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75 lines
2.4 KiB
75 lines
2.4 KiB
2 years ago
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#include <medusa/Medusa_fwd.hpp>
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#include <medusa/bits/domains/BasicRelax.hpp>
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#include <medusa/bits/domains/GeneralFill.hpp>
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#include <Eigen/SparseCore>
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#include <Eigen/IterativeLinearSolvers>
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/// Solution of the Poisson equation on an irregular domain in 3D, with mixed bc's.
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/// This example will combine all the knowledge from the previous ones along with
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/// presenting XML and HDF classes
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/// that are key for I/O in bigger programs.
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using namespace mm; // NOLINT
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int main() {
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XML conf("poisson_dirichlet_3D_irregular_params.xml");
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// Obtain parameters
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double dx = conf.get<double>("num.dx");
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int n = conf.get<int>("approximations.n");
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int m = conf.get<int>("approximations.m");
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double sigma = conf.get<double>("approximations.sigma");
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BoxShape<Vec3d> box(0.0, 1.0);
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BallShape<Vec3d> s1({0.8, 0.8, 0.9}, 0.5); // sphere to subtract from the box
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DomainDiscretization <Vec3d> domain = box.discretizeBoundaryWithStep(dx);
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auto d = s1.discretizeBoundaryWithStep(dx);
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domain -= d; // subtract the domains
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// fill the interior using GeneralFill
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GeneralFill <Vec3d> fill;
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domain.fill(fill, dx);
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BasicRelax relax;
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// relax the domain
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relax.iterations(20).initialHeat(0.8).numNeighbours(3).projectionType(
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BasicRelax::DO_NOT_PROJECT);
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relax(domain, dx);
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int N = domain.size();
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domain.findSupport(FindClosest(n));
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WLS<Gaussians<Vec3d>, NoWeight<Vec3d>, ScaleToFarthest,
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Eigen::LLT<Eigen::MatrixXd>> wls({m, sigma});
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auto storage = domain.computeShapes<sh::lap>(wls);
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Eigen::SparseMatrix<double, Eigen::RowMajor> M(N, N);
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Eigen::VectorXd rhs(N); rhs.setZero();
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auto op = storage.implicitOperators(M, rhs);
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M.reserve(storage.supportSizes());
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for (int i : domain.interior()) {
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double x = domain.pos(i, 0);
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double y = domain.pos(i, 1);
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double z = domain.pos(i, 2);
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op.lap(i) = -3 * PI * PI * std::sin(PI * x) * std::sin(PI * y) * std::sin(PI * z);
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}
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for (int i : domain.boundary()) {
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op.value(i) = 0.0;
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}
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Eigen::BiCGSTAB<decltype(M), Eigen::IncompleteLUT<double>> solver;
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solver.compute(M);
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ScalarFieldd u = solver.solve(rhs);
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HDF hdf("poisson_dirichlet_3D_irregular.h5", HDF::DESTROY);
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hdf.writeDoubleArray("solution", u);
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hdf.writeDouble2DArray("positions", domain.positions());
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hdf.close();
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return 0;
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}
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