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85 lines
2.9 KiB
85 lines
2.9 KiB
#include <medusa/Medusa.hpp>
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#include <Eigen/SparseCore>
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#include <Eigen/IterativeLinearSolvers>
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/// Basic medusa example, we are solving 2D Poisson's equation on a NURBS domain
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/// with Dirichlet boundary conditions.
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/// http://e6.ijs.si/medusa/wiki/index.php/NURBS_domains
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using namespace mm; // NOLINT
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int main() {
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// Points to be used in NURBS creation.
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Range<Vec2d> pts{{210, -132.5}, {205, -115}, {125, -35}, {85, -61}, {85, -61}, {85, -61},
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{80, -65}, {75, -58}, {75, -58}, {65, 45}, {25, 25}, {-15, -16}, {-15, -16},
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{-15, -16}, {-35, -28}, {-40, -32.375}, {-40, -32.375}, {-43, -35}, {-27, -40},
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{-5, -40}, {-5, -40}, {50, -38}, {35, -65}, {15, -75}, {15, -75}, {-15, -95},
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{-20, -140}, {45, -146}, {45, -146}, {95, -150}, {215, -150}, {210, -132.5}};
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// Calculate NURBS patches' control points, weights, knot vector and order.
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int p = 3;
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Range<double> weights{1, 1, 1, 1};
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Range<double> knot_vector{0, 0, 0, 0, 1, 1, 1, 1};
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Range<NURBSPatch<Vec2d, Vec1d>> patches;
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for (int i = 0; i < 8; i++) {
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Range<Vec2d> control_points;
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for (int j = 0; j < 4; j++) {
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control_points.push_back(pts[4 * i + j]);
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}
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NURBSPatch<Vec2d, Vec1d> patch(control_points, weights, {knot_vector}, {p});
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patches.push_back(patch);
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}
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// Create NURBS shape from a range of patches.
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NURBSShape<Vec2d, Vec1d> shape(patches);
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// Fill the domain.
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double h = 0.5;
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DomainDiscretization<Vec2d> domain = shape.discretizeBoundaryWithStep(h);
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GeneralFill<Vec2d> gf;
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gf(domain, h);
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// Construct the approximation engine.
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int m = 2; // basis order
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Monomials<Vec2d> mon(m);
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RBFFD<Polyharmonic<double, 3>, Vec2d> approx({}, mon);
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// Find support for the nodes.
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int N = domain.size();
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domain.findSupport(FindClosest(mon.size()));
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// Compute the shapes (we only need the Laplacian).
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auto storage = domain.computeShapes<sh::lap>(approx);
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Eigen::SparseMatrix<double, Eigen::RowMajor> M(N, N);
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Eigen::VectorXd rhs(N);
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rhs.setZero();
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M.reserve(storage.supportSizes());
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// Construct implicit operators over our storage.
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auto op = storage.implicitOperators(M, rhs);
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for (int i : domain.interior()) {
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// set the case for nodes in the domain
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op.lap(i) = 20.0;
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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);
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// Write the solution into file.
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std::ofstream out_file("poisson_NURBS_2D_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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