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pmesh-optimizer.cpp
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pmesh-optimizer.cpp
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// Copyright (c) 2010-2024, 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.
//
// ---------------------------------------------------------------------
// Mesh Optimizer Miniapp: Optimize high-order meshes - Parallel Version
// ---------------------------------------------------------------------
//
// This miniapp performs mesh optimization using the Target-Matrix Optimization
// Paradigm (TMOP) by P.Knupp et al., and a global variational minimization
// approach. It minimizes the quantity sum_T int_T mu(J(x)), where T are the
// target (ideal) elements, J is the Jacobian of the transformation from the
// target to the physical element, and mu is the mesh quality metric. This
// metric can measure shape, size or alignment of the region around each
// quadrature point. The combination of targets & quality metrics is used to
// optimize the physical node positions, i.e., they must be as close as possible
// to the shape / size / alignment of their targets. This code also demonstrates
// a possible use of nonlinear operators (the class TMOP_QualityMetric, defining
// mu(J), and the class TMOP_Integrator, defining int mu(J)), as well as their
// coupling to Newton methods for solving minimization problems. Note that the
// utilized Newton methods are oriented towards avoiding invalid meshes with
// negative Jacobian determinants. Each Newton step requires the inversion of a
// Jacobian matrix, which is done through an inner linear solver.
//
// Compile with: make pmesh-optimizer
//
// Sample runs:
// Adapted analytic shape:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 2 -tid 4 -ni 200 -bnd -qt 1 -qo 8
// Adapted analytic size+orientation:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 14 -tid 4 -ni 200 -bnd -qt 1 -qo 8
// Adapted analytic shape+orientation:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 85 -tid 4 -ni 100 -bnd -qt 1 -qo 8 -fd
//
// Adapted analytic shape and/or size with hr-adaptivity:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -tid 9 -ni 50 -li 20 -hmid 55 -mid 7 -hr
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -tid 10 -ni 50 -li 20 -hmid 55 -mid 7 -hr
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -tid 11 -ni 50 -li 20 -hmid 58 -mid 7 -hr
//
// Adapted discrete size:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor
// (requires GSLIB):
// * mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 80 -tid 5 -ni 50 -qo 4 -nor -mno 1 -ae 1
// Adapted discrete size NC mesh;
// mpirun -np 4 pmesh-optimizer -m amr-quad-q2.mesh -o 2 -rs 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor
// Adapted discrete size 3D with PA:
// mpirun -np 4 pmesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 321 -tid 5 -ls 3 -nor -pa
// Adapted discrete size 3D with PA on device (requires CUDA):
// * mpirun -n 4 pmesh-optimizer -m cube.mesh -o 3 -rs 3 -mid 321 -tid 5 -ls 3 -nor -lc 0.1 -pa -d cuda
// Adapted discrete size; explicit combo of metrics; mixed tri/quad mesh:
// mpirun -np 4 pmesh-optimizer -m ../../data/square-mixed.mesh -o 2 -rs 2 -mid 2 -tid 5 -ni 200 -bnd -qo 6 -cmb 2 -nor
// Adapted discrete size+aspect_ratio:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100 -qo 6 -ex -st 1 -nor
// Adapted discrete size+orientation:
// mpirun -np 4 pmesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -fd -nor
// Adapted discrete aspect ratio (3D):
// mpirun -np 4 pmesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 302 -tid 7 -ni 20 -bnd -qt 1 -qo 8
//
// Adaptive limiting:
// mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 0.5
// Adaptive limiting through the L-BFGS solver:
// mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 400 -qo 5 -nor -vl 1 -alc 0.5 -st 1
// Adaptive limiting through FD (requires GSLIB):
// * mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 0.5 -fd -ae 1
//
// Blade shape:
// mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8
// (requires CUDA):
// * mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8 -d cuda
// Blade shape with FD-based solver:
// mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 4 -bnd -qt 1 -qo 8 -fd
// Blade limited shape:
// mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -bnd -qt 1 -qo 8 -lc 5000
// ICF shape and equal size:
// mpirun -np 4 pmesh-optimizer -o 3 -mid 80 -bec -tid 2 -ni 25 -ls 3 -art 2 -qo 5
// ICF shape and initial size:
// mpirun -np 4 pmesh-optimizer -o 3 -mid 9 -tid 3 -ni 30 -ls 3 -bnd -qt 1 -qo 8
// ICF shape:
// mpirun -np 4 pmesh-optimizer -o 3 -mid 1 -tid 1 -ni 100 -bnd -qt 1 -qo 8
// ICF limited shape:
// mpirun -np 4 pmesh-optimizer -o 3 -mid 1 -tid 1 -ni 100 -bnd -qt 1 -qo 8 -lc 10
// ICF combo shape + size (rings, slow convergence):
// mpirun -np 4 pmesh-optimizer -o 3 -mid 1 -tid 1 -ni 1000 -bnd -qt 1 -qo 8 -cmb 1
// Mixed tet / cube / hex mesh with limiting:
// mpirun -np 4 pmesh-optimizer -m ../../data/fichera-mixed-p2.mesh -o 4 -rs 1 -mid 301 -tid 1 -fix-bnd -qo 6 -nor -lc 0.25
// 3D pinched sphere shape (the mesh is in the mfem/data GitHub repository):
// * mpirun -np 4 pmesh-optimizer -m ../../../mfem_data/ball-pert.mesh -o 4 -mid 303 -tid 1 -ni 20 -li 500 -fix-bnd
// 2D non-conforming shape and equal size:
// mpirun -np 4 pmesh-optimizer -m ./amr-quad-q2.mesh -o 2 -rs 1 -mid 9 -tid 2 -ni 200 -bnd -qt 1 -qo 8
//
// 2D untangling:
// mpirun -np 4 pmesh-optimizer -m jagged.mesh -o 2 -mid 22 -tid 1 -ni 50 -li 50 -qo 4 -fd -vl 1
// 2D untangling with shifted barrier metric:
// mpirun -np 4 pmesh-optimizer -m jagged.mesh -o 2 -mid 4 -tid 1 -ni 50 -qo 4 -fd -vl 1 -btype 1
// 3D untangling (the mesh is in the mfem/data GitHub repository):
// * mpirun -np 4 pmesh-optimizer -m ../../../mfem_data/cube-holes-inv.mesh -o 3 -mid 313 -tid 1 -rtol 1e-5 -li 50 -qo 4 -fd -vl 1
// Shape optimization for a Kershaw transformed mesh using partial assembly:
// Mesh for Kershaw transformation must be a Cartesian mesh with nx % 6 = ny % 2 = nz % 2 = 0.
// Kershaw transformation can be imposed using the transformation ('t') feature in the mesh-explorer miniapp.
// * mpirun - np 6 pmesh-optimizer -m kershaw-24x24x24.mesh -mid 303 -tid 1 -bnd -ni 100 -art 1 -ls 3 -qo 8 -li 40 -o 2 -qo 8 -ker -pa
#include "mfem.hpp"
#include "../common/mfem-common.hpp"
#include <iostream>
#include <fstream>
#include "mesh-optimizer.hpp"
using namespace mfem;
using namespace std;
int main (int argc, char *argv[])
{
// 0. Initialize MPI and HYPRE.
Mpi::Init(argc, argv);
int myid = Mpi::WorldRank();
Hypre::Init();
// 1. Set the method's default parameters.
const char *mesh_file = "icf.mesh";
int mesh_poly_deg = 1;
int rs_levels = 0;
int rp_levels = 0;
real_t jitter = 0.0;
int metric_id = 1;
int target_id = 1;
real_t lim_const = 0.0;
real_t adapt_lim_const = 0.0;
int quad_type = 1;
int quad_order = 8;
int solver_type = 0;
int solver_iter = 20;
#ifdef MFEM_USE_SINGLE
real_t solver_rtol = 1e-4;
#else
real_t solver_rtol = 1e-10;
#endif
int solver_art_type = 0;
int lin_solver = 2;
int max_lin_iter = 100;
bool move_bnd = true;
int combomet = 0;
bool bal_expl_combo = false;
bool hradaptivity = false;
int h_metric_id = -1;
bool normalization = false;
bool visualization = true;
int verbosity_level = 0;
bool fdscheme = false;
int adapt_eval = 0;
bool exactaction = false;
bool integ_over_targ = true;
const char *devopt = "cpu";
bool pa = false;
int n_hr_iter = 5;
int n_h_iter = 1;
int mesh_node_ordering = 0;
int barrier_type = 0;
int worst_case_type = 0;
// 2. Parse command-line options.
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&mesh_poly_deg, "-o", "--order",
"Polynomial degree of mesh finite element space.");
args.AddOption(&rs_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&rp_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&jitter, "-ji", "--jitter",
"Random perturbation scaling factor.");
args.AddOption(&metric_id, "-mid", "--metric-id",
"Mesh optimization metric:\n\t"
"T-metrics\n\t"
"1 : |T|^2 -- 2D no type\n\t"
"2 : 0.5|T|^2/tau-1 -- 2D shape (condition number)\n\t"
"7 : |T-T^-t|^2 -- 2D shape+size\n\t"
"9 : tau*|T-T^-t|^2 -- 2D shape+size\n\t"
"14 : |T-I|^2 -- 2D shape+size+orientation\n\t"
"22 : 0.5(|T|^2-2*tau)/(tau-tau_0) -- 2D untangling\n\t"
"50 : 0.5|T^tT|^2/tau^2-1 -- 2D shape\n\t"
"55 : (tau-1)^2 -- 2D size\n\t"
"56 : 0.5(sqrt(tau)-1/sqrt(tau))^2 -- 2D size\n\t"
"58 : |T^tT|^2/(tau^2)-2*|T|^2/tau+2 -- 2D shape\n\t"
"77 : 0.5(tau-1/tau)^2 -- 2D size\n\t"
"80 : (1-gamma)mu_2 + gamma mu_77 -- 2D shape+size\n\t"
"85 : |T-|T|/sqrt(2)I|^2 -- 2D shape+orientation\n\t"
"90 : balanced combo mu_50 & mu_77 -- 2D shape+size\n\t"
"94 : balanced combo mu_2 & mu_56 -- 2D shape+size\n\t"
"98 : (1/tau)|T-I|^2 -- 2D shape+size+orientation\n\t"
// "211: (tau-1)^2-tau+sqrt(tau^2+eps) -- 2D untangling\n\t"
// "252: 0.5(tau-1)^2/(tau-tau_0) -- 2D untangling\n\t"
"301: (|T||T^-1|)/3-1 -- 3D shape\n\t"
"302: (|T|^2|T^-1|^2)/9-1 -- 3D shape\n\t"
"303: (|T|^2)/3/tau^(2/3)-1 -- 3D shape\n\t"
"304: (|T|^3)/3^{3/2}/tau-1 -- 3D shape\n\t"
// "311: (tau-1)^2-tau+sqrt(tau^2+eps)-- 3D untangling\n\t"
"313: (|T|^2)(tau-tau0)^(-2/3)/3 -- 3D untangling\n\t"
"315: (tau-1)^2 -- 3D no type\n\t"
"316: 0.5(sqrt(tau)-1/sqrt(tau))^2 -- 3D no type\n\t"
"321: |T-T^-t|^2 -- 3D shape+size\n\t"
"322: |T-adjT^-t|^2 -- 3D shape+size\n\t"
"323: |J|^3-3sqrt(3)ln(det(J))-3sqrt(3) -- 3D shape+size\n\t"
"328: balanced combo mu_301 & mu_316 -- 3D shape+size\n\t"
"332: (1-gamma) mu_302 + gamma mu_315 -- 3D shape+size\n\t"
"333: (1-gamma) mu_302 + gamma mu_316 -- 3D shape+size\n\t"
"334: (1-gamma) mu_303 + gamma mu_316 -- 3D shape+size\n\t"
"328: balanced combo mu_302 & mu_318 -- 3D shape+size\n\t"
"347: (1-gamma) mu_304 + gamma mu_316 -- 3D shape+size\n\t"
// "352: 0.5(tau-1)^2/(tau-tau_0) -- 3D untangling\n\t"
"360: (|T|^3)/3^{3/2}-tau -- 3D shape\n\t"
"A-metrics\n\t"
"11 : (1/4*alpha)|A-(adjA)^T(W^TW)/omega|^2 -- 2D shape\n\t"
"36 : (1/alpha)|A-W|^2 -- 2D shape+size+orientation\n\t"
"107: (1/2*alpha)|A-|A|/|W|W|^2 -- 2D shape+orientation\n\t"
"126: (1-gamma)nu_11 + gamma*nu_14a -- 2D shape+size\n\t"
);
args.AddOption(&target_id, "-tid", "--target-id",
"Target (ideal element) type:\n\t"
"1: Ideal shape, unit size\n\t"
"2: Ideal shape, equal size\n\t"
"3: Ideal shape, initial size\n\t"
"4: Given full analytic Jacobian (in physical space)\n\t"
"5: Ideal shape, given size (in physical space)");
args.AddOption(&lim_const, "-lc", "--limit-const", "Limiting constant.");
args.AddOption(&adapt_lim_const, "-alc", "--adapt-limit-const",
"Adaptive limiting coefficient constant.");
args.AddOption(&quad_type, "-qt", "--quad-type",
"Quadrature rule type:\n\t"
"1: Gauss-Lobatto\n\t"
"2: Gauss-Legendre\n\t"
"3: Closed uniform points");
args.AddOption(&quad_order, "-qo", "--quad_order",
"Order of the quadrature rule.");
args.AddOption(&solver_type, "-st", "--solver-type",
" Type of solver: (default) 0: Newton, 1: LBFGS");
args.AddOption(&solver_iter, "-ni", "--newton-iters",
"Maximum number of Newton iterations.");
args.AddOption(&solver_rtol, "-rtol", "--newton-rel-tolerance",
"Relative tolerance for the Newton solver.");
args.AddOption(&solver_art_type, "-art", "--adaptive-rel-tol",
"Type of adaptive relative linear solver tolerance:\n\t"
"0: None (default)\n\t"
"1: Eisenstat-Walker type 1\n\t"
"2: Eisenstat-Walker type 2");
args.AddOption(&lin_solver, "-ls", "--lin-solver",
"Linear solver:\n\t"
"0: l1-Jacobi\n\t"
"1: CG\n\t"
"2: MINRES\n\t"
"3: MINRES + Jacobi preconditioner\n\t"
"4: MINRES + l1-Jacobi preconditioner");
args.AddOption(&max_lin_iter, "-li", "--lin-iter",
"Maximum number of iterations in the linear solve.");
args.AddOption(&move_bnd, "-bnd", "--move-boundary", "-fix-bnd",
"--fix-boundary",
"Enable motion along horizontal and vertical boundaries.");
args.AddOption(&combomet, "-cmb", "--combo-type",
"Combination of metrics options:\n\t"
"0: Use single metric\n\t"
"1: Shape + space-dependent size given analytically\n\t"
"2: Shape + adapted size given discretely; shared target");
args.AddOption(&bal_expl_combo, "-bec", "--balance-explicit-combo",
"-no-bec", "--balance-explicit-combo",
"Automatic balancing of explicit combo metrics.");
args.AddOption(&hradaptivity, "-hr", "--hr-adaptivity", "-no-hr",
"--no-hr-adaptivity",
"Enable hr-adaptivity.");
args.AddOption(&h_metric_id, "-hmid", "--h-metric",
"Same options as metric_id. Used to determine refinement"
" type for each element if h-adaptivity is enabled.");
args.AddOption(&normalization, "-nor", "--normalization", "-no-nor",
"--no-normalization",
"Make all terms in the optimization functional unitless.");
args.AddOption(&fdscheme, "-fd", "--fd_approximation",
"-no-fd", "--no-fd-approx",
"Enable finite difference based derivative computations.");
args.AddOption(&exactaction, "-ex", "--exact_action",
"-no-ex", "--no-exact-action",
"Enable exact action of TMOP_Integrator.");
args.AddOption(&integ_over_targ, "-it", "--integrate-target",
"-ir", "--integrate-reference",
"Integrate over target (-it) or reference (-ir) element.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&verbosity_level, "-vl", "--verbosity-level",
"Verbosity level for the involved iterative solvers:\n\t"
"0: no output\n\t"
"1: Newton iterations\n\t"
"2: Newton iterations + linear solver summaries\n\t"
"3: newton iterations + linear solver iterations");
args.AddOption(&adapt_eval, "-ae", "--adaptivity-evaluator",
"0 - Advection based (DEFAULT), 1 - GSLIB.");
args.AddOption(&devopt, "-d", "--device",
"Device configuration string, see Device::Configure().");
args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
"--no-partial-assembly", "Enable Partial Assembly.");
args.AddOption(&n_hr_iter, "-nhr", "--n_hr_iter",
"Number of hr-adaptivity iterations.");
args.AddOption(&n_h_iter, "-nh", "--n_h_iter",
"Number of h-adaptivity iterations per r-adaptivity"
"iteration.");
args.AddOption(&mesh_node_ordering, "-mno", "--mesh_node_ordering",
"Ordering of mesh nodes."
"0 (default): byNodes, 1: byVDIM");
args.AddOption(&barrier_type, "-btype", "--barrier-type",
"0 - None,"
"1 - Shifted Barrier,"
"2 - Pseudo Barrier.");
args.AddOption(&worst_case_type, "-wctype", "--worst-case-type",
"0 - None,"
"1 - Beta,"
"2 - PMean.");
args.Parse();
if (!args.Good())
{
if (myid == 0) { args.PrintUsage(cout); }
return 1;
}
if (myid == 0) { args.PrintOptions(cout); }
if (h_metric_id < 0) { h_metric_id = metric_id; }
if (hradaptivity)
{
MFEM_VERIFY(strcmp(devopt,"cpu")==0, "HR-adaptivity is currently only"
" supported on cpus.");
}
Device device(devopt);
if (myid == 0) { device.Print();}
// 3. Initialize and refine the starting mesh.
Mesh *mesh = new Mesh(mesh_file, 1, 1, false);
for (int lev = 0; lev < rs_levels; lev++)
{
mesh->UniformRefinement();
}
const int dim = mesh->Dimension();
if (hradaptivity) { mesh->EnsureNCMesh(); }
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < rp_levels; lev++)
{
pmesh->UniformRefinement();
}
// 4. Define a finite element space on the mesh. Here we use vector finite
// elements which are tensor products of quadratic finite elements. The
// number of components in the vector finite element space is specified by
// the last parameter of the FiniteElementSpace constructor.
FiniteElementCollection *fec;
if (mesh_poly_deg <= 0)
{
fec = new QuadraticPosFECollection;
mesh_poly_deg = 2;
}
else { fec = new H1_FECollection(mesh_poly_deg, dim); }
ParFiniteElementSpace *pfespace = new ParFiniteElementSpace(pmesh, fec, dim,
mesh_node_ordering);
// 5. Make the mesh curved based on the above finite element space. This
// means that we define the mesh elements through a fespace-based
// transformation of the reference element.
pmesh->SetNodalFESpace(pfespace);
// 7. Get the mesh nodes (vertices and other degrees of freedom in the finite
// element space) as a finite element grid function in fespace. Note that
// changing x automatically changes the shapes of the mesh elements.
ParGridFunction x(pfespace);
pmesh->SetNodalGridFunction(&x);
// 8. Define a vector representing the minimal local mesh size in the mesh
// nodes. We index the nodes using the scalar version of the degrees of
// freedom in pfespace. Note: this is partition-dependent.
//
// In addition, compute average mesh size and total volume.
Vector h0(pfespace->GetNDofs());
h0 = infinity();
real_t vol_loc = 0.0;
Array<int> dofs;
for (int i = 0; i < pmesh->GetNE(); i++)
{
// Get the local scalar element degrees of freedom in dofs.
pfespace->GetElementDofs(i, dofs);
// Adjust the value of h0 in dofs based on the local mesh size.
const real_t hi = pmesh->GetElementSize(i);
for (int j = 0; j < dofs.Size(); j++)
{
h0(dofs[j]) = min(h0(dofs[j]), hi);
}
vol_loc += pmesh->GetElementVolume(i);
}
real_t vol_glb;
MPI_Allreduce(&vol_loc, &vol_glb, 1, MPITypeMap<real_t>::mpi_type,
MPI_SUM, MPI_COMM_WORLD);
const real_t small_phys_size = pow(vol_glb, 1.0 / dim) / 100.0;
// 9. Add a random perturbation to the nodes in the interior of the domain.
// We define a random grid function of fespace and make sure that it is
// zero on the boundary and its values are locally of the order of h0.
// The latter is based on the DofToVDof() method which maps the scalar to
// the vector degrees of freedom in pfespace.
ParGridFunction rdm(pfespace);
rdm.Randomize();
rdm -= 0.25; // Shift to random values in [-0.5,0.5].
rdm *= jitter;
rdm.HostReadWrite();
// Scale the random values to be of order of the local mesh size.
for (int i = 0; i < pfespace->GetNDofs(); i++)
{
for (int d = 0; d < dim; d++)
{
rdm(pfespace->DofToVDof(i,d)) *= h0(i);
}
}
Array<int> vdofs;
for (int i = 0; i < pfespace->GetNBE(); i++)
{
// Get the vector degrees of freedom in the boundary element.
pfespace->GetBdrElementVDofs(i, vdofs);
// Set the boundary values to zero.
for (int j = 0; j < vdofs.Size(); j++) { rdm(vdofs[j]) = 0.0; }
}
x -= rdm;
// Set the perturbation of all nodes from the true nodes.
x.SetTrueVector();
x.SetFromTrueVector();
// 10. Save the starting (prior to the optimization) mesh to a file. This
// output can be viewed later using GLVis: "glvis -m perturbed -np
// num_mpi_tasks".
{
ostringstream mesh_name;
mesh_name << "perturbed.mesh";
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->PrintAsOne(mesh_ofs);
}
// 11. Store the starting (prior to the optimization) positions.
ParGridFunction x0(pfespace);
x0 = x;
// 12. Form the integrator that uses the chosen metric and target.
real_t min_detJ = -0.1;
TMOP_QualityMetric *metric = NULL;
switch (metric_id)
{
// T-metrics
case 1: metric = new TMOP_Metric_001; break;
case 2: metric = new TMOP_Metric_002; break;
case 4: metric = new TMOP_Metric_004; break;
case 7: metric = new TMOP_Metric_007; break;
case 9: metric = new TMOP_Metric_009; break;
case 14: metric = new TMOP_Metric_014; break;
case 22: metric = new TMOP_Metric_022(min_detJ); break;
case 50: metric = new TMOP_Metric_050; break;
case 55: metric = new TMOP_Metric_055; break;
case 56: metric = new TMOP_Metric_056; break;
case 58: metric = new TMOP_Metric_058; break;
case 66: metric = new TMOP_Metric_066(0.5); break;
case 77: metric = new TMOP_Metric_077; break;
case 80: metric = new TMOP_Metric_080(0.5); break;
case 85: metric = new TMOP_Metric_085; break;
case 90: metric = new TMOP_Metric_090; break;
case 94: metric = new TMOP_Metric_094; break;
case 98: metric = new TMOP_Metric_098; break;
// case 211: metric = new TMOP_Metric_211; break;
// case 252: metric = new TMOP_Metric_252(min_detJ); break;
case 301: metric = new TMOP_Metric_301; break;
case 302: metric = new TMOP_Metric_302; break;
case 303: metric = new TMOP_Metric_303; break;
case 304: metric = new TMOP_Metric_304; break;
// case 311: metric = new TMOP_Metric_311; break;
case 313: metric = new TMOP_Metric_313(min_detJ); break;
case 315: metric = new TMOP_Metric_315; break;
case 316: metric = new TMOP_Metric_316; break;
case 321: metric = new TMOP_Metric_321; break;
case 322: metric = new TMOP_Metric_322; break;
case 323: metric = new TMOP_Metric_323; break;
case 328: metric = new TMOP_Metric_328; break;
case 332: metric = new TMOP_Metric_332(0.5); break;
case 333: metric = new TMOP_Metric_333(0.5); break;
case 334: metric = new TMOP_Metric_334(0.5); break;
case 338: metric = new TMOP_Metric_338; break;
case 347: metric = new TMOP_Metric_347(0.5); break;
// case 352: metric = new TMOP_Metric_352(min_detJ); break;
case 360: metric = new TMOP_Metric_360; break;
// A-metrics
case 11: metric = new TMOP_AMetric_011; break;
case 36: metric = new TMOP_AMetric_036; break;
case 107: metric = new TMOP_AMetric_107a; break;
case 126: metric = new TMOP_AMetric_126(0.9); break;
default:
if (myid == 0) { cout << "Unknown metric_id: " << metric_id << endl; }
return 3;
}
TMOP_QualityMetric *h_metric = NULL;
if (hradaptivity)
{
switch (h_metric_id)
{
case 1: h_metric = new TMOP_Metric_001; break;
case 2: h_metric = new TMOP_Metric_002; break;
case 7: h_metric = new TMOP_Metric_007; break;
case 9: h_metric = new TMOP_Metric_009; break;
case 55: h_metric = new TMOP_Metric_055; break;
case 56: h_metric = new TMOP_Metric_056; break;
case 58: h_metric = new TMOP_Metric_058; break;
case 77: h_metric = new TMOP_Metric_077; break;
case 315: h_metric = new TMOP_Metric_315; break;
case 316: h_metric = new TMOP_Metric_316; break;
case 321: h_metric = new TMOP_Metric_321; break;
default: cout << "Metric_id not supported for h-adaptivity: " << h_metric_id <<
endl;
return 3;
}
}
TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType btype;
switch (barrier_type)
{
case 0: btype = TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::None;
break;
case 1: btype = TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::Shifted;
break;
case 2: btype = TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::Pseudo;
break;
default: cout << "barrier_type not supported: " << barrier_type << endl;
return 3;
}
TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType wctype;
switch (worst_case_type)
{
case 0: wctype = TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::None;
break;
case 1: wctype = TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::Beta;
break;
case 2: wctype = TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::PMean;
break;
default: cout << "worst_case_type not supported: " << worst_case_type << endl;
return 3;
}
TMOP_QualityMetric *untangler_metric = NULL;
if (barrier_type > 0 || worst_case_type > 0)
{
if (barrier_type > 0)
{
MFEM_VERIFY(metric_id == 4 || metric_id == 14 || metric_id == 66,
"Metric not supported for shifted/pseudo barriers.");
}
untangler_metric = new TMOP_WorstCaseUntangleOptimizer_Metric(*metric,
2,
1.5,
0.001,//0.01 for pseudo barrier
0.001,
btype,
wctype);
}
if (metric_id < 300 || h_metric_id < 300)
{
MFEM_VERIFY(dim == 2, "Incompatible metric for 3D meshes");
}
if (metric_id >= 300 || h_metric_id >= 300)
{
MFEM_VERIFY(dim == 3, "Incompatible metric for 2D meshes");
}
TargetConstructor::TargetType target_t;
TargetConstructor *target_c = NULL;
HessianCoefficient *adapt_coeff = NULL;
HRHessianCoefficient *hr_adapt_coeff = NULL;
H1_FECollection ind_fec(mesh_poly_deg, dim);
ParFiniteElementSpace ind_fes(pmesh, &ind_fec);
ParFiniteElementSpace ind_fesv(pmesh, &ind_fec, dim);
ParGridFunction size(&ind_fes), aspr(&ind_fes), ori(&ind_fes);
ParGridFunction aspr3d(&ind_fesv);
const AssemblyLevel al =
pa ? AssemblyLevel::PARTIAL : AssemblyLevel::LEGACY;
switch (target_id)
{
case 1: target_t = TargetConstructor::IDEAL_SHAPE_UNIT_SIZE; break;
case 2: target_t = TargetConstructor::IDEAL_SHAPE_EQUAL_SIZE; break;
case 3: target_t = TargetConstructor::IDEAL_SHAPE_GIVEN_SIZE; break;
case 4:
{
target_t = TargetConstructor::GIVEN_FULL;
AnalyticAdaptTC *tc = new AnalyticAdaptTC(target_t);
adapt_coeff = new HessianCoefficient(dim, metric_id);
tc->SetAnalyticTargetSpec(NULL, NULL, adapt_coeff);
target_c = tc;
break;
}
case 5: // Discrete size 2D or 3D
{
target_t = TargetConstructor::IDEAL_SHAPE_GIVEN_SIZE;
DiscreteAdaptTC *tc = new DiscreteAdaptTC(target_t);
if (adapt_eval == 0)
{
tc->SetAdaptivityEvaluator(new AdvectorCG(al));
}
else
{
#ifdef MFEM_USE_GSLIB
tc->SetAdaptivityEvaluator(new InterpolatorFP);
#else
MFEM_ABORT("MFEM is not built with GSLIB.");
#endif
}
ConstructSizeGF(size);
tc->SetParDiscreteTargetSize(size);
target_c = tc;
break;
}
case 6: // material indicator 2D
{
ParGridFunction d_x(&ind_fes), d_y(&ind_fes), disc(&ind_fes);
target_t = TargetConstructor::GIVEN_SHAPE_AND_SIZE;
DiscreteAdaptTC *tc = new DiscreteAdaptTC(target_t);
FunctionCoefficient mat_coeff(material_indicator_2d);
disc.ProjectCoefficient(mat_coeff);
if (adapt_eval == 0)
{
tc->SetAdaptivityEvaluator(new AdvectorCG(al));
}
else
{
#ifdef MFEM_USE_GSLIB
tc->SetAdaptivityEvaluator(new InterpolatorFP);
#else
MFEM_ABORT("MFEM is not built with GSLIB.");
#endif
}
// Diffuse the interface
DiffuseField(disc,2);
// Get partials with respect to x and y of the grid function
disc.GetDerivative(1,0,d_x);
disc.GetDerivative(1,1,d_y);
// Compute the squared magnitude of the gradient
for (int i = 0; i < size.Size(); i++)
{
size(i) = std::pow(d_x(i),2)+std::pow(d_y(i),2);
}
const real_t max = size.Max();
real_t max_all;
MPI_Allreduce(&max, &max_all, 1, MPITypeMap<real_t>::mpi_type,
MPI_MAX, MPI_COMM_WORLD);
for (int i = 0; i < d_x.Size(); i++)
{
d_x(i) = std::abs(d_x(i));
d_y(i) = std::abs(d_y(i));
}
const real_t eps = 0.01;
const real_t aspr_ratio = 20.0;
const real_t size_ratio = 40.0;
for (int i = 0; i < size.Size(); i++)
{
size(i) = (size(i)/max_all);
aspr(i) = (d_x(i)+eps)/(d_y(i)+eps);
aspr(i) = 0.1 + 0.9*(1-size(i))*(1-size(i));
if (aspr(i) > aspr_ratio) {aspr(i) = aspr_ratio;}
if (aspr(i) < 1.0/aspr_ratio) {aspr(i) = 1.0/aspr_ratio;}
}
Vector vals;
const int NE = pmesh->GetNE();
real_t volume = 0.0, volume_ind = 0.0;
for (int i = 0; i < NE; i++)
{
ElementTransformation *Tr = pmesh->GetElementTransformation(i);
const IntegrationRule &ir =
IntRules.Get(pmesh->GetElementBaseGeometry(i), Tr->OrderJ());
size.GetValues(i, ir, vals);
for (int j = 0; j < ir.GetNPoints(); j++)
{
const IntegrationPoint &ip = ir.IntPoint(j);
Tr->SetIntPoint(&ip);
volume += ip.weight * Tr->Weight();
volume_ind += vals(j) * ip.weight * Tr->Weight();
}
}
real_t volume_all, volume_ind_all;
MPI_Allreduce(&volume, &volume_all, 1, MPITypeMap<real_t>::mpi_type,
MPI_SUM, MPI_COMM_WORLD);
MPI_Allreduce(&volume_ind, &volume_ind_all, 1,
MPITypeMap<real_t>::mpi_type, MPI_SUM, MPI_COMM_WORLD);
const int NE_ALL = pmesh->GetGlobalNE();
const real_t avg_zone_size = volume_all / NE_ALL;
const real_t small_avg_ratio =
(volume_ind_all + (volume_all - volume_ind_all) / size_ratio)
/ volume_all;
const real_t small_zone_size = small_avg_ratio * avg_zone_size;
const real_t big_zone_size = size_ratio * small_zone_size;
for (int i = 0; i < size.Size(); i++)
{
const real_t val = size(i);
const real_t a = (big_zone_size - small_zone_size) / small_zone_size;
size(i) = big_zone_size / (1.0+a*val);
}
DiffuseField(size, 2);
DiffuseField(aspr, 2);
tc->SetParDiscreteTargetSize(size);
tc->SetParDiscreteTargetAspectRatio(aspr);
target_c = tc;
break;
}
case 7: // Discrete aspect ratio 3D
{
target_t = TargetConstructor::GIVEN_SHAPE_AND_SIZE;
DiscreteAdaptTC *tc = new DiscreteAdaptTC(target_t);
if (adapt_eval == 0)
{
tc->SetAdaptivityEvaluator(new AdvectorCG(al));
}
else
{
#ifdef MFEM_USE_GSLIB
tc->SetAdaptivityEvaluator(new InterpolatorFP);
#else
MFEM_ABORT("MFEM is not built with GSLIB.");
#endif
}
VectorFunctionCoefficient fd_aspr3d(dim, discrete_aspr_3d);
aspr3d.ProjectCoefficient(fd_aspr3d);
tc->SetParDiscreteTargetAspectRatio(aspr3d);
target_c = tc;
break;
}
case 8: // shape/size + orientation 2D
{
target_t = TargetConstructor::GIVEN_SHAPE_AND_SIZE;
DiscreteAdaptTC *tc = new DiscreteAdaptTC(target_t);
if (adapt_eval == 0)
{
tc->SetAdaptivityEvaluator(new AdvectorCG(al));
}
else
{
#ifdef MFEM_USE_GSLIB
tc->SetAdaptivityEvaluator(new InterpolatorFP);
#else
MFEM_ABORT("MFEM is not built with GSLIB.");
#endif
}
ConstantCoefficient size_coeff(0.1*0.1);
size.ProjectCoefficient(size_coeff);
tc->SetParDiscreteTargetSize(size);
FunctionCoefficient ori_coeff(discrete_ori_2d);
ori.ProjectCoefficient(ori_coeff);
tc->SetParDiscreteTargetOrientation(ori);
target_c = tc;
break;
}
// Targets used for hr-adaptivity tests.
case 9: // size target in an annular region.
case 10: // size+aspect-ratio in an annular region.
case 11: // size+aspect-ratio target for a rotate sine wave
{
target_t = TargetConstructor::GIVEN_FULL;
AnalyticAdaptTC *tc = new AnalyticAdaptTC(target_t);
hr_adapt_coeff = new HRHessianCoefficient(dim, target_id - 9);
tc->SetAnalyticTargetSpec(NULL, NULL, hr_adapt_coeff);
target_c = tc;
break;
}
default:
if (myid == 0) { cout << "Unknown target_id: " << target_id << endl; }
return 3;
}
if (target_c == NULL)
{
target_c = new TargetConstructor(target_t, MPI_COMM_WORLD);
}
target_c->SetNodes(x0);
// Automatically balanced gamma in composite metrics.
auto metric_combo = dynamic_cast<TMOP_Combo_QualityMetric *>(metric);
if (metric_combo && bal_expl_combo)
{
Vector bal_weights;
metric_combo->ComputeBalancedWeights(x, *target_c, bal_weights);
metric_combo->SetWeights(bal_weights);
}
TMOP_QualityMetric *metric_to_use = barrier_type > 0 || worst_case_type > 0
? untangler_metric
: metric;
auto tmop_integ = new TMOP_Integrator(metric_to_use, target_c, h_metric);
tmop_integ->IntegrateOverTarget(integ_over_targ);
if (barrier_type > 0 || worst_case_type > 0)
{
tmop_integ->ComputeUntangleMetricQuantiles(x, *pfespace);
}
// Finite differences for computations of derivatives.
if (fdscheme)
{
MFEM_VERIFY(pa == false, "PA for finite differences is not implemented.");
tmop_integ->EnableFiniteDifferences(x);
}
tmop_integ->SetExactActionFlag(exactaction);
// Setup the quadrature rules for the TMOP integrator.
IntegrationRules *irules = NULL;
switch (quad_type)
{
case 1: irules = &IntRulesLo; break;
case 2: irules = &IntRules; break;
case 3: irules = &IntRulesCU; break;
default:
if (myid == 0) { cout << "Unknown quad_type: " << quad_type << endl; }
return 3;
}
tmop_integ->SetIntegrationRules(*irules, quad_order);
if (myid == 0 && dim == 2)
{
cout << "Triangle quadrature points: "
<< irules->Get(Geometry::TRIANGLE, quad_order).GetNPoints()
<< "\nQuadrilateral quadrature points: "
<< irules->Get(Geometry::SQUARE, quad_order).GetNPoints() << endl;
}
if (myid == 0 && dim == 3)
{
cout << "Tetrahedron quadrature points: "
<< irules->Get(Geometry::TETRAHEDRON, quad_order).GetNPoints()
<< "\nHexahedron quadrature points: "
<< irules->Get(Geometry::CUBE, quad_order).GetNPoints()
<< "\nPrism quadrature points: "
<< irules->Get(Geometry::PRISM, quad_order).GetNPoints() << endl;
}
// Limit the node movement.
// The limiting distances can be given by a general function of space.
ParFiniteElementSpace dist_pfespace(pmesh, fec); // scalar space
ParGridFunction dist(&dist_pfespace);
dist = 1.0;
// The small_phys_size is relevant only with proper normalization.
if (normalization) { dist = small_phys_size; }
ConstantCoefficient lim_coeff(lim_const);
if (lim_const != 0.0) { tmop_integ->EnableLimiting(x0, dist, lim_coeff); }
// Adaptive limiting.
ParGridFunction adapt_lim_gf0(&ind_fes);
ConstantCoefficient adapt_lim_coeff(adapt_lim_const);
AdaptivityEvaluator *adapt_lim_eval = NULL;
if (adapt_lim_const > 0.0)
{
MFEM_VERIFY(pa == false, "PA is not implemented for adaptive limiting");
FunctionCoefficient adapt_lim_gf0_coeff(adapt_lim_fun);
adapt_lim_gf0.ProjectCoefficient(adapt_lim_gf0_coeff);
if (adapt_eval == 0) { adapt_lim_eval = new AdvectorCG(al); }
else if (adapt_eval == 1)
{
#ifdef MFEM_USE_GSLIB
adapt_lim_eval = new InterpolatorFP;
#else
MFEM_ABORT("MFEM is not built with GSLIB support!");
#endif
}
else { MFEM_ABORT("Bad interpolation option."); }
tmop_integ->EnableAdaptiveLimiting(adapt_lim_gf0, adapt_lim_coeff,
*adapt_lim_eval);
if (visualization)
{
socketstream vis1;
common::VisualizeField(vis1, "localhost", 19916, adapt_lim_gf0, "Zeta 0",
300, 600, 300, 300);
}
}
// Has to be after the enabling of the limiting / alignment, as it computes
// normalization factors for these terms as well.
if (normalization) { tmop_integ->ParEnableNormalization(x0); }
// 13. Setup the final NonlinearForm (which defines the integral of interest,
// its first and second derivatives). Here we can use a combination of
// metrics, i.e., optimize the sum of two integrals, where both are
// scaled by used-defined space-dependent weights. Note that there are
// no command-line options for the weights and the type of the second
// metric; one should update those in the code.
ParNonlinearForm a(pfespace);
if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
ConstantCoefficient *metric_coeff1 = NULL;
TMOP_QualityMetric *metric2 = NULL;
TargetConstructor *target_c2 = NULL;
FunctionCoefficient metric_coeff2(weight_fun);
// Explicit combination of metrics.
if (combomet > 0)
{
// First metric.
metric_coeff1 = new ConstantCoefficient(1.0);
tmop_integ->SetCoefficient(*metric_coeff1);
// Second metric.
if (dim == 2) { metric2 = new TMOP_Metric_077; }
else { metric2 = new TMOP_Metric_315; }
TMOP_Integrator *tmop_integ2 = NULL;
if (combomet == 1)
{
target_c2 = new TargetConstructor(
TargetConstructor::IDEAL_SHAPE_EQUAL_SIZE, MPI_COMM_WORLD);
target_c2->SetVolumeScale(0.01);
target_c2->SetNodes(x0);
tmop_integ2 = new TMOP_Integrator(metric2, target_c2, h_metric);
tmop_integ2->SetCoefficient(metric_coeff2);
}
else { tmop_integ2 = new TMOP_Integrator(metric2, target_c, h_metric); }
tmop_integ2->IntegrateOverTarget(integ_over_targ);
tmop_integ2->SetIntegrationRules(*irules, quad_order);
if (fdscheme) { tmop_integ2->EnableFiniteDifferences(x); }
tmop_integ2->SetExactActionFlag(exactaction);
TMOPComboIntegrator *combo = new TMOPComboIntegrator;
combo->AddTMOPIntegrator(tmop_integ);
combo->AddTMOPIntegrator(tmop_integ2);
if (normalization) { combo->ParEnableNormalization(x0); }
if (lim_const != 0.0) { combo->EnableLimiting(x0, dist, lim_coeff); }
a.AddDomainIntegrator(combo);
}
else
{
a.AddDomainIntegrator(tmop_integ);
}
if (pa) { a.Setup(); }
// Compute the minimum det(J) of the starting mesh.
min_detJ = infinity();
const int NE = pmesh->GetNE();
for (int i = 0; i < NE; i++)
{
const IntegrationRule &ir =
irules->Get(pfespace->GetFE(i)->GetGeomType(), quad_order);
ElementTransformation *transf = pmesh->GetElementTransformation(i);
for (int j = 0; j < ir.GetNPoints(); j++)
{
transf->SetIntPoint(&ir.IntPoint(j));
min_detJ = min(min_detJ, transf->Jacobian().Det());
}
}
real_t minJ0;
MPI_Allreduce(&min_detJ, &minJ0, 1, MPITypeMap<real_t>::mpi_type,
MPI_MIN, MPI_COMM_WORLD);
min_detJ = minJ0;
if (myid == 0)
{ cout << "Minimum det(J) of the original mesh is " << min_detJ << endl; }
if (min_detJ < 0.0 && barrier_type == 0
&& metric_id != 22 && metric_id != 211 && metric_id != 252
&& metric_id != 311 && metric_id != 313 && metric_id != 352)
{
MFEM_ABORT("The input mesh is inverted! Try an untangling metric.");
}
if (min_detJ < 0.0)
{
MFEM_VERIFY(target_t == TargetConstructor::IDEAL_SHAPE_UNIT_SIZE,
"Untangling is supported only for ideal targets.");
const DenseMatrix &Wideal =
Geometries.GetGeomToPerfGeomJac(pfespace->GetFE(0)->GetGeomType());
min_detJ /= Wideal.Det();
real_t h0min = h0.Min(), h0min_all;
MPI_Allreduce(&h0min, &h0min_all, 1, MPITypeMap<real_t>::mpi_type,
MPI_MIN, MPI_COMM_WORLD);
// Slightly below minJ0 to avoid div by 0.
min_detJ -= 0.01 * h0min_all;