1263 lines
51 KiB
C++
1263 lines
51 KiB
C++
// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
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// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
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// LICENSE and NOTICE for details. LLNL-CODE-806117.
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//
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// This file is part of the MFEM library. For more information and source code
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// availability visit https://mfem.org.
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//
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// MFEM is free software; you can redistribute it and/or modify it under the
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// terms of the BSD-3 license. We welcome feedback and contributions, see file
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// CONTRIBUTING.md for details.
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//
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// --------------------------------------------------
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// Mesh Optimizer Miniapp: Optimize high-order meshes
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// --------------------------------------------------
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//
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// This miniapp performs mesh optimization using the Target-Matrix Optimization
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// Paradigm (TMOP) by P.Knupp et al., and a global variational minimization
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// approach. It minimizes the quantity sum_T int_T mu(J(x)), where T are the
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// target (ideal) elements, J is the Jacobian of the transformation from the
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// target to the physical element, and mu is the mesh quality metric. This
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// metric can measure shape, size or alignment of the region around each
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// quadrature point. The combination of targets & quality metrics is used to
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// optimize the physical node positions, i.e., they must be as close as possible
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// to the shape / size / alignment of their targets. This code also demonstrates
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// a possible use of nonlinear operators (the class TMOP_QualityMetric, defining
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// mu(J), and the class TMOP_Integrator, defining int mu(J)), as well as their
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// coupling to Newton methods for solving minimization problems. Note that the
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// utilized Newton methods are oriented towards avoiding invalid meshes with
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// negative Jacobian determinants. Each Newton step requires the inversion of a
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// Jacobian matrix, which is done through an inner linear solver.
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//
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// Compile with: make mesh-optimizer
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//
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// Sample runs:
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// Adapted analytic shape:
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// mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 2 -tid 4 -ni 200 -bnd -qt 1 -qo 8
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// Adapted analytic size+orientation:
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// mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 14 -tid 4 -ni 100 -bnd -qt 1 -qo 8
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// Adapted analytic shape+orientation (AD):
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// mesh-optimizer -m square01.mesh -o 3 -rs 2 -mid 85 -tid 4 -ni 100 -bnd -qt 1 -qo 8 -rtol 1e-6
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//
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// Adapted analytic shape and/or size with hr-adaptivity:
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// mesh-optimizer -m square01.mesh -o 2 -tid 9 -ni 50 -li 20 -hmid 55 -mid 7 -hr
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// mesh-optimizer -m square01.mesh -o 2 -tid 10 -ni 50 -li 20 -hmid 55 -mid 7 -hr
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// mesh-optimizer -m square01.mesh -o 2 -tid 11 -ni 50 -li 20 -hmid 58 -mid 7 -hr
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//
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// Adapted discrete size:
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// mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor
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// (requires GSLIB):
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// * mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 80 -tid 5 -ni 50 -qo 4 -nor -mno 1 -ae 1
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// Adapted discrete size NC mesh;
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// mesh-optimizer -m amr-quad-q2.mesh -o 2 -rs 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor
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// Adapted discrete size 3D with PA:
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// mesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 321 -tid 5 -ls 3 -nor -pa -rtol 1e-8
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// Adapted discrete size 3D with PA on device (requires CUDA):
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// * mesh-optimizer -m cube.mesh -o 3 -rs 3 -mid 321 -tid 5 -ls 3 -nor -lc 0.1 -pa -d cuda
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// Adapted discrete size; explicit combo of metrics; mixed tri/quad mesh:
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// mesh-optimizer -m ../../data/square-mixed.mesh -o 2 -rs 2 -mid 2 -tid 5 -ni 200 -bnd -qo 6 -cmb 2 -nor
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// Adapted discrete size+aspect_ratio:
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// mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 7 -tid 6 -ni 100
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// Adapted discrete size+orientation (AD):
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// mesh-optimizer -m square01.mesh -o 2 -rs 2 -mid 36 -tid 8 -qo 4 -nor -rtol 1e-6
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// Adapted discrete aspect ratio (3D):
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// mesh-optimizer -m cube.mesh -o 2 -rs 2 -mid 302 -tid 7 -ni 20 -bnd -qt 1 -qo 8
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//
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// Periodic 2D + adapted discrete size:
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// mesh-optimizer -m ../../data/periodic-square.mesh -o 2 -rs 4 -mid 94 -tid 5 -qo 4 -nor
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// mesh-optimizer -m periodic-tri.mesh -o 2 -rs 4 -mid 94 -tid 5 -qo 4 -nor
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// Periodic 3D + adapted discrete size + PA:
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// mesh-optimizer -m periodic-cube.mesh -o 2 -rs 2 -mid 338 -tid 5 -nor -rtol 1e-6 -qo 4 -pa
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// Periodic 2D NC mesh + adapted discrete size + PA:
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// (the mesh is in the mfem/data GitHub repository)
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// * mesh-optimizer -m ../../../data/periodic/per-amr-square.mesh -o 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor -pa
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//
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// Adaptive limiting:
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// mesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 0.5
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// Adaptive limiting through the L-BFGS solver:
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// mesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 400 -qo 5 -nor -vl 1 -alc 0.5 -st 1 -rtol 1e-8
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//
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// Blade shape:
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// mesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8
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// Blade shape (AD):
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// mesh-optimizer -m blade.mesh -o 4 -mid 11 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8
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// (requires CUDA):
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// * mesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8 -d cuda
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// Blade limited shape:
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// mesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -bnd -qt 1 -qo 8 -lc 5000
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// ICF shape and equal size:
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// mesh-optimizer -o 3 -mid 80 -bec -tid 2 -ni 25 -ls 3 -art 2 -qo 5
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// ICF shape and initial size:
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// mesh-optimizer -o 3 -mid 9 -tid 3 -ni 30 -ls 3 -bnd -qt 1 -qo 8
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// ICF shape:
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// mesh-optimizer -o 3 -mid 1 -tid 1 -ni 100 -bnd -qt 1 -qo 8
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// ICF limited shape:
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// mesh-optimizer -o 3 -mid 1 -tid 1 -ni 100 -bnd -qt 1 -qo 8 -lc 10
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// ICF combo shape + size (rings, slow convergence):
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// mesh-optimizer -o 3 -mid 1 -tid 1 -ni 1000 -bnd -qt 1 -qo 8 -cmb 1
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// Mixed tet / cube / hex mesh with limiting:
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// mesh-optimizer -m ../../data/fichera-mixed-p2.mesh -o 4 -rs 1 -mid 301 -tid 1 -fix-bnd -qo 6 -nor -lc 0.25
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// 3D pinched sphere shape (the mesh is in the mfem/data GitHub repository):
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// * mesh-optimizer -m ../../../mfem_data/ball-pert.mesh -o 4 -mid 303 -tid 1 -ni 20 -li 500 -fix-bnd
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// 2D non-conforming shape and equal size:
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// mesh-optimizer -m ./amr-quad-q2.mesh -o 2 -rs 1 -mid 9 -tid 2 -ni 200 -bnd -qt 1 -qo 8
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//
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// 2D untangling:
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// mesh-optimizer -m jagged.mesh -o 2 -mid 22 -tid 1 -ni 50 -li 50 -qo 4 -fd -vl 1
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// 2D untangling with shifted barrier metric:
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// mesh-optimizer -m jagged.mesh -o 2 -mid 4 -tid 1 -ni 50 -qo 4 -vl 1 -btype 1
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// 3D untangling (the mesh is in the mfem/data GitHub repository):
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// * mesh-optimizer -m ../../../mfem_data/cube-holes-inv.mesh -o 3 -mid 313 -tid 1 -rtol 1e-5 -li 50 -qo 4 -fd -vl 1
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#include "mfem.hpp"
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#include "../common/mfem-common.hpp"
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#include <fstream>
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#include <iostream>
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#include "mesh-optimizer.hpp"
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using namespace mfem;
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using namespace std;
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int main(int argc, char *argv[])
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{
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// Set the method's default parameters.
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const char *mesh_file = "icf.mesh";
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int mesh_poly_deg = 1;
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int rs_levels = 0;
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real_t jitter = 0.0;
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int metric_id = 1;
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int target_id = 1;
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real_t lim_const = 0.0;
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real_t adapt_lim_const = 0.0;
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int quad_type = 1;
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int quad_order = 8;
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int solver_type = 0;
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int solver_iter = 20;
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#ifdef MFEM_USE_SINGLE
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real_t solver_rtol = 1e-4;
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#else
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real_t solver_rtol = 1e-10;
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#endif
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int solver_art_type = 0;
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int lin_solver = 2;
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int max_lin_iter = 100;
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bool move_bnd = true;
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int combomet = 0;
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bool bal_expl_combo = false;
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bool hradaptivity = false;
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int h_metric_id = -1;
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bool normalization = false;
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bool visualization = true;
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int verbosity_level = 0;
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bool fdscheme = false;
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int adapt_eval = 0;
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bool exactaction = false;
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bool integ_over_targ = true;
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const char *devopt = "cpu";
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bool pa = false;
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int n_hr_iter = 5;
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int n_h_iter = 1;
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int mesh_node_order = 0;
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int barrier_type = 0;
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int worst_case_type = 0;
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// Parse command-line options.
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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh",
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"Mesh file to use.");
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args.AddOption(&mesh_poly_deg, "-o", "--order",
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"Polynomial degree of mesh finite element space.");
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args.AddOption(&rs_levels, "-rs", "--refine-serial",
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"Number of times to refine the mesh uniformly in serial.");
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args.AddOption(&jitter, "-ji", "--jitter",
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"Random perturbation scaling factor.");
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args.AddOption(&metric_id, "-mid", "--metric-id",
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"Mesh optimization metric:\n\t"
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"T-metrics\n\t"
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"1 : |T|^2 -- 2D no type\n\t"
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"2 : 0.5|T|^2/tau-1 -- 2D shape (condition number)\n\t"
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"7 : |T-T^-t|^2 -- 2D shape+size\n\t"
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"9 : tau*|T-T^-t|^2 -- 2D shape+size\n\t"
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"14 : |T-I|^2 -- 2D shape+size+orientation\n\t"
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"22 : 0.5(|T|^2-2*tau)/(tau-tau_0) -- 2D untangling\n\t"
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"50 : 0.5|T^tT|^2/tau^2-1 -- 2D shape\n\t"
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"55 : (tau-1)^2 -- 2D size\n\t"
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"56 : 0.5(sqrt(tau)-1/sqrt(tau))^2 -- 2D size\n\t"
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"58 : |T^tT|^2/(tau^2)-2*|T|^2/tau+2 -- 2D shape\n\t"
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"77 : 0.5(tau-1/tau)^2 -- 2D size\n\t"
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"80 : (1-gamma)mu_2 + gamma mu_77 -- 2D shape+size\n\t"
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"85 : |T-|T|/sqrt(2)I|^2 -- 2D shape+orientation\n\t"
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"90 : balanced combo mu_50 & mu_77 -- 2D shape+size\n\t"
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"94 : balanced combo mu_2 & mu_56 -- 2D shape+size\n\t"
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"98 : (1/tau)|T-I|^2 -- 2D shape+size+orientation\n\t"
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// "211: (tau-1)^2-tau+sqrt(tau^2+eps) -- 2D untangling\n\t"
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// "252: 0.5(tau-1)^2/(tau-tau_0) -- 2D untangling\n\t"
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"301: (|T||T^-1|)/3-1 -- 3D shape\n\t"
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"302: (|T|^2|T^-1|^2)/9-1 -- 3D shape\n\t"
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"303: (|T|^2)/3/tau^(2/3)-1 -- 3D shape\n\t"
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"304: (|T|^3)/3^{3/2}/tau-1 -- 3D shape\n\t"
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//"311: (tau-1)^2-tau+sqrt(tau^2+eps)-- 3D untangling\n\t"
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"313: (|T|^2)(tau-tau0)^(-2/3)/3 -- 3D untangling\n\t"
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"315: (tau-1)^2 -- 3D no type\n\t"
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"316: 0.5(sqrt(tau)-1/sqrt(tau))^2 -- 3D no type\n\t"
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"321: |T-T^-t|^2 -- 3D shape+size\n\t"
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"322: |T-adjT^-t|^2 -- 3D shape+size\n\t"
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"323: |J|^3-3sqrt(3)ln(det(J))-3sqrt(3) -- 3D shape+size\n\t"
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"328: balanced combo mu_301 & mu_316 -- 3D shape+size\n\t"
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"332: (1-gamma) mu_302 + gamma mu_315 -- 3D shape+size\n\t"
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"333: (1-gamma) mu_302 + gamma mu_316 -- 3D shape+size\n\t"
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"334: (1-gamma) mu_303 + gamma mu_316 -- 3D shape+size\n\t"
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"328: balanced combo mu_302 & mu_318 -- 3D shape+size\n\t"
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"347: (1-gamma) mu_304 + gamma mu_316 -- 3D shape+size\n\t"
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// "352: 0.5(tau-1)^2/(tau-tau_0) -- 3D untangling\n\t"
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"360: (|T|^3)/3^{3/2}-tau -- 3D shape\n\t"
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"A-metrics\n\t"
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"11 : (1/4*alpha)|A-(adjA)^T(W^TW)/omega|^2 -- 2D shape\n\t"
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"36 : (1/alpha)|A-W|^2 -- 2D shape+size+orientation\n\t"
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"49 : (1-gamma) mu_2 + gamma nu_50 -- 2D shape+skew\n\t"
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"51 : see fem/tmop.hpp -- 2D size+skew\n\t"
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"107: (1/2*alpha)|A-|A|/|W|W|^2 -- 2D shape+orientation\n\t"
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"126: (1-gamma)nu_11 + gamma*nu_14a -- 2D shape+size\n\t"
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);
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args.AddOption(&target_id, "-tid", "--target-id",
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"Target (ideal element) type:\n\t"
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"1: Ideal shape, unit size\n\t"
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"2: Ideal shape, equal size\n\t"
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"3: Ideal shape, initial size\n\t"
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"4: Given full analytic Jacobian (in physical space)\n\t"
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"5: Ideal shape, given size (in physical space)");
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args.AddOption(&lim_const, "-lc", "--limit-const", "Limiting constant.");
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args.AddOption(&adapt_lim_const, "-alc", "--adapt-limit-const",
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"Adaptive limiting coefficient constant.");
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args.AddOption(&quad_type, "-qt", "--quad-type",
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"Quadrature rule type:\n\t"
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"1: Gauss-Lobatto\n\t"
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"2: Gauss-Legendre\n\t"
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"3: Closed uniform points");
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args.AddOption(&quad_order, "-qo", "--quad_order",
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"Order of the quadrature rule.");
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args.AddOption(&solver_type, "-st", "--solver-type",
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" Type of solver: (default) 0: Newton, 1: LBFGS");
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args.AddOption(&solver_iter, "-ni", "--newton-iters",
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"Maximum number of Newton iterations.");
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args.AddOption(&solver_rtol, "-rtol", "--newton-rel-tolerance",
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"Relative tolerance for the Newton solver.");
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args.AddOption(&solver_art_type, "-art", "--adaptive-rel-tol",
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"Type of adaptive relative linear solver tolerance:\n\t"
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"0: None (default)\n\t"
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"1: Eisenstat-Walker type 1\n\t"
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"2: Eisenstat-Walker type 2");
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args.AddOption(&lin_solver, "-ls", "--lin-solver",
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"Linear solver:\n\t"
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"0: l1-Jacobi\n\t"
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"1: CG\n\t"
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"2: MINRES\n\t"
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"3: MINRES + Jacobi preconditioner\n\t"
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"4: MINRES + l1-Jacobi preconditioner");
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args.AddOption(&max_lin_iter, "-li", "--lin-iter",
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"Maximum number of iterations in the linear solve.");
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args.AddOption(&move_bnd, "-bnd", "--move-boundary", "-fix-bnd",
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"--fix-boundary",
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"Enable motion along horizontal and vertical boundaries.");
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args.AddOption(&combomet, "-cmb", "--combo-type",
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"Combination of metrics options:\n\t"
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"0: Use single metric\n\t"
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"1: Shape + space-dependent size given analytically\n\t"
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"2: Shape + adapted size given discretely; shared target");
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args.AddOption(&bal_expl_combo, "-bec", "--balance-explicit-combo",
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"-no-bec", "--balance-explicit-combo",
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"Automatic balancing of explicit combo metrics.");
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args.AddOption(&hradaptivity, "-hr", "--hr-adaptivity", "-no-hr",
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"--no-hr-adaptivity",
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"Enable hr-adaptivity.");
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args.AddOption(&h_metric_id, "-hmid", "--h-metric",
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"Same options as metric_id. Used to determine refinement"
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" type for each element if h-adaptivity is enabled.");
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args.AddOption(&normalization, "-nor", "--normalization", "-no-nor",
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"--no-normalization",
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"Make all terms in the optimization functional unitless.");
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args.AddOption(&fdscheme, "-fd", "--fd_approximation",
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"-no-fd", "--no-fd-approx",
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"Enable finite difference based derivative computations.");
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args.AddOption(&exactaction, "-ex", "--exact_action",
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"-no-ex", "--no-exact-action",
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"Enable exact action of TMOP_Integrator.");
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args.AddOption(&integ_over_targ, "-it", "--integrate-target",
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"-ir", "--integrate-reference",
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"Integrate over target (-it) or reference (-ir) element.");
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args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
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"--no-visualization",
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"Enable or disable GLVis visualization.");
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args.AddOption(&verbosity_level, "-vl", "--verbosity-level",
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"Verbosity level for the involved iterative solvers:\n\t"
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"0: no output\n\t"
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"1: Newton iterations\n\t"
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"2: Newton iterations + linear solver summaries\n\t"
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"3: newton iterations + linear solver iterations");
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args.AddOption(&adapt_eval, "-ae", "--adaptivity-evaluator",
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"0 - Advection based (DEFAULT), 1 - GSLIB.");
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args.AddOption(&devopt, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
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"--no-partial-assembly", "Enable Partial Assembly.");
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args.AddOption(&n_hr_iter, "-nhr", "--n_hr_iter",
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"Number of hr-adaptivity iterations.");
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args.AddOption(&n_h_iter, "-nh", "--n_h_iter",
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"Number of h-adaptivity iterations per r-adaptivity"
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"iteration.");
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args.AddOption(&mesh_node_order, "-mno", "--mesh_node_ordering",
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"Ordering of mesh nodes."
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"0 (default): byNodes, 1: byVDIM");
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args.AddOption(&barrier_type, "-btype", "--barrier-type",
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"0 - None,"
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"1 - Shifted Barrier,"
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"2 - Pseudo Barrier.");
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args.AddOption(&worst_case_type, "-wctype", "--worst-case-type",
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"0 - None,"
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"1 - Beta,"
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"2 - PMean.");
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args.Parse();
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if (!args.Good())
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{
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args.PrintUsage(cout);
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return 1;
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}
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args.PrintOptions(cout);
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if (h_metric_id < 0) { h_metric_id = metric_id; }
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if (hradaptivity)
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{
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MFEM_VERIFY(strcmp(devopt,"cpu")==0, "HR-adaptivity is currently only"
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" supported on cpus.");
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}
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Device device(devopt);
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device.Print();
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// Initialize and refine the starting mesh.
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Mesh *mesh = new Mesh(mesh_file, 1, 1, false);
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for (int lev = 0; lev < rs_levels; lev++) { mesh->UniformRefinement(); }
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const int dim = mesh->Dimension();
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if (hradaptivity) { mesh->EnsureNCMesh(); }
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auto s = mesh->GetNodalFESpace();
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const bool periodic = (s && s->IsDGSpace()) ? true : false;
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// Define a FE space on the mesh, based on the input order. This space will
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// also be used to represent the nodal positions of the mesh. We use a vector
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// FE space which is a tensor product of a scalar FE space. The number of
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// components in the vector finite element space matches the dimension.
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FiniteElementCollection *fec;
|
|
if (mesh_poly_deg <= 0) { mesh_poly_deg = 2; }
|
|
if (periodic)
|
|
{
|
|
fec = new L2_FECollection(mesh_poly_deg, dim, BasisType::GaussLobatto);
|
|
}
|
|
else { fec = new H1_FECollection(mesh_poly_deg, dim); }
|
|
auto fespace = new FiniteElementSpace(mesh, fec, dim, mesh_node_order);
|
|
|
|
// Make the starting mesh curved. This means we define the mesh elements
|
|
// through a FE-based transformation of the reference element.
|
|
mesh->SetNodalFESpace(fespace);
|
|
|
|
// Get the mesh nodes (vertices and other DOFs in the FE space) as a FE grid
|
|
// function in pfespace. Note that changing x automatically changes the
|
|
// shapes of the mesh elements.
|
|
GridFunction x(fespace);
|
|
mesh->SetNodalGridFunction(&x);
|
|
|
|
// We create an H1 space for the mesh displacement. The displacement is
|
|
// always in a continuous space, even if the mesh is periodic.
|
|
// The nonlinear problem will be solved for the continuous displacement.
|
|
H1_FECollection fec_h1(mesh_poly_deg, dim);
|
|
FiniteElementSpace fes_h1(mesh, &fec_h1, dim, mesh_node_order);
|
|
GridFunction dx(&fes_h1); dx = 0.0;
|
|
|
|
// Define a vector representing the minimal local mesh size in the mesh
|
|
// nodes. We index the nodes by the scalar version of the DOFs in pfespace.
|
|
// In addition, compute average mesh size and total volume.
|
|
Vector h0(fes_h1.GetNDofs());
|
|
h0 = infinity();
|
|
real_t mesh_volume = 0.0;
|
|
Array<int> dofs;
|
|
for (int i = 0; i < mesh->GetNE(); i++)
|
|
{
|
|
// Get the local scalar element degrees of freedom in dofs.
|
|
fes_h1.GetElementDofs(i, dofs);
|
|
// Adjust the value of h0 in dofs based on the local mesh size.
|
|
const real_t hi = mesh->GetElementSize(i);
|
|
for (int j = 0; j < dofs.Size(); j++)
|
|
{
|
|
h0(dofs[j]) = min(h0(dofs[j]), hi);
|
|
}
|
|
mesh_volume += mesh->GetElementVolume(i);
|
|
}
|
|
const real_t small_phys_size = pow(mesh_volume, 1.0 / dim) / 100.0;
|
|
|
|
// Add a random perturbation to the nodes in the interior of the domain.
|
|
// We define a random grid function of pfespace 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.
|
|
if (jitter > 0)
|
|
{
|
|
GridFunction rdm(&fes_h1);
|
|
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 < fes_h1.GetNDofs(); i++)
|
|
{
|
|
for (int d = 0; d < dim; d++)
|
|
{
|
|
rdm(fes_h1.DofToVDof(i,d)) *= h0(i);
|
|
}
|
|
}
|
|
// Set the boundary values to zero. Note that periodic periodic boundaries
|
|
// will be free to move.
|
|
Array<int> vdofs;
|
|
for (int i = 0; i < fes_h1.GetNBE(); i++)
|
|
{
|
|
fespace->GetBdrElementVDofs(i, vdofs);
|
|
for (int j = 0; j < vdofs.Size(); j++) { rdm(vdofs[j]) = 0.0; }
|
|
}
|
|
|
|
if (periodic)
|
|
{
|
|
// For H1 the perturbation is controlled by the true nodes.
|
|
rdm.SetFromTrueVector();
|
|
GridFunction rdm_l2(fespace);
|
|
rdm_l2.ProjectGridFunction(rdm);
|
|
x -= rdm_l2;
|
|
}
|
|
else
|
|
{
|
|
x -= rdm;
|
|
// For H1 the perturbation is controlled by the true nodes.
|
|
x.SetFromTrueVector();
|
|
}
|
|
|
|
if (visualization)
|
|
{
|
|
socketstream vis1;
|
|
common::VisualizeMesh(vis1, "localhost", 19916, *mesh, "Perturbed",
|
|
300, 600, 300, 300);
|
|
}
|
|
}
|
|
|
|
// Save the starting (prior to the optimization) mesh to a file. This
|
|
// output can be viewed later using GLVis: "glvis -m perturbed.mesh".
|
|
{
|
|
ofstream mesh_ofs("perturbed.mesh");
|
|
mesh->Print(mesh_ofs);
|
|
}
|
|
|
|
// Store the starting (prior to the optimization) positions.
|
|
GridFunction x0(x);
|
|
|
|
// 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 49: metric = new TMOP_AMetric_049(0.9); break;
|
|
case 51: metric = new TMOP_AMetric_051; break;
|
|
case 107: metric = new TMOP_AMetric_107; break;
|
|
case 126: metric = new TMOP_AMetric_126(0.9); break;
|
|
default:
|
|
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;
|
|
int ind_fec_order = (target_id >= 5 && target_id <= 8 && !fdscheme) ?
|
|
1 : mesh_poly_deg;
|
|
H1_FECollection ind_fec(ind_fec_order, dim);
|
|
FiniteElementSpace ind_fes(mesh, &ind_fec);
|
|
FiniteElementSpace ind_fesv(mesh, &ind_fec, dim);
|
|
GridFunction size(&ind_fes), aspr(&ind_fes), ori(&ind_fes);
|
|
GridFunction 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: // Analytic
|
|
{
|
|
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->SetSerialDiscreteTargetSize(size);
|
|
tc->SetMinSizeForTargets(size.Min());
|
|
target_c = tc;
|
|
break;
|
|
}
|
|
case 6: // Discrete size + aspect ratio - 2D
|
|
{
|
|
GridFunction 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();
|
|
|
|
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);
|
|
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 = mesh->GetNE();
|
|
real_t volume = 0.0, volume_ind = 0.0;
|
|
|
|
for (int i = 0; i < NE; i++)
|
|
{
|
|
ElementTransformation *Tr = mesh->GetElementTransformation(i);
|
|
const IntegrationRule &ir =
|
|
IntRules.Get(mesh->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();
|
|
}
|
|
}
|
|
|
|
const real_t avg_zone_size = volume / NE;
|
|
|
|
const real_t small_avg_ratio = (volume_ind + (volume - volume_ind) /
|
|
size_ratio) /
|
|
volume;
|
|
|
|
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->SetSerialDiscreteTargetSize(size);
|
|
tc->SetMinSizeForTargets(size.Min());
|
|
tc->SetSerialDiscreteTargetAspectRatio(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->SetSerialDiscreteTargetAspectRatio(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->SetSerialDiscreteTargetSize(size);
|
|
tc->SetMinSizeForTargets(size.Min());
|
|
|
|
FunctionCoefficient ori_coeff(discrete_ori_2d);
|
|
ori.ProjectCoefficient(ori_coeff);
|
|
tc->SetSerialDiscreteTargetOrientation(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: cout << "Unknown target_id: " << target_id << endl; return 3;
|
|
}
|
|
if (target_c == NULL)
|
|
{
|
|
target_c = new TargetConstructor(target_t);
|
|
}
|
|
target_c->SetNodes(x0);
|
|
|
|
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, *fespace);
|
|
}
|
|
|
|
// 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: cout << "Unknown quad_type: " << quad_type << endl; return 3;
|
|
}
|
|
tmop_integ->SetIntegrationRules(*irules, quad_order);
|
|
if (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 (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;
|
|
}
|
|
|
|
// Automatically balanced gamma in composite metrics.
|
|
auto metric_combo = dynamic_cast<TMOP_Combo_QualityMetric *>(metric);
|
|
if (metric_combo && bal_expl_combo)
|
|
{
|
|
Vector bal_weights;
|
|
auto ir = irules->Get(mesh->GetTypicalElementGeometry(), quad_order);
|
|
metric_combo->ComputeBalancedWeights(x, *target_c, bal_weights, pa, &ir);
|
|
metric_combo->SetWeights(bal_weights);
|
|
}
|
|
|
|
// Limit the node movement.
|
|
// The limiting distances can be given by a general function of space.
|
|
FiniteElementSpace dist_fespace(mesh, &fec_h1); // scalar space
|
|
GridFunction dist(&dist_fespace);
|
|
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.
|
|
GridFunction 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);
|
|
}
|
|
}
|
|
|
|
//
|
|
// Setup the NonlinearForm which defines the integral of interest, its
|
|
// first and second derivatives.
|
|
//
|
|
// Note that the TMOP optimization always operates on H1 spaces. For periodic
|
|
// meshes, TMOP solves for a continuous periodic displacement.
|
|
NonlinearForm a(&fes_h1);
|
|
if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
|
|
// 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.
|
|
ConstantCoefficient *metric_coeff1 = NULL;
|
|
TMOP_QualityMetric *metric2 = NULL;
|
|
TargetConstructor *target_c2 = NULL;
|
|
FunctionCoefficient metric_coeff2(weight_fun);
|
|
TMOPComboIntegrator *combo = nullptr;
|
|
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);
|
|
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);
|
|
|
|
combo = new TMOPComboIntegrator;
|
|
combo->AddTMOPIntegrator(tmop_integ);
|
|
combo->AddTMOPIntegrator(tmop_integ2);
|
|
if (lim_const != 0.0) { combo->EnableLimiting(x0, dist, lim_coeff); }
|
|
|
|
a.AddDomainIntegrator(combo);
|
|
}
|
|
else { a.AddDomainIntegrator(tmop_integ); }
|
|
// The PA setup must be performed after all integrators have been added.
|
|
if (pa) { a.Setup(); }
|
|
|
|
// Has to be after the enabling of the limiting / alignment, as it computes
|
|
// normalization factors for these terms as well.
|
|
if (normalization)
|
|
{
|
|
tmop_integ->EnableNormalization(x0);
|
|
if (combomet) { combo->EnableNormalization(x0); }
|
|
}
|
|
|
|
// Compute the minimum det(J) of the starting mesh.
|
|
min_detJ = infinity();
|
|
const int NE = mesh->GetNE();
|
|
for (int i = 0; i < NE; i++)
|
|
{
|
|
const IntegrationRule &ir =
|
|
irules->Get(fespace->GetFE(i)->GetGeomType(), quad_order);
|
|
ElementTransformation *transf = mesh->GetElementTransformation(i);
|
|
for (int j = 0; j < ir.GetNPoints(); j++)
|
|
{
|
|
transf->SetIntPoint(&ir.IntPoint(j));
|
|
min_detJ = min(min_detJ, transf->Jacobian().Det());
|
|
}
|
|
}
|
|
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(mesh->GetTypicalElementGeometry());
|
|
min_detJ /= Wideal.Det();
|
|
|
|
// Slightly below minJ0 to avoid div by 0.
|
|
min_detJ -= 0.01 * h0.Min();
|
|
}
|
|
|
|
// For HR tests, the energy is normalized by the number of elements.
|
|
if (periodic) { tmop_integ->SetInitialMeshPos(&x0); }
|
|
const real_t init_energy = a.GetGridFunctionEnergy(periodic ? dx : x) /
|
|
(hradaptivity ? mesh->GetNE() : 1);
|
|
real_t init_metric_energy = init_energy;
|
|
if (lim_const > 0.0 || adapt_lim_const > 0.0)
|
|
{
|
|
lim_coeff.constant = 0.0;
|
|
adapt_lim_coeff.constant = 0.0;
|
|
init_metric_energy = a.GetGridFunctionEnergy(periodic ? dx : x) /
|
|
(hradaptivity ? mesh->GetNE() : 1);
|
|
lim_coeff.constant = lim_const;
|
|
adapt_lim_coeff.constant = adapt_lim_const;
|
|
}
|
|
|
|
// Visualize the starting mesh and metric values.
|
|
// Note that for combinations of metrics, this only shows the first metric.
|
|
if (visualization)
|
|
{
|
|
char title[] = "Initial metric values";
|
|
vis_tmop_metric_s(mesh_poly_deg, *metric, *target_c, *mesh, title, 0);
|
|
}
|
|
|
|
// Fix all boundary nodes, or fix only a given component depending on the
|
|
// boundary attributes of the given mesh.
|
|
// Attributes 1/2/3 correspond to fixed x/y/z components of the node.
|
|
// Attribute 4 corresponds to an entirely fixed node.
|
|
// All other attributes represent unconstrained boundary nodes.
|
|
if (move_bnd == false)
|
|
{
|
|
Array<int> ess_bdr(mesh->bdr_attributes.Max());
|
|
ess_bdr = 1;
|
|
a.SetEssentialBC(ess_bdr);
|
|
}
|
|
else
|
|
{
|
|
int n = 0;
|
|
for (int i = 0; i < mesh->GetNBE(); i++)
|
|
{
|
|
const int nd = fes_h1.GetBE(i)->GetDof();
|
|
const int attr = mesh->GetBdrElement(i)->GetAttribute();
|
|
MFEM_VERIFY(!(dim == 2 && attr == 3),
|
|
"Boundary attribute 3 must be used only for 3D meshes. "
|
|
"Adjust the attributes (1/2/3/4 for fixed x/y/z/all "
|
|
"components, rest for free nodes), or use -fix-bnd.");
|
|
if (attr == 1 || attr == 2 || attr == 3) { n += nd; }
|
|
if (attr == 4) { n += nd * dim; }
|
|
}
|
|
Array<int> vdofs, ess_vdofs(n);
|
|
n = 0;
|
|
for (int i = 0; i < mesh->GetNBE(); i++)
|
|
{
|
|
const int nd = fes_h1.GetBE(i)->GetDof();
|
|
const int attr = mesh->GetBdrElement(i)->GetAttribute();
|
|
fes_h1.GetBdrElementVDofs(i, vdofs);
|
|
if (attr == 1) // Fix x components.
|
|
{
|
|
for (int j = 0; j < nd; j++)
|
|
{ ess_vdofs[n++] = vdofs[j]; }
|
|
}
|
|
else if (attr == 2) // Fix y components.
|
|
{
|
|
for (int j = 0; j < nd; j++)
|
|
{ ess_vdofs[n++] = vdofs[j+nd]; }
|
|
}
|
|
else if (attr == 3) // Fix z components.
|
|
{
|
|
for (int j = 0; j < nd; j++)
|
|
{ ess_vdofs[n++] = vdofs[j+2*nd]; }
|
|
}
|
|
else if (attr == 4) // Fix all components.
|
|
{
|
|
for (int j = 0; j < vdofs.Size(); j++)
|
|
{ ess_vdofs[n++] = vdofs[j]; }
|
|
}
|
|
}
|
|
a.SetEssentialVDofs(ess_vdofs);
|
|
}
|
|
|
|
// As we use the inexact Newton method to solve the resulting nonlinear
|
|
// system, here we setup the linear solver for the system's Jacobian.
|
|
Solver *S = NULL, *S_prec = NULL;
|
|
#ifdef MFEM_USE_SINGLE
|
|
const real_t linsol_rtol = 1e-5;
|
|
#else
|
|
const real_t linsol_rtol = 1e-12;
|
|
#endif
|
|
// Level of output.
|
|
IterativeSolver::PrintLevel linsolver_print;
|
|
if (verbosity_level == 2)
|
|
{ linsolver_print.Errors().Warnings().FirstAndLast(); }
|
|
if (verbosity_level > 2)
|
|
{ linsolver_print.Errors().Warnings().Iterations(); }
|
|
if (lin_solver == 0)
|
|
{
|
|
S = new DSmoother(1, 1.0, max_lin_iter);
|
|
}
|
|
else if (lin_solver == 1)
|
|
{
|
|
CGSolver *cg = new CGSolver;
|
|
cg->SetMaxIter(max_lin_iter);
|
|
cg->SetRelTol(linsol_rtol);
|
|
cg->SetAbsTol(0.0);
|
|
cg->SetPrintLevel(linsolver_print);
|
|
S = cg;
|
|
}
|
|
else
|
|
{
|
|
MINRESSolver *minres = new MINRESSolver;
|
|
minres->SetMaxIter(max_lin_iter);
|
|
minres->SetRelTol(linsol_rtol);
|
|
minres->SetAbsTol(0.0);
|
|
minres->SetPrintLevel(linsolver_print);
|
|
if (lin_solver == 3 || lin_solver == 4)
|
|
{
|
|
if (pa)
|
|
{
|
|
MFEM_VERIFY(lin_solver != 4, "PA l1-Jacobi is not implemented");
|
|
auto js = new OperatorJacobiSmoother;
|
|
js->SetPositiveDiagonal(true);
|
|
S_prec = js;
|
|
}
|
|
else
|
|
{
|
|
auto ds = new DSmoother((lin_solver == 3) ? 0 : 1, 1.0, 1);
|
|
ds->SetPositiveDiagonal(true);
|
|
S_prec = ds;
|
|
}
|
|
minres->SetPreconditioner(*S_prec);
|
|
}
|
|
S = minres;
|
|
}
|
|
|
|
//
|
|
// Perform the nonlinear optimization.
|
|
//
|
|
const IntegrationRule &ir =
|
|
irules->Get(mesh->GetTypicalElementGeometry(), quad_order);
|
|
TMOPNewtonSolver solver(ir, solver_type);
|
|
// Provide all integration rules in case of a mixed mesh.
|
|
solver.SetIntegrationRules(*irules, quad_order);
|
|
// Specify linear solver when we use a Newton-based solver.
|
|
if (solver_type == 0) { solver.SetPreconditioner(*S); }
|
|
// For untangling, the solver will update the min det(T) values.
|
|
solver.SetMinDetPtr(&min_detJ);
|
|
solver.SetMaxIter(solver_iter);
|
|
solver.SetRelTol(solver_rtol);
|
|
solver.SetAbsTol(0.0);
|
|
if (solver_art_type > 0)
|
|
{
|
|
solver.SetAdaptiveLinRtol(solver_art_type, 0.5, 0.9);
|
|
}
|
|
// Level of output.
|
|
IterativeSolver::PrintLevel newton_print;
|
|
if (verbosity_level > 0) { newton_print.Errors().Warnings().Iterations(); }
|
|
else { newton_print.Errors().Warnings(); }
|
|
solver.SetPrintLevel(newton_print);
|
|
// hr-adaptivity solver.
|
|
// If hr-adaptivity is disabled, r-adaptivity is done once using the
|
|
// TMOPNewtonSolver.
|
|
// Otherwise, "hr_iter" iterations of r-adaptivity are done followed by
|
|
// "h_per_r_iter" iterations of h-adaptivity after each r-adaptivity.
|
|
// The solver terminates if an h-adaptivity iteration does not modify
|
|
// any element in the mesh.
|
|
TMOPHRSolver hr_solver(*mesh, a, solver,
|
|
x, move_bnd, hradaptivity,
|
|
mesh_poly_deg, h_metric_id,
|
|
n_hr_iter, n_h_iter);
|
|
hr_solver.AddGridFunctionForUpdate(&x0);
|
|
hr_solver.AddFESpaceForUpdate(&fes_h1);
|
|
if (adapt_lim_const > 0.)
|
|
{
|
|
hr_solver.AddGridFunctionForUpdate(&adapt_lim_gf0);
|
|
hr_solver.AddFESpaceForUpdate(&ind_fes);
|
|
}
|
|
hr_solver.Mult();
|
|
|
|
// Save the optimized mesh to a file. This output can be viewed later
|
|
// using GLVis: "glvis -m optimized.mesh".
|
|
{
|
|
ofstream mesh_ofs("optimized.mesh");
|
|
mesh_ofs.precision(14);
|
|
mesh->Print(mesh_ofs);
|
|
}
|
|
|
|
// Report the final energy of the functional.
|
|
if (periodic)
|
|
{
|
|
GridFunction dx_L2(x); dx_L2 -= x0;
|
|
// Assumes Gauss-Lobatto and continuity in x and x_0 across faces.
|
|
dx.ProjectGridFunction(dx_L2);
|
|
}
|
|
if (periodic) { tmop_integ->SetInitialMeshPos(&x0); }
|
|
const real_t fin_energy = a.GetGridFunctionEnergy(periodic ? dx : x) /
|
|
(hradaptivity ? mesh->GetNE() : 1);
|
|
real_t fin_metric_energy = fin_energy;
|
|
if (lim_const > 0.0 || adapt_lim_const > 0.0)
|
|
{
|
|
lim_coeff.constant = 0.0;
|
|
adapt_lim_coeff.constant = 0.0;
|
|
fin_metric_energy = a.GetGridFunctionEnergy(periodic ? dx : x) /
|
|
(hradaptivity ? mesh->GetNE() : 1);
|
|
lim_coeff.constant = lim_const;
|
|
adapt_lim_coeff.constant = adapt_lim_const;
|
|
}
|
|
std::cout << std::scientific << std::setprecision(4);
|
|
cout << "Initial strain energy: " << init_energy
|
|
<< " = metrics: " << init_metric_energy
|
|
<< " + extra terms: " << init_energy - init_metric_energy << endl;
|
|
cout << " Final strain energy: " << fin_energy
|
|
<< " = metrics: " << fin_metric_energy
|
|
<< " + extra terms: " << fin_energy - fin_metric_energy << endl;
|
|
cout << "The strain energy decreased by: "
|
|
<< (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
|
|
|
|
// Visualize the final mesh and metric values.
|
|
if (visualization)
|
|
{
|
|
char title[] = "Final metric values";
|
|
vis_tmop_metric_s(mesh_poly_deg, *metric, *target_c, *mesh, title, 600);
|
|
}
|
|
|
|
if (adapt_lim_const > 0.0 && visualization)
|
|
{
|
|
socketstream vis0;
|
|
common::VisualizeField(vis0, "localhost", 19916, adapt_lim_gf0, "Xi 0",
|
|
600, 600, 300, 300);
|
|
}
|
|
|
|
// Visualize the mesh displacement.
|
|
if (visualization)
|
|
{
|
|
osockstream sock(19916, "localhost");
|
|
sock << "solution\n";
|
|
mesh->Print(sock);
|
|
x0 -= x;
|
|
x0.Save(sock);
|
|
sock.send();
|
|
sock << "window_title 'Displacements'\n"
|
|
<< "window_geometry "
|
|
<< 1200 << " " << 0 << " " << 600 << " " << 600 << "\n"
|
|
<< "keys jRmclA" << endl;
|
|
}
|
|
|
|
delete S;
|
|
delete S_prec;
|
|
delete target_c2;
|
|
delete metric2;
|
|
delete metric_coeff1;
|
|
delete adapt_lim_eval;
|
|
delete target_c;
|
|
delete hr_adapt_coeff;
|
|
delete adapt_coeff;
|
|
delete h_metric;
|
|
delete metric;
|
|
delete untangler_metric;
|
|
delete fespace;
|
|
delete fec;
|
|
delete mesh;
|
|
|
|
return 0;
|
|
}
|