1350 lines
43 KiB
C++
1350 lines
43 KiB
C++
// MFEM Example 5
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//
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// Compile with: make ex5
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//
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// Sample runs: ex5 -m ../data/square-disc.mesh
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// ex5 -m ../data/star.mesh
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// ex5 -m ../data/star.mesh -pa
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// ex5 -m ../data/beam-tet.mesh
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// ex5 -m ../data/beam-hex.mesh
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// ex5 -m ../data/beam-hex.mesh -pa
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// ex5 -m ../data/escher.mesh
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// ex5 -m ../data/fichera.mesh
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//
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// Device sample runs:
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// ex5 -m ../data/star.mesh -pa -d cuda
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// ex5 -m ../data/star.mesh -pa -d raja-cuda
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// ex5 -m ../data/star.mesh -pa -d raja-omp
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// ex5 -m ../data/beam-hex.mesh -pa -d cuda
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//
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// Description: This example code solves a simple 2D/3D asymptotic heat diffusion
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// problem in the mixed formulation corresponding to the system
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//
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// k^-1.q + grad T = g
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// div q + div(T*c) + a T = -f
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//
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// with natural boundary condition q.n = 0, where n is the outer
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// normal. The tensor k represents the heat conductivity, where its
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// symmetric and antisymmetric parts can be adjusted. The scalar a
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// is then the heat capacity, which can be zero, changing the problem
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// to steady-state, indefinite, saddle-point. The r.h.s. is f = 0 and
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// g = -a * <initial temperature> for the definite problem and
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// g = -<initial temperature> for the indefinite one. These problems
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// are offered:
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// 1) sine diffusion - with the asymptotic (a -> infinity) reference
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// solution with the first order correction
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// 2) MFEM logo convection-diffusion - random Gaussian blobs of
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// conductivity and circular velocity
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// with ASCII art of MFEM text as IC
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// We discretize with Raviart-Thomas finite elements (heat flux q)
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// and piecewise discontinuous polynomials (temperature T). Alternatively,
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// the piecewise discontinuous polynomials are used for both quantities.
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//
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// The example demonstrates the use of the DarcyForm class, as
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// well as hybridization of mixed systems and the collective saving
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// of several grid functions in VisIt (visit.llnl.gov) and ParaView
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// (paraview.org) formats.
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//
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// We recommend viewing examples 1-4 before viewing this example.
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#include "mfem.hpp"
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#include "darcyop.hpp"
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#include <fstream>
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#include <iostream>
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#include <algorithm>
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using namespace std;
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using namespace mfem;
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// Define the analytical solution and forcing terms / boundary conditions
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typedef std::function<real_t(const Vector &, real_t)> TFunc;
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typedef std::function<void(const Vector &, Vector &)> VecFunc;
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typedef std::function<void(const Vector &, real_t, Vector &)> VecTFunc;
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typedef std::function<void(const Vector &, DenseMatrix &)> MatFunc;
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enum Problem
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{
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SteadyDiffusion = 1,
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MFEMLogo,
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DiffusionRing,
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};
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constexpr real_t epsilon = numeric_limits<real_t>::epsilon();
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MatFunc GetKFun(Problem prob, real_t k, real_t ks, real_t ka);
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TFunc GetTFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun,
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real_t c);
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VecTFunc GetQFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun,
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real_t c);
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VecFunc GetCFun(Problem prob, real_t c);
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TFunc GetFFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun,
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real_t c);
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FluxFunction* GetFluxFun(Problem prob, VectorCoefficient &ccoeff);
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MixedFluxFunction* GetHeatFluxFun(Problem prob, real_t k, real_t ks, real_t ka,
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int dim);
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int main(int argc, char *argv[])
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{
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StopWatch chrono;
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// 1. Parse command-line options.
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const char *mesh_file = "";
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int nx = 0;
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int ny = 0;
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real_t sx = 1.;
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real_t sy = 1.;
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int order = 1;
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bool dg = false;
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bool upwinded = false;
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int iproblem = Problem::SteadyDiffusion;
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real_t tf = 1.;
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int nt = 0;
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int ode = 1;
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real_t k = 1.;
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real_t ks = 1.;
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real_t ka = 0.;
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real_t a = 0.;
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real_t c = 1.;
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real_t td = 0.5;
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bool bc_neumann = false;
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bool reduction = false;
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bool hybridization = false;
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bool nonlinear = false;
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bool nonlinear_conv = false;
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bool nonlinear_diff = false;
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int hdg_scheme = 1;
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int solver_type = (int)DarcyOperator::SolverType::LBFGS;
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bool pa = false;
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const char *device_config = "cpu";
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bool mfem = false;
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bool visit = false;
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bool paraview = false;
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bool visualization = true;
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int vis_iters = -1;
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bool analytic = false;
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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(&nx, "-nx", "--ncells-x",
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"Number of cells in x.");
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args.AddOption(&ny, "-ny", "--ncells-y",
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"Number of cells in y.");
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args.AddOption(&sx, "-sx", "--size-x",
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"Size along x axis.");
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args.AddOption(&sy, "-sy", "--size-y",
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"Size along y axis.");
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree).");
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args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
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"--no-discontinuous", "Enable DG elements for fluxes.");
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args.AddOption(&upwinded, "-up", "--upwinded", "-ce", "--centered",
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"Switches between upwinded (1) and centered (0=default) stabilization.");
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args.AddOption(&iproblem, "-p", "--problem",
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"Problem to solve:\n\t\t"
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"1=sine diffusion\n\t\t"
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"2=MFEM logo\n\t\t"
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"3=diffusion ring\n\t\t");
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args.AddOption(&tf, "-tf", "--time-final",
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"Final time.");
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args.AddOption(&nt, "-nt", "--ntimesteps",
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"Number of time steps.");
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args.AddOption(&ode, "-ode", "--ode-solver",
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"ODE time solver (1=Bacward Euler, 2=RK23L, 3=RK23A, 4=RK34).");
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args.AddOption(&k, "-k", "--kappa",
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"Heat conductivity");
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args.AddOption(&ks, "-ks", "--kappa_sym",
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"Symmetric anisotropy of the heat conductivity tensor");
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args.AddOption(&ka, "-ka", "--kappa_anti",
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"Antisymmetric anisotropy of the heat conductivity tensor");
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args.AddOption(&a, "-a", "--heat_capacity",
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"Heat capacity coefficient (0=indefinite problem)");
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args.AddOption(&c, "-c", "--velocity",
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"Convection velocity");
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args.AddOption(&td, "-td", "--stab_diff",
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"Diffusion stabilization factor (1/2=default)");
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args.AddOption(&bc_neumann, "-bcn", "--bc-neumann", "-no-bcn",
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"--no-bc-neumann", "Enable Neumann outflow boundary condition.");
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args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
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"--no-reduction", "Enable reduction.");
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args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
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"--no-hybridization", "Enable hybridization.");
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args.AddOption(&nonlinear, "-nl", "--nonlinear", "-no-nl",
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"--no-nonlinear", "Enable non-linear regime.");
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args.AddOption(&nonlinear_conv, "-nlc", "--nonlinear-convection", "-no-nlc",
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"--no-nonlinear-convection", "Enable non-linear convection regime.");
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args.AddOption(&nonlinear_diff, "-nld", "--nonlinear-diffusion", "-no-nld",
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"--no-nonlinear-diffusion", "Enable non-linear diffusion regime.");
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args.AddOption(&hdg_scheme, "-hdg", "--hdg_scheme",
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"HDG scheme (1=HDG-I, 2=HDG-II, 3=Rusanov, 4=Godunov).");
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args.AddOption(&solver_type, "-nls", "--nonlinear-solver",
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"Nonlinear solver type (1=LBFGS, 2=LBB, 3=Newton).");
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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(&device_config, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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args.AddOption(&mfem, "-mfem", "--mfem", "-no-mfem",
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"--no-mfem",
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"Enable or disable MFEM output.");
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args.AddOption(&visit, "-visit", "--visit", "-no-visit",
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"--no-visit",
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"Enable or disable Visit output.");
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args.AddOption(¶view, "-paraview", "--paraview", "-no-paraview",
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"--no-paraview",
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"Enable or disable ParaView output.");
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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(&vis_iters, "-vis-its", "--visualization-iters",
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"Set step for GLVis visualization of the solver iterations (<0=off).");
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args.AddOption(&analytic, "-anal", "--analytic", "-no-anal",
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"--no-analytic",
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"Enable or disable analytic solution.");
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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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// Set the problem options
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Problem problem = (Problem)iproblem;
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bool bconv = false, bnlconv = false, bnldiff = nonlinear_diff, btime = false;
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switch (problem)
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{
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case Problem::SteadyDiffusion:
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case Problem::DiffusionRing:
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break;
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case Problem::MFEMLogo:
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bconv = true;
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break;
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default:
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cerr << "Unknown problem" << endl;
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return 1;
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}
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if (bnldiff && reduction)
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{
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cerr << "Reduction is not possible with non-linear diffusion" << endl;
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return 1;
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}
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if (!bconv && !bnlconv && upwinded)
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{
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cerr << "Upwinded scheme cannot work without advection" << endl;
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return 1;
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}
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if (bnlconv && !nonlinear)
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{
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cerr << "Nonlinear convection can only work in the nonlinear regime" << endl;
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return 1;
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}
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if (nonlinear && !hybridization)
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{
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cerr << "Warning: A linear solver is used" << endl;
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}
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if (btime && nt <= 0)
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{
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cerr << "You must specify the number of time steps for time evolving problems"
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<< endl;
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return 1;
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}
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// 2. Enable hardware devices such as GPUs, and programming models such as
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// CUDA, OCCA, RAJA and OpenMP based on command line options.
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Device device(device_config);
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device.Print();
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// 3. Read the mesh from the given mesh file. We can handle triangular,
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// quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
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// the same code.
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if (ny <= 0)
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{
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ny = nx;
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}
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Mesh *mesh = NULL;
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if (strlen(mesh_file) > 0)
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{
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mesh = new Mesh(mesh_file, 1, 1);
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}
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else
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{
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mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL, false,
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sx, sy));
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}
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int dim = mesh->Dimension();
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// Mark boundary conditions
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Array<int> bdr_is_dirichlet(mesh->bdr_attributes.Max());
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Array<int> bdr_is_neumann(mesh->bdr_attributes.Max());
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bdr_is_dirichlet = 0;
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bdr_is_neumann = 0;
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switch (problem)
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{
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case Problem::SteadyDiffusion:
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case Problem::MFEMLogo:
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case Problem::DiffusionRing:
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//free (zero Dirichlet)
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if (bc_neumann)
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{
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bdr_is_neumann[1] = -1;//outflow
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bdr_is_neumann[2] = -1;//outflow
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}
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break;
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}
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// 4. Refine the mesh to increase the resolution. In this example we do
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// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
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// largest number that gives a final mesh with no more than 10,000
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// elements.
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if (strlen(mesh_file) > 0)
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{
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int ref_levels =
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(int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
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for (int l = 0; l < ref_levels; l++)
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{
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mesh->UniformRefinement();
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}
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}
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// 5. Define a finite element space on the mesh. Here we use the
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// Raviart-Thomas finite elements of the specified order.
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FiniteElementCollection *V_coll;
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if (dg)
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{
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// In the case of LDG formulation, we chose a closed basis as it
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// is customary for HDG to match trace DOFs, but an open basis can
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// be used instead.
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V_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
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}
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else
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{
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V_coll = new RT_FECollection(order, dim);
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}
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FiniteElementCollection *W_coll = new L2_FECollection(order, dim,
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BasisType::GaussLobatto);
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FiniteElementSpace *V_space = new FiniteElementSpace(mesh, V_coll,
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(dg)?(dim):(1));
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FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
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DarcyForm *darcy = new DarcyForm(V_space, W_space);
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// 6. Define the coefficients, analytical solution, and rhs of the PDE.
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const real_t t_0 = 1.; //base temperature
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ConstantCoefficient acoeff(a);
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constexpr unsigned int seed = 0;
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srand(seed);// init random number generator
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auto kFun = GetKFun(problem, k, ks, ka);
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MatrixFunctionCoefficient kcoeff(dim, kFun);
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InverseMatrixCoefficient ikcoeff(kcoeff);
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auto cFun = GetCFun(problem, c);
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VectorFunctionCoefficient ccoeff(dim, cFun);
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auto tFun = GetTFun(problem, t_0, a, kFun, c);
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FunctionCoefficient tcoeff(tFun);
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SumCoefficient gcoeff(0., tcoeff, 1., -1.);
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auto fFun = GetFFun(problem, t_0, a, kFun, c);
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FunctionCoefficient fcoeff(fFun);
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auto qFun = GetQFun(problem, t_0, a, kFun, c);
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VectorFunctionCoefficient qcoeff(dim, qFun);
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ConstantCoefficient one;
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VectorSumCoefficient qtcoeff_(ccoeff, qcoeff, tcoeff, one);//total flux
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VectorCoefficient &qtcoeff = (bconv)?((VectorCoefficient&)qtcoeff_)
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:((VectorCoefficient&)qcoeff);//<--velocity is undefined
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// 7. Assemble the finite element matrices for the Darcy operator
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//
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// D = [ M B^T ]
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// [ B 0 ]
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// where:
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//
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// M = \int_\Omega k u_h \cdot v_h d\Omega q_h, v_h \in V_h
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// B = -\int_\Omega \div u_h q_h d\Omega q_h \in V_h, w_h \in W_h
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BilinearForm *Mq =(!nonlinear && !bnldiff)?(darcy->GetFluxMassForm()):(NULL);
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NonlinearForm *Mqnl = (nonlinear && !bnldiff)?
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(darcy->GetFluxMassNonlinearForm()):(NULL);
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BlockNonlinearForm *Mnl = (bnldiff)?(darcy->GetBlockNonlinearForm()):(NULL);
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MixedBilinearForm *B = darcy->GetFluxDivForm();
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BilinearForm *Mt = (!nonlinear && ((dg && td > 0.) || bconv || btime ||
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a > 0.))?
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(darcy->GetPotentialMassForm()):(NULL);
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NonlinearForm *Mtnl = (nonlinear && ((dg && td > 0.) || bconv || bnlconv ||
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a > 0. || btime))?
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(darcy->GetPotentialMassNonlinearForm()):(NULL);
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FluxFunction *FluxFun = NULL;
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RiemannSolver *FluxSolver = NULL;
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MixedFluxFunction *HeatFluxFun = NULL;
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//diffusion
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if (!bnldiff)
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{
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//linear diffusion
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if (dg)
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{
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if (Mq)
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{
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Mq->AddDomainIntegrator(new VectorMassIntegrator(ikcoeff));
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}
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if (Mqnl)
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{
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Mqnl->AddDomainIntegrator(new VectorMassIntegrator(ikcoeff));
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}
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}
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else
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{
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if (Mq)
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{
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Mq->AddDomainIntegrator(new VectorFEMassIntegrator(ikcoeff));
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}
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if (Mqnl)
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{
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Mqnl->AddDomainIntegrator(new VectorFEMassIntegrator(ikcoeff));
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}
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}
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}
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else
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{
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//nonlinear diffusion
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HeatFluxFun = GetHeatFluxFun(problem, k, ks, ka, dim);
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if (dg)
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{
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Mnl->AddDomainIntegrator(new MixedConductionNLFIntegrator(*HeatFluxFun));
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}
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else
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{
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Mnl->AddDomainIntegrator(new MixedConductionNLFIntegrator(*HeatFluxFun));
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}
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}
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//diffusion stabilization
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if (dg)
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{
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if (bnldiff)
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{
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cerr << "Warning: Using linear stabilization for non-linear diffusion" << endl;
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}
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if (upwinded && td > 0. && hybridization)
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{
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if (Mt)
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{
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Mt->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ccoeff, kcoeff, td));
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Mt->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(ccoeff, kcoeff, td),
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bdr_is_neumann);
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}
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if (Mtnl)
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{
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Mtnl->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ccoeff, kcoeff, td));
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Mtnl->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(ccoeff, kcoeff, td),
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bdr_is_neumann);
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}
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}
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else if (!upwinded && td > 0.)
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{
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if (Mt)
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{
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Mt->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td));
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Mt->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td),
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bdr_is_neumann);
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}
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if (Mtnl)
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{
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Mtnl->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td));
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Mtnl->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td),
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bdr_is_neumann);
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}
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}
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}
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//divergence/weak gradient
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|
|
if (dg)
|
|
{
|
|
B->AddDomainIntegrator(new VectorDivergenceIntegrator());
|
|
if (upwinded)
|
|
{
|
|
B->AddInteriorFaceIntegrator(new TransposeIntegrator(
|
|
new DGNormalTraceIntegrator(ccoeff, -1.)));
|
|
B->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
|
|
ccoeff, -1.)), bdr_is_neumann);
|
|
}
|
|
else
|
|
{
|
|
B->AddInteriorFaceIntegrator(new TransposeIntegrator(
|
|
new DGNormalTraceIntegrator(-1.)));
|
|
B->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
|
|
-1.)), bdr_is_neumann);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
B->AddDomainIntegrator(new VectorFEDivergenceIntegrator());
|
|
}
|
|
|
|
//linear convection in the linear regime
|
|
|
|
if (bconv && Mt)
|
|
{
|
|
Mt->AddDomainIntegrator(new ConservativeConvectionIntegrator(ccoeff));
|
|
if (upwinded)
|
|
{
|
|
Mt->AddInteriorFaceIntegrator(new HDGConvectionUpwindedIntegrator(ccoeff));
|
|
Mt->AddBdrFaceIntegrator(new HDGConvectionUpwindedIntegrator(ccoeff));
|
|
}
|
|
else
|
|
{
|
|
Mt->AddInteriorFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff));
|
|
if (hybridization)
|
|
{
|
|
//centered scheme does not work with Dirichlet when hybridized,
|
|
//giving an diverging system, we use the full BC flux here
|
|
Mt->AddBdrFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff),
|
|
bdr_is_neumann);
|
|
}
|
|
else
|
|
{
|
|
Mt->AddBdrFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff));
|
|
}
|
|
}
|
|
}
|
|
|
|
//linear convection in the nonlinear regime
|
|
|
|
if (bconv && Mtnl)
|
|
{
|
|
Mtnl->AddDomainIntegrator(new ConservativeConvectionIntegrator(ccoeff));
|
|
if (upwinded)
|
|
{
|
|
Mtnl->AddInteriorFaceIntegrator(new HDGConvectionUpwindedIntegrator(ccoeff));
|
|
Mtnl->AddBdrFaceIntegrator(new HDGConvectionUpwindedIntegrator(ccoeff));
|
|
}
|
|
else
|
|
{
|
|
Mtnl->AddInteriorFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff));
|
|
if (hybridization)
|
|
{
|
|
//centered scheme does not work with Dirichlet when hybridized,
|
|
//giving an diverging system, we use the full BC flux here
|
|
Mtnl->AddBdrFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff),
|
|
bdr_is_neumann);
|
|
}
|
|
else
|
|
{
|
|
Mtnl->AddBdrFaceIntegrator(new HDGConvectionCenteredIntegrator(ccoeff));
|
|
}
|
|
}
|
|
}
|
|
|
|
//nonlinear convection in the nonlinear regime
|
|
|
|
if (bnlconv && Mtnl)
|
|
{
|
|
FluxFun = GetFluxFun(problem, ccoeff);
|
|
switch (hdg_scheme)
|
|
{
|
|
case 1: FluxSolver = new HDGFlux(*FluxFun, HDGFlux::HDGScheme::HDG_1); break;
|
|
case 2: FluxSolver = new HDGFlux(*FluxFun, HDGFlux::HDGScheme::HDG_2); break;
|
|
case 3: FluxSolver = new RusanovFlux(*FluxFun); break;
|
|
case 4: FluxSolver = new GodunovFlux(*FluxFun); break;
|
|
default:
|
|
cerr << "Unknown HDG scheme" << endl;
|
|
exit(1);
|
|
}
|
|
Mtnl->AddDomainIntegrator(new HyperbolicFormIntegrator(*FluxSolver, 0, -1.));
|
|
Mtnl->AddInteriorFaceIntegrator(new HyperbolicFormIntegrator(
|
|
*FluxSolver, 0, -1.));
|
|
Mtnl->AddBdrFaceIntegrator(new HyperbolicFormIntegrator(
|
|
*FluxSolver, 0, -1.));
|
|
}
|
|
|
|
//inertial term
|
|
|
|
if (a > 0.)
|
|
{
|
|
if (Mt)
|
|
{
|
|
Mt->AddDomainIntegrator(new MassIntegrator(acoeff));
|
|
}
|
|
else
|
|
{
|
|
Mtnl->AddDomainIntegrator(new MassIntegrator(acoeff));
|
|
}
|
|
}
|
|
|
|
//set hybridization / assembly level
|
|
|
|
Array<int> ess_flux_tdofs_list;
|
|
if (!dg)
|
|
{
|
|
V_space->GetEssentialTrueDofs(bdr_is_neumann, ess_flux_tdofs_list);
|
|
}
|
|
|
|
FiniteElementCollection *trace_coll = NULL;
|
|
FiniteElementSpace *trace_space = NULL;
|
|
|
|
|
|
if (hybridization)
|
|
{
|
|
chrono.Clear();
|
|
chrono.Start();
|
|
|
|
trace_coll = new RT_Trace_FECollection(order, dim, 0);
|
|
//trace_coll = new DG_Interface_FECollection(order, dim, 0);
|
|
trace_space = new FiniteElementSpace(mesh, trace_coll);
|
|
darcy->EnableHybridization(trace_space,
|
|
new NormalTraceJumpIntegrator(),
|
|
ess_flux_tdofs_list);
|
|
|
|
chrono.Stop();
|
|
std::cout << "Hybridization init took " << chrono.RealTime() << "s.\n";
|
|
}
|
|
else if (reduction)
|
|
{
|
|
chrono.Clear();
|
|
chrono.Start();
|
|
|
|
if (dg)
|
|
{
|
|
darcy->EnableFluxReduction();
|
|
}
|
|
else if (!bconv && !bnlconv)
|
|
{
|
|
darcy->EnablePotentialReduction(ess_flux_tdofs_list);
|
|
}
|
|
else
|
|
{
|
|
std::cerr << "No possible reduction!" << std::endl;
|
|
return 1;
|
|
}
|
|
|
|
chrono.Stop();
|
|
std::cout << "Reduction init took " << chrono.RealTime() << "s.\n";
|
|
}
|
|
|
|
if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
|
|
|
|
// 8. Define the BlockStructure of the problem, i.e. define the array of
|
|
// offsets for each variable. The last component of the Array is the sum
|
|
// of the dimensions of each block.
|
|
const Array<int> block_offsets(DarcyOperator::ConstructOffsets(*darcy));
|
|
|
|
std::cout << "***********************************************************\n";
|
|
if (!reduction || (reduction && !dg))
|
|
{
|
|
std::cout << "dim(V) = " << block_offsets[1] - block_offsets[0] << "\n";
|
|
}
|
|
if (!reduction || (reduction && dg))
|
|
{
|
|
std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
|
|
}
|
|
if (!reduction)
|
|
{
|
|
if (hybridization)
|
|
{
|
|
std::cout << "dim(M) = " << block_offsets[3] - block_offsets[2] << "\n";
|
|
std::cout << "dim(V+W+M) = " << block_offsets.Last() << "\n";
|
|
}
|
|
else
|
|
{
|
|
std::cout << "dim(V+W) = " << block_offsets.Last() << "\n";
|
|
}
|
|
}
|
|
std::cout << "***********************************************************\n";
|
|
|
|
// 9. Allocate memory (x, rhs) for the analytical solution and the right hand
|
|
// side. Define the GridFunction q,t for the finite element solution and
|
|
// linear forms fform and gform for the right hand side. The data
|
|
// allocated by x and rhs are passed as a reference to the grid functions
|
|
// (q,t) and the linear forms (fform, gform).
|
|
MemoryType mt = device.GetMemoryType();
|
|
BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
|
|
|
|
x = 0.;
|
|
GridFunction q_h, t_h;
|
|
q_h.MakeRef(V_space, x.GetBlock(0), 0);
|
|
t_h.MakeRef(W_space, x.GetBlock(1), 0);
|
|
|
|
if (btime)
|
|
{
|
|
t_h.ProjectCoefficient(tcoeff); //initial condition
|
|
}
|
|
|
|
if (!dg)
|
|
{
|
|
q_h.ProjectBdrCoefficientNormal(qcoeff,
|
|
bdr_is_neumann); //essential Neumann BC
|
|
}
|
|
|
|
LinearForm *gform(new LinearForm);
|
|
gform->Update(V_space, rhs.GetBlock(0), 0);
|
|
if (dg)
|
|
{
|
|
gform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(gcoeff),
|
|
bdr_is_dirichlet);
|
|
}
|
|
else
|
|
{
|
|
gform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(gcoeff),
|
|
bdr_is_dirichlet);
|
|
}
|
|
|
|
LinearForm *fform(new LinearForm);
|
|
fform->Update(W_space, rhs.GetBlock(1), 0);
|
|
fform->AddDomainIntegrator(new DomainLFIntegrator(fcoeff));
|
|
if (!hybridization)
|
|
{
|
|
if (upwinded)
|
|
fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, qtcoeff, +1.),
|
|
bdr_is_neumann);
|
|
else
|
|
fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, qtcoeff, +1., 0.),
|
|
bdr_is_neumann);
|
|
}
|
|
if (bconv)
|
|
{
|
|
if (upwinded)
|
|
fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(tcoeff, ccoeff, +1.),
|
|
bdr_is_dirichlet);
|
|
else
|
|
{
|
|
if (hybridization)
|
|
fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(tcoeff, ccoeff, +2., 0.),
|
|
bdr_is_dirichlet);//<-- full BC flux, see above
|
|
else
|
|
fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(tcoeff, ccoeff, +1., 0.),
|
|
bdr_is_dirichlet);
|
|
}
|
|
}
|
|
|
|
//prepare (reduced) solution and rhs vectors
|
|
|
|
LinearForm *hform = NULL;
|
|
|
|
//Neumann BC for the hybridized system
|
|
|
|
if (hybridization)
|
|
{
|
|
hform = new LinearForm();
|
|
hform->Update(trace_space, rhs.GetBlock(2), 0);
|
|
//note that Neumann BC must be applied only for the heat flux
|
|
//and not the total flux for stability reasons
|
|
hform->AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(qcoeff, 2),
|
|
bdr_is_neumann);
|
|
}
|
|
|
|
//construct the operator
|
|
|
|
Array<Coefficient*> coeffs({(Coefficient*)&gcoeff,
|
|
(Coefficient*)&fcoeff,
|
|
(Coefficient*)&qtcoeff});
|
|
|
|
DarcyOperator op(ess_flux_tdofs_list, darcy, gform, fform, hform, coeffs,
|
|
(DarcyOperator::SolverType) solver_type, false, btime);
|
|
|
|
if (vis_iters >= 0)
|
|
{
|
|
op.EnableIterationsVisualization(vis_iters);
|
|
}
|
|
|
|
//construct the time solver
|
|
|
|
ODESolver *ode_solver;
|
|
|
|
switch (ode)
|
|
{
|
|
case 1: ode_solver = new BackwardEulerSolver(); break;
|
|
case 2: ode_solver = new SDIRK23Solver(2); break;
|
|
case 3: ode_solver = new SDIRK23Solver(); break;
|
|
case 4: ode_solver = new SDIRK34Solver(); break;
|
|
default:
|
|
MFEM_ABORT("Unknown solver");
|
|
return 1;
|
|
}
|
|
|
|
ode_solver->Init(op);
|
|
|
|
//iterate in time
|
|
|
|
if (!btime) { nt = 1; }
|
|
|
|
const real_t dt = tf / nt; //time step
|
|
|
|
for (int ti = 0; ti < nt; ti++)
|
|
{
|
|
//set current time
|
|
|
|
real_t t = tf * ti / nt;
|
|
|
|
//perform time step
|
|
|
|
real_t dt_ = dt;//<---ignore time step changes
|
|
ode_solver->Step(x, t, dt_);
|
|
|
|
// 12. Compute the L2 error norms.
|
|
|
|
int order_quad = max(2, 2*order+1);
|
|
const IntegrationRule *irs[Geometry::NumGeom];
|
|
for (int i=0; i < Geometry::NumGeom; ++i)
|
|
{
|
|
irs[i] = &(IntRules.Get(i, order_quad));
|
|
}
|
|
|
|
real_t err_q = q_h.ComputeL2Error(qcoeff, irs);
|
|
real_t norm_q = ComputeLpNorm(2., qcoeff, *mesh, irs);
|
|
real_t err_t = t_h.ComputeL2Error(tcoeff, irs);
|
|
real_t norm_t = ComputeLpNorm(2., tcoeff, *mesh, irs);
|
|
|
|
if (btime)
|
|
{
|
|
cout << "iter:\t" << ti
|
|
<< "\ttime:\t" << t
|
|
<< "\tq_err:\t" << err_q / norm_q
|
|
<< "\tt_err:\t" << err_t / norm_t
|
|
<< endl;
|
|
}
|
|
else
|
|
{
|
|
cout << "|| q_h - q_ex || / || q_ex || = " << err_q / norm_q << "\n";
|
|
cout << "|| t_h - t_ex || / || t_ex || = " << err_t / norm_t << "\n";
|
|
}
|
|
|
|
// Project the analytic solution
|
|
|
|
static GridFunction q_a, qt_a, t_a, c_gf;
|
|
|
|
q_a.SetSpace(V_space);
|
|
q_a.ProjectCoefficient(qcoeff);
|
|
|
|
qt_a.SetSpace(V_space);
|
|
qt_a.ProjectCoefficient(qtcoeff);
|
|
|
|
t_a.SetSpace(W_space);
|
|
t_a.ProjectCoefficient(tcoeff);
|
|
|
|
if (bconv)
|
|
{
|
|
c_gf.SetSpace(V_space);
|
|
c_gf.ProjectCoefficient(ccoeff);
|
|
}
|
|
|
|
// 13. Save the mesh and the solution. This output can be viewed later using
|
|
// GLVis: "glvis -m ex5.mesh -g sol_q.gf" or "glvis -m ex5.mesh -g
|
|
// sol_t.gf".
|
|
if (mfem)
|
|
{
|
|
stringstream ss;
|
|
ss.str("");
|
|
ss << "ex5";
|
|
if (btime) { ss << "_" << ti; }
|
|
ss << ".mesh";
|
|
ofstream mesh_ofs(ss.str());
|
|
mesh_ofs.precision(8);
|
|
mesh->Print(mesh_ofs);
|
|
|
|
ss.str("");
|
|
ss << "sol_q";
|
|
if (btime) { ss << "_" << ti; }
|
|
ss << ".gf";
|
|
ofstream q_ofs(ss.str());
|
|
q_ofs.precision(8);
|
|
q_h.Save(q_ofs);
|
|
|
|
ss.str("");
|
|
ss << "sol_t";
|
|
if (btime) { ss << "_" << ti; }
|
|
ss << ".gf";
|
|
ofstream t_ofs(ss.str());
|
|
t_ofs.precision(8);
|
|
t_h.Save(t_ofs);
|
|
}
|
|
|
|
// 14. Save data in the VisIt format
|
|
if (visit)
|
|
{
|
|
static VisItDataCollection visit_dc("Example5", mesh);
|
|
if (ti == 0)
|
|
{
|
|
visit_dc.RegisterField("heat flux", &q_h);
|
|
visit_dc.RegisterField("temperature", &t_h);
|
|
if (analytic)
|
|
{
|
|
visit_dc.RegisterField("heat flux analytic", &q_a);
|
|
visit_dc.RegisterField("temperature analytic", &t_a);
|
|
}
|
|
}
|
|
visit_dc.SetCycle(ti);
|
|
visit_dc.SetTime(t); // set the time
|
|
visit_dc.Save();
|
|
}
|
|
|
|
// 15. Save data in the ParaView format
|
|
if (paraview)
|
|
{
|
|
static ParaViewDataCollection paraview_dc("Example5", mesh);
|
|
if (ti == 0)
|
|
{
|
|
paraview_dc.SetPrefixPath("ParaView");
|
|
paraview_dc.SetLevelsOfDetail(order);
|
|
paraview_dc.SetDataFormat(VTKFormat::BINARY);
|
|
paraview_dc.SetHighOrderOutput(true);
|
|
paraview_dc.RegisterField("heat flux",&q_h);
|
|
paraview_dc.RegisterField("temperature",&t_h);
|
|
if (analytic)
|
|
{
|
|
paraview_dc.RegisterField("heat flux analytic", &q_a);
|
|
paraview_dc.RegisterField("temperature analytic", &t_a);
|
|
}
|
|
}
|
|
paraview_dc.SetCycle(ti);
|
|
paraview_dc.SetTime(t); // set the time
|
|
paraview_dc.Save();
|
|
}
|
|
|
|
// 16. Send the solution by socket to a GLVis server.
|
|
if (visualization)
|
|
{
|
|
const char vishost[] = "localhost";
|
|
const int visport = 19916;
|
|
static socketstream q_sock(vishost, visport);
|
|
q_sock.precision(8);
|
|
q_sock << "solution\n" << *mesh << q_h << endl;
|
|
if (ti == 0)
|
|
{
|
|
q_sock << "window_title 'Heat flux'" << endl;
|
|
q_sock << "keys Rljvvvvvmmc" << endl;
|
|
}
|
|
static socketstream t_sock(vishost, visport);
|
|
t_sock.precision(8);
|
|
t_sock << "solution\n" << *mesh << t_h << endl;
|
|
if (ti == 0)
|
|
{
|
|
t_sock << "window_title 'Temperature'" << endl;
|
|
t_sock << "keys Rljmmc" << endl;
|
|
}
|
|
if (analytic)
|
|
{
|
|
static socketstream qa_sock(vishost, visport);
|
|
qa_sock.precision(8);
|
|
qa_sock << "solution\n" << *mesh << q_a << endl;
|
|
if (ti == 0)
|
|
{
|
|
qa_sock << "window_title 'Heat flux analytic'" << endl;
|
|
qa_sock << "keys Rljvvvvvmmc" << endl;
|
|
}
|
|
if (bconv || bnlconv)
|
|
{
|
|
static socketstream qta_sock(vishost, visport);
|
|
qta_sock.precision(8);
|
|
qta_sock << "solution\n" << *mesh << qt_a << endl;
|
|
if (ti == 0)
|
|
{
|
|
qta_sock << "window_title 'Total flux analytic'" << endl;
|
|
qta_sock << "keys Rljvvvvvmmc" << endl;
|
|
}
|
|
}
|
|
static socketstream ta_sock(vishost, visport);
|
|
ta_sock.precision(8);
|
|
ta_sock << "solution\n" << *mesh << t_a << endl;
|
|
if (ti == 0)
|
|
{
|
|
ta_sock << "window_title 'Temperature analytic'" << endl;
|
|
ta_sock << "keys Rljmmc" << endl;
|
|
}
|
|
if (bconv)
|
|
{
|
|
static socketstream c_sock(vishost, visport);
|
|
c_sock.precision(8);
|
|
c_sock << "solution\n" << *mesh << c_gf << endl;
|
|
if (ti == 0)
|
|
{
|
|
c_sock << "window_title 'Velocity'" << endl;
|
|
c_sock << "keys Rljvvvvvmmc" << endl;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// 17. Free the used memory.
|
|
|
|
delete ode_solver;
|
|
delete HeatFluxFun;
|
|
delete FluxFun;
|
|
delete FluxSolver;
|
|
delete fform;
|
|
delete gform;
|
|
delete hform;
|
|
delete darcy;
|
|
delete W_space;
|
|
delete V_space;
|
|
delete trace_space;
|
|
delete W_coll;
|
|
delete V_coll;
|
|
delete trace_coll;
|
|
delete mesh;
|
|
|
|
return 0;
|
|
}
|
|
|
|
MatFunc GetKFun(Problem prob, real_t k, real_t ks, real_t ka)
|
|
{
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
return [=](const Vector &x, DenseMatrix &kappa)
|
|
{
|
|
const int ndim = x.Size();
|
|
kappa.Diag(k, ndim);
|
|
kappa(0,0) *= ks;
|
|
kappa(0,1) = +ka * k;
|
|
kappa(1,0) = -ka * k;
|
|
if (ndim > 2)
|
|
{
|
|
kappa(0,2) = +ka * k;
|
|
kappa(2,0) = -ka * k;
|
|
}
|
|
};
|
|
case Problem::MFEMLogo:
|
|
{
|
|
constexpr int n = 80;
|
|
constexpr real_t xmax = 1.;
|
|
constexpr real_t ymax = 1.;
|
|
constexpr real_t wmax = .05;
|
|
constexpr real_t kmax = .8;
|
|
DenseMatrix bubbles(5, n);
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
bubbles(0, i) = rand_real() * xmax;
|
|
bubbles(1, i) = rand_real() * ymax;
|
|
bubbles(2, i) = rand_real() * wmax;
|
|
bubbles(3, i) = rand_real() * k * kmax;
|
|
bubbles(4, i) = rand_real() * ks;
|
|
//bubbles(5, i) = rand_real() * ka;
|
|
}
|
|
|
|
return [=](const Vector &x, DenseMatrix &kappa)
|
|
{
|
|
real_t kap = 0.;
|
|
real_t kap_s = 0.;
|
|
real_t kap_a = 0.;
|
|
for (int i = 0; i < bubbles.Width(); i++)
|
|
{
|
|
const real_t dx = x(0) - bubbles(0,i);
|
|
const real_t dy = x(1) - bubbles(1,i);
|
|
const real_t w = bubbles(2,i);
|
|
const real_t k = bubbles(3,i) * exp(-(dx*dx+dy*dy)/(w*w));
|
|
kap += k;
|
|
kap_s += k * bubbles(4,i);
|
|
//kap_a += k * bubbles(5, i);
|
|
}
|
|
const int ndim = x.Size();
|
|
const real_t kmin = (1. - kmax) * k;
|
|
kappa.Diag(kmin + kap, ndim);
|
|
kappa(0,0) = kmin + kap_s;
|
|
kappa(0,1) = +kap_a * k;
|
|
kappa(1,0) = -kap_a * k;
|
|
if (ndim > 2)
|
|
{
|
|
kappa(0,2) = +kap_a * k;
|
|
kappa(2,0) = -kap_a * k;
|
|
}
|
|
};
|
|
}
|
|
case Problem::DiffusionRing:
|
|
return [=](const Vector &x, DenseMatrix &kappa)
|
|
{
|
|
const int ndim = x.Size();
|
|
Vector b(ndim);
|
|
b = 0.;
|
|
|
|
Vector dx(x);
|
|
dx -= .5;
|
|
const real_t r = hypot(dx(0), dx(1));
|
|
b(0) = (r>0.)?(-dx(1) / r):(1.);
|
|
b(1) = (r>0.)?(+dx(0) / r):(0.);
|
|
|
|
kappa.Diag(ks * k, ndim);
|
|
if (ks != 1.)
|
|
{
|
|
AddMult_a_VVt((1. - ks) * k, b, kappa);
|
|
}
|
|
};
|
|
}
|
|
return MatFunc();
|
|
}
|
|
|
|
TFunc GetTFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun, real_t c)
|
|
{
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
return [=](const Vector &x, real_t t) -> real_t
|
|
{
|
|
const int ndim = x.Size();
|
|
real_t t0 = t_0 * sin(M_PI*x(0)) * sin(M_PI*x(1));
|
|
if (ndim > 2)
|
|
{
|
|
t0 *= sin(M_PI*x(2));
|
|
}
|
|
|
|
if (a <= 0.) { return t0; }
|
|
|
|
Vector ddT((ndim<=2)?(2):(4));
|
|
ddT(0) = -t_0 * M_PI*M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1));//xx,yy
|
|
ddT(1) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * cos(M_PI*x(1));//xy
|
|
if (ndim > 2)
|
|
{
|
|
ddT(0) *= sin(M_PI*x(2));//xx,yy,zz
|
|
ddT(1) *= sin(M_PI*x(2));//xy
|
|
//xz
|
|
ddT(2) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(2));
|
|
//yz
|
|
ddT(3) = +t_0 * M_PI*M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1)) * cos(M_PI*x(2));
|
|
|
|
}
|
|
|
|
DenseMatrix kappa;
|
|
kFun(x, kappa);
|
|
|
|
real_t div = -(kappa(0,0) + kappa(1,1)) * ddT(0) - (kappa(0,1) + kappa(1,0)) * ddT(1);
|
|
if (ndim > 2)
|
|
{
|
|
div += -kappa(2,2) * ddT(0) - (kappa(0,2) + kappa(2,0)) * ddT(2)
|
|
- (kappa(1,2) + kappa(2,1)) * ddT(3);
|
|
}
|
|
return t0 - div / a * t;
|
|
};
|
|
case Problem::MFEMLogo:
|
|
return [=](const Vector &x, real_t t) -> real_t
|
|
{
|
|
#if 1
|
|
//Banner
|
|
constexpr int iw = 38;
|
|
constexpr int ih = 7;
|
|
static const unsigned char logo[ih][iw] = {
|
|
"## ## ######## ######## ## ##",
|
|
"### ### ## ## ### ###",
|
|
"#### #### ## ## #### ####",
|
|
"## ### ## ###### ###### ## ### ##",
|
|
"## ## ## ## ## ##",
|
|
"## ## ## ## ## ##",
|
|
"## ## ## ######## ## ##",
|
|
};
|
|
#else
|
|
//Collosal
|
|
constexpr int iw = 50;
|
|
constexpr int ih = 8;
|
|
static const unsigned char logo[ih][iw] = {
|
|
"888b d888 8888888888 8888888888 888b d888",
|
|
"8888b d8888 888 888 8888b d8888",
|
|
"88888b.d88888 888 888 88888b.d88888",
|
|
"888Y88888P888 8888888 8888888 888Y88888P888",
|
|
"888 Y888P 888 888 888 888 Y888P 888",
|
|
"888 Y8P 888 888 888 888 Y8P 888",
|
|
"888 8 888 888 888 888 8 888",
|
|
"888 888 888 8888888888 888 888",
|
|
};
|
|
#endif
|
|
|
|
constexpr real_t w = 0.8;
|
|
constexpr real_t h = (w * ih) / iw;
|
|
constexpr real_t xo = 0.5;
|
|
constexpr real_t yo = 0.5;
|
|
const real_t dx = x(0) - xo;
|
|
const real_t dy = x(1) - yo;
|
|
|
|
const int ix = (dx/w + 0.5) * iw;
|
|
const int iy = (dy/h + 0.5) * ih;
|
|
|
|
if (ix < 0 || ix >= iw || iy < 0 || iy >= ih)
|
|
{
|
|
return 0.;
|
|
}
|
|
|
|
const real_t T = (logo[ih-1-iy][ix] != ' ')?(t_0):(0.);
|
|
return T;
|
|
};
|
|
case Problem::DiffusionRing:
|
|
return [=](const Vector &x, real_t t) -> real_t
|
|
{
|
|
constexpr real_t r0 = 0.25;
|
|
constexpr real_t r1 = 0.35;
|
|
constexpr real_t dr01 = 0.025;
|
|
constexpr real_t theta0 = 11./12. * M_PI;
|
|
constexpr real_t dtheta0 = 1./48. * M_PI;
|
|
|
|
Vector dx(x);
|
|
dx -= .5;
|
|
const real_t r = hypot(dx(0), dx(1));
|
|
const real_t theta = fabs(atan2(dx(1), dx(0)));
|
|
|
|
if (r < r0 - dr01 || r > r1 + dr01 || theta < theta0 - dtheta0)
|
|
{
|
|
return 0.;
|
|
}
|
|
|
|
const real_t dr = min(r - r0 + dr01, r1 + dr01 - r) / dr01;
|
|
const real_t dth = (theta - theta0 + dtheta0) / dtheta0;
|
|
return min(1., dr) * min(1., dth) * t_0;
|
|
};
|
|
}
|
|
return TFunc();
|
|
}
|
|
|
|
VecTFunc GetQFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun,
|
|
real_t c)
|
|
{
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
return [=](const Vector &x, real_t, Vector &v)
|
|
{
|
|
const int vdim = x.Size();
|
|
v.SetSize(vdim);
|
|
|
|
Vector gT(vdim);
|
|
gT = 0.;
|
|
gT(0) = t_0 * M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1));
|
|
gT(1) = t_0 * M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1));
|
|
if (vdim > 2)
|
|
{
|
|
gT(0) *= sin(M_PI*x(2));
|
|
gT(1) *= sin(M_PI*x(2));
|
|
gT(2) = t_0 * M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(2));
|
|
}
|
|
|
|
DenseMatrix kappa;
|
|
kFun(x, kappa);
|
|
|
|
if (vdim <= 2)
|
|
{
|
|
v(0) = -kappa(0,0) * gT(0) -kappa(0,1) * gT(1);
|
|
v(1) = -kappa(1,0) * gT(0) -kappa(1,1) * gT(1);
|
|
}
|
|
else
|
|
{
|
|
kappa.Mult(gT, v);
|
|
v.Neg();
|
|
}
|
|
};
|
|
case Problem::MFEMLogo:
|
|
case Problem::DiffusionRing:
|
|
return [=](const Vector &x, real_t, Vector &v)
|
|
{
|
|
const int vdim = x.Size();
|
|
v.SetSize(vdim);
|
|
v = 0.;
|
|
};
|
|
}
|
|
return VecTFunc();
|
|
}
|
|
|
|
VecFunc GetCFun(Problem prob, real_t c)
|
|
{
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
case Problem::DiffusionRing:
|
|
// null
|
|
break;
|
|
case Problem::MFEMLogo:
|
|
{
|
|
constexpr int n = 80;
|
|
constexpr real_t xmax = 1.;
|
|
constexpr real_t ymax = 1.;
|
|
constexpr real_t wmax = .05;
|
|
DenseMatrix bubbles(4, n);
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
bubbles(0, i) = rand_real() * xmax;
|
|
bubbles(1, i) = rand_real() * ymax;
|
|
bubbles(2, i) = rand_real() * wmax;
|
|
bubbles(3, i) = (rand_real() * 2. - 1.) * c;
|
|
}
|
|
|
|
return [=](const Vector &x, Vector &v)
|
|
{
|
|
const int vdim = x.Size();
|
|
v.SetSize(vdim);
|
|
v = 0.;
|
|
for (int i = 0; i < bubbles.Width(); i++)
|
|
{
|
|
const real_t dx = x(0) - bubbles(0,i);
|
|
const real_t dy = x(1) - bubbles(1,i);
|
|
const real_t w = bubbles(2,i);
|
|
const real_t c = bubbles(3,i) * exp(-(dx*dx+dy*dy)/(w*w));
|
|
v(0) += +c * dy;
|
|
v(1) += -c * dx;
|
|
}
|
|
};
|
|
}
|
|
}
|
|
return VecFunc();
|
|
}
|
|
|
|
TFunc GetFFun(Problem prob, real_t t_0, real_t a, const MatFunc &kFun, real_t c)
|
|
{
|
|
auto TFun = GetTFun(prob, t_0, a, kFun, c);
|
|
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
case Problem::MFEMLogo:
|
|
case Problem::DiffusionRing:
|
|
return [=](const Vector &x, real_t) -> real_t
|
|
{
|
|
const real_t T = TFun(x, 0);
|
|
return -((a > 0.)?(a):(1.)) * T;
|
|
};
|
|
}
|
|
return TFunc();
|
|
}
|
|
|
|
FluxFunction* GetFluxFun(Problem prob, VectorCoefficient &ccoef)
|
|
{
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
case Problem::MFEMLogo:
|
|
case Problem::DiffusionRing:
|
|
//null
|
|
break;
|
|
}
|
|
|
|
return NULL;
|
|
}
|
|
|
|
MixedFluxFunction* GetHeatFluxFun(Problem prob, real_t k, real_t ks, real_t ka,
|
|
int dim)
|
|
{
|
|
auto KFun = GetKFun(prob, k, ks, ka);
|
|
|
|
switch (prob)
|
|
{
|
|
case Problem::SteadyDiffusion:
|
|
case Problem::MFEMLogo:
|
|
case Problem::DiffusionRing:
|
|
static MatrixFunctionCoefficient kappa(dim, KFun);
|
|
static InverseMatrixCoefficient ikappa(kappa);
|
|
return new LinearDiffusionFlux(ikappa);
|
|
}
|
|
|
|
return NULL;
|
|
}
|