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62 lines
2.2 KiB
62 lines
2.2 KiB
1 year ago
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#include <medusa/Medusa_fwd.hpp>
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#include <Eigen/SparseCore>
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#include <Eigen/Geometry>
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#include <Eigen/IterativeLinearSolvers>
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/// Basic medusa example, we are solving 3D Poisson's equation on rotated and translated unit cube
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/// with Dirichlet boundary conditions.
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/// http://e6.ijs.si/medusa/wiki/index.php/Poisson%27s_equation
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using namespace mm; // NOLINT
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int main() {
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// Create the domain and discretize it
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BoxShape <Vec3d> box(0.0, 1.0);
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double dx = 0.05;
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DomainDiscretization <Vec3d> domain = box.discretizeWithStep(dx);
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Eigen::AngleAxisd Q(PI/3, Vec3d(1, 1, 1).normalized());
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domain.rotate(Q.toRotationMatrix()).translate({-2.5, 0.4, 1.2});
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// Find support for the nodes
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int N = domain.size();
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domain.findSupport(FindClosest(9)); // the support for each node is the closest 9 nodes
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// Construct the approximation engine, in this case a weighted least squares using Gaussians
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// as basis functions, no weight, and scale to farthest
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WLS <Gaussians<Vec3d>, NoWeight<Vec3d>, ScaleToFarthest,
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Eigen::LLT<Eigen::MatrixXd>> wls({9, 30.0});
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auto storage = domain.computeShapes<sh::lap>(wls); // compute the shapes using our 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); // construct implicit operators over our storage
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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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// set the case for nodes in the domain
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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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// enforce the boundary conditions
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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); // solve the system
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// Write the solution into file
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std::ofstream out_file("poisson_dirichlet_3D_data.m");
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out_file << "positions = " << domain.positions() << ";" << std::endl;
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out_file << "solution = " << u << ";" << std::endl;
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out_file.close();
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return 0;
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}
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