra = rb;
rb = rc;
}
double xa = xu*a;
if ( h > 0.0 )
{
xu.Add(-xa/(h*h),a);
}
double xp = xu.Norml2();
if ( xa >= 0.0 && xa <= h*h && xp >= ra && xp <= rb )
{
ju(0) = a(1) * xu(2) - a(2) * xu(1);
ju(1) = a(2) * xu(0) - a(0) * xu(2);
ju(2) = a(0) * xu(1) - a(1) * xu(0);
ju /= h;
j.Add(cr_params_[2*x.Size()+2]/(h*(rb-ra)),ju);
}
}
// A Cylindrical Rod of constant magnetization. The cylinder has two
// axis end points, a radius, and a constant magnetic field oriented
// along the axis.
void bar_magnet(const Vector &x, Vector &m)
{
m.SetSize(x.Size());
m = 0.0;
Vector a(x.Size()); // Normalized Axis vector
Vector xu(x.Size()); // x vector relative to the axis end-point
xu = x;
for (int i=0; i<x.Size(); i++)
{
xu[i] -= bm_params_[i];
a[i] = bm_params_[x.Size()+i] - bm_params_[i];
}
double h = a.Norml2();
if ( h == 0.0 )
{
return;
}
double r = bm_params_[2*x.Size()];
double xa = xu*a;
if ( h > 0.0 )
{
xu.Add(-xa/(h*h),a);
}
double xp = xu.Norml2();
if ( xa >= 0.0 && xa <= h*h && xp <= r )
{
m.Add(bm_params_[2*x.Size()+1]/h,a);
}
}
// A Square Rod of rotating magnetized segments. The rod is defined
// by a bounding box and a number of segments. The magnetization in
// each segment is constant and follows a rotating pattern.
void halbach_array(const Vector &x, Vector &m)
{
m.SetSize(x.Size());
m = 0.0;
// Check Bounding Box
if ( x[0] < ha_params_[0] || x[0] > ha_params_[3] ||
x[1] < ha_params_[1] || x[1] > ha_params_[4] ||
x[2] < ha_params_[2] || x[2] > ha_params_[5] )
{
return;
}
int ai = (int)ha_params_[6];
int ri = (int)ha_params_[7];
int n = (int)ha_params_[8];
int i = (int)n * (x[ai] - ha_params_[ai]) /
(ha_params_[ai+3] - ha_params_[ai]);
m[(ri + 1 + (i % 2)) % 3] = pow(-1.0,i/2);
}
// To produce a uniform magnetic flux the vector potential can be set
// to ( By z, Bz x, Bx y).
void a_bc_uniform(const Vector & x, Vector & a)
{
a.SetSize(3);
a(0) = b_uniform_(1) * x(2);
a(1) = b_uniform_(2) * x(0);
a(2) = b_uniform_(0) * x(1);
}
// To produce a uniform magnetic field the scalar potential can be set
// to -z (or -y in 2D).
double phi_m_bc_uniform(const Vector &x)
{
return -x(x.Size()-1);
}