test_Mesh_to_FEM.cpp 11.7 KB
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#include "test_Library_Integration.hpp"

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std::string SAVE_DIR = "./test/output/Integration/";
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TEST(Library_Integration, Full_Circle_Uniform_Current_Density) {
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    // Create Sketch
    Sketch sk;
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    auto v0 = sk.new_element<Vertex>(0.0, 0.0);
    auto v1 = sk.new_element<Vertex>(1.0, 0.0);
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    auto v2 = sk.new_element<Vertex>(1.0 * std::cos(M_PI * 2.0 / 3.0), 1.0 * std::sin(M_PI * 2.0 / 3.0));
    auto v3 = sk.new_element<Vertex>(1.0 * std::cos(-M_PI * 2.0 / 3.0), 1.0 * std::sin(-M_PI * 2.0 / 3.0));
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    auto c0 = sk.new_element<CircularArc>(v1, v2, v0, 1.0);
    auto c1 = sk.new_element<CircularArc>(v2, v3, v0, 1.0);
    auto c2 = sk.new_element<CircularArc>(v3, v1, v0, 1.0);
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    auto f0 = sk.new_element<Fixation>(v0);
    auto f1 = sk.new_element<Fixation>(v1);
    auto f2 = sk.new_element<Fixation>(v2);
    auto f3 = sk.new_element<Fixation>(v3);
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    double_t tol = sk.solve();
    EXPECT_LE(tol, FLT_EPSILON);
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    bool result = sk.build();
    EXPECT_TRUE(result);
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    EXPECT_EQ(sk.size_contours(), 1);
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    sk.save_as<SaveMethod::Rasterize>(SAVE_DIR, std::string("circle_sketch"));
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    // Create Refineable Mesh
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    Mesh me{sk};
    me.create();

    me.MinimumElementSize = 0.01;
    me.MaximumElementSize = 0.1;
    me.MinimumElementQuality = 0.5;

    me.refine();

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    me.save_as(SAVE_DIR, std::string("circle_mesh"));
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    // Convert to FiniteElementMesh
    FiniteElementMesh<2, 1> fem{me};

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    for (std::shared_ptr<Boundary<2>> const &b : fem.boundaries()) {
        double_t a0{-2 * M_PI};
        for (size_t i : b->nodes()) {
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            XY const &p = fem.node(i);

            // Test radius of boundary
            EXPECT_NEAR(1.0, std::hypot(p.x(), p.y()), FLT_EPSILON);

            // Test ordering of boundary nodes
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            double_t a1{std::atan2(p.y(), p.x())};
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            if (a1 < 0 || (a1 == 0 && a0 > M_PI)) {
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                a1 += 2 * M_PI;
            }
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            EXPECT_TRUE(a1 > a0);
            a0 = a1;
        }
    }

    // Create magnetostatic physics
    Magnetostatic<2, 1, 1, FieldVariable::A> msph{fem};

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    msph.add_current_density([](double t) { return 1.0 / (2.0 * M_PI * 1e-7); }, {fem.region(0)});
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    msph.add_magnetic_insulation({fem.boundary(0), fem.boundary(1), fem.boundary(2)});

    msph.build_matrices();

    msph.apply_conditions();

    // Initialize matrices
    auto J = msph.init_unknown_matrix();
    auto v = msph.init_unknown_vector();
    auto r = msph.init_unknown_vector();
    auto f = msph.init_unknown_vector();
    auto Fx = msph.init_element_array();
    auto Fy = msph.init_element_array();
    auto dFxdx = msph.init_element_array();
    auto dFydy = msph.init_element_array();
    auto dFxdy = msph.init_element_array();

    //
    // Set time
    msph.time(0.0);
    msph.calculate_forcing(f);
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    // Linearize
    v.setZero();
    msph.linearize(J, v, r, f, Fx, Fy, dFxdx, dFydy, dFxdy);
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    // Factor
    Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> ldlt;
    ldlt.compute(J);
    ASSERT_EQ(ldlt.info(), Eigen::Success);

    // Solve
    v -= ldlt.solve(r);

    // Test
    msph.linearize(J, v, r, f, Fx, Fy, dFxdx, dFydy, dFxdy);

    for (size_t i = 0; i != r.size(); ++i) {
        EXPECT_NEAR(r(i), 0.0, FLT_EPSILON);
    }

    // Test flux-density values
    Eigen::ArrayXd Bx = msph.derivatives().dy(0).transpose() * v;
    Eigen::ArrayXd By = -msph.derivatives().dx(0).transpose() * v;

    Eigen::ArrayXd Bmag(By.size());
    Eigen::ArrayXd Bang(By.size());

    for (size_t i = 0; i != By.size(); ++i) {
        Bmag(i) = hypot(Bx(i), By(i));
        Bang(i) = atan2(By(i), Bx(i)) * 180.0 / M_PI;
    }

    std::vector<std::vector<XY>> qp = fem.quadrature_points<1>();

    for (size_t i = 0; i != qp.size(); ++i) {
        double_t r = std::hypot(qp[i][0].x(), qp[i][0].y());

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        EXPECT_NEAR(Bmag(i), r, 1.0 * 0.05);
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        double_t a = std::atan2(qp[i][0].y(), qp[i][0].x()) * 180 / M_PI + 90.0;

        if (a > 180.0) { a -= 360.0; }
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        if (a - Bang(i) > 180.0) { a -= 360.0; }
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        if (a - Bang(i) < -180.0) { a += 360.0; }
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        EXPECT_NEAR(Bang(i), a, 360 * 0.05);
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    }
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}

TEST(Library_Integration, Quadrter_Circle_Mirror_Copy_Uniform_Current_Density) {
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    GTEST_NONFATAL_FAILURE_("TODO: antiperiodic boundary conditions");

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    // Create Sketch
    Sketch sk;

    auto v0 = sk.new_element<Vertex>(0.0, 0.0);
    auto v1 = sk.new_element<Vertex>(1.0, 0.0);
    auto v2 = sk.new_element<Vertex>(2.0, 0.0);
    auto v3 = sk.new_element<Vertex>(M_SQRT1_2, M_SQRT1_2);
    auto v4 = sk.new_element<Vertex>(M_SQRT2, M_SQRT2);

    auto f0 = sk.new_element<Fixation>(v0);

    auto l01 = sk.new_element<LineSegment>(v0, v1);
    auto l12 = sk.new_element<LineSegment>(v1, v2);

    auto l04 = sk.new_element<LineSegment>(v0, v4, true);

    auto h01 = sk.new_element<Horizontal>(l01);
    auto h12 = sk.new_element<Horizontal>(l12);

    auto a0103 = sk.new_element<Angle>(l01, l04, 45.0);

    auto c013 = sk.new_element<CircularArc>(v1, v3, v0, 1.0);
    auto c024 = sk.new_element<CircularArc>(v2, v4, v0, 2.0);

    auto r013 = sk.new_element<Radius>(c013, 1.0);
    auto r024 = sk.new_element<Radius>(c024, 2.0);

    std::vector<std::shared_ptr<Curve const>> vec{l01, l12, c013, c024};
    auto m04 = sk.new_element<MirrorCopy>(vec, l04);

    double residual = sk.solve();
    EXPECT_LE(residual, FLT_EPSILON);

    bool result = sk.build();
    ASSERT_TRUE(result);

    sk.save_as<SaveMethod::Rasterize>(SAVE_DIR, "quarter_circle_mirror_copy_sketch");

    auto periodic_boundary = sk.select_periodic_boundary_pairs(v0, 90.0);
    {
        for (auto &bp : periodic_boundary) {
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            if (bp.curve0().get() == l01.get()) {
                EXPECT_EQ(bp.curve1()->is_identical(l01, v0, 90.0), MatchOrientation::Reverse);
            } else if (bp.curve0().get() == l12.get()) {
                EXPECT_EQ(bp.curve1()->is_identical(l12, v0, 90.0), MatchOrientation::Reverse);
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            } else {
                GTEST_NONFATAL_FAILURE_("No matching boundary found");
            }
        }
    }

    auto radial_boundary = sk.select_radial_boundary(v0, 2.0);
    {
        for (auto &c : radial_boundary) {
            auto cc = std::dynamic_pointer_cast<CircularArc const>(c);
            if (cc) {
                EXPECT_NEAR(cc->radius(), 2.0, FLT_EPSILON);
                EXPECT_EQ(cc->center().get(), v0.get());
            } else {
                GTEST_NONFATAL_FAILURE_("dynamic_cast of Curve to CircularArc failed");
            }
        }
    }

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    auto v1p = sk.select_periodic_vertex(v1, v0, 90.0);
    {
        ASSERT_TRUE(v1p); // Make sure that returned vertex pointer is not null
        double_t x0 = v0->x();
        double_t y0 = v0->y();
        double_t x1 = v1->x();
        double_t y1 = v1->y();
        double_t x2 = v1p->x();
        double_t y2 = v1p->y();

        double_t dx = x1 - x0;
        double_t dy = y1 - y0;
        double_t dr = std::hypot(dx, dy);
        double_t da = std::atan2(dy, dx);

        da += M_PI / 2.0;
        x1 = x0 + dr * std::cos(da);
        y1 = y0 + dr * std::sin(da);

        EXPECT_NEAR(x1, x2, dr * FLT_EPSILON);
        EXPECT_NEAR(y1, y2, dr * FLT_EPSILON);
    }
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    // Create Mesh
    Mesh me{sk};
    me.create();

    me.MaximumElementSize = 0.1;
    me.MinimumElementSize = 0.01;
    me.MinimumElementQuality = 0.5;

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    for (auto &pb : periodic_boundary) {
        auto bc0 = me.boundary_constraint(pb.curve0());
        if (bc0) {
            bc0->uniform_discretization(true);
        } else {
            GTEST_NONFATAL_FAILURE_("No matching boundary found.");
        }

        auto bc1 = me.boundary_constraint(pb.curve1());
        if (bc1) {
            bc1->uniform_discretization(true);
        } else {
            GTEST_NONFATAL_FAILURE_("No matching boundary found.");
        }
    }

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    result = me.refine();
    ASSERT_TRUE(result);

    me.save_as(SAVE_DIR, std::string("quarter_circle_mirror_copy_mesh"));
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    // Create FiniteElementMesh
    FiniteElementMesh<2,1> fem{me};

    for (auto & pb : periodic_boundary) {
        auto const &nodes0 = fem.boundary(pb.curve0())->nodes();
        auto const &nodes1 = fem.boundary(pb.curve1())->nodes();

        for (size_t i = 0; i != nodes0.size(); ++i) {
            auto const &n0 = fem.node(nodes0[i]);
            auto const &n1 = fem.node(nodes1[nodes0.size() - 1 - i]);

            EXPECT_NEAR(n0.y(), 0.0, FLT_EPSILON);
            EXPECT_NEAR(n1.x(), 0.0, FLT_EPSILON);
            EXPECT_NEAR(n0.x(), n1.y(), FLT_EPSILON);
        }
    }

    // Create Physics
    Magnetostatic<2, 1, 1, FieldVariable::A> msph{fem};

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    // TODO: Need a method for selecting Contour from Sketch and selecting FiniteElementMesh Region<2> given a contour
    // TODO: Add std::shared_ptr<Contour const> to Region<2>
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    GTEST_NONFATAL_FAILURE_("TODO: region selection");
    msph.add_current_density([](double t) { return 1.0 / (2.0 * M_PI * 1e-7); }, {fem.region(1)});
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    msph.add_magnetic_insulation(radial_boundary);
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    msph.add_periodic_boundary(periodic_boundary, false);
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    msph.build_matrices();

    msph.apply_conditions();

    auto J = msph.init_unknown_matrix();
    auto v = msph.init_unknown_vector();
    auto r = msph.init_unknown_vector();
    auto f = msph.init_unknown_vector();
    auto Fx = msph.init_element_array();
    auto Fy = msph.init_element_array();
    auto dFxdx = msph.init_element_array();
    auto dFydy = msph.init_element_array();
    auto dFxdy = msph.init_element_array();

    v.setZero();

    msph.calculate_forcing(f);

    msph.linearize(J, v, r, f, Fx, Fy, dFxdx, dFydy, dFxdy);

    Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> ldlt;
    ldlt.compute(J);
    ASSERT_EQ(ldlt.info(), Eigen::Success);
    v -= ldlt.solve(r);

    // Verify equation is solved
    msph.linearize(J, v, r, f, Fx, Fy, dFxdx, dFydy, dFxdy);
    for (size_t i = 0; i != r.size(); ++i) {
        EXPECT_NEAR(r(i), 0.0, FLT_EPSILON);
    }

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    // Test solution:
    // A = a_f * r^2 + c_f in forced inner region
    // A = a_h * log(r) + c_h in homogeneous outer region
    Eigen::VectorXd vv = msph.recover_boundary(v);

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    fem.write_scalar(vv, SAVE_DIR, std::string("quarter_circle_mvp"));

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    double_t a_f = -0.5;
    double_t c_f = -2.0 * a_f * std::log(2.0) - a_f;
    double_t a_h = 2 * a_f;
    double_t c_h = -2.0 * a_f * log(2.0);
    for(size_t i = 0; i!= fem.size_nodes(); ++i) {
        XY const &n = fem.node(i);
        double_t r = std::hypot(n.x(), n.y());
        if (r <= 1.0) {
            double_t val = a_f * r * r + c_f;
            EXPECT_NEAR(val, vv(i), c_f * 0.01);
        } else {
            double_t val = a_h * log(r) + c_h;
            EXPECT_NEAR(val, vv(i), c_h * 0.01);
        }
    }

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    // Test flux-density values
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    // B_r = 2 * a_f * r in forced inner region
    // B_r = a_h / r in homogenous outer region
    // TODO: The correct way to test may be to calculate average flux in the element from analytical solution
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    Eigen::ArrayXd Bx = msph.derivatives().dy(0).transpose() * v;
    Eigen::ArrayXd By = -msph.derivatives().dx(0).transpose() * v;

    Eigen::ArrayXd Bmag(By.size());
    Eigen::ArrayXd Bang(By.size());

    for (size_t i = 0; i != By.size(); ++i) {
        Bmag(i) = hypot(Bx(i), By(i));
        Bang(i) = atan2(By(i), Bx(i)) * 180.0 / M_PI;
    }

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    std::vector<std::vector<XY>> qp = fem.quadrature_points<1>();
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    for (size_t i = 0; i != qp.size(); ++i) {
        double_t r = std::hypot(qp[i][0].x(), qp[i][0].y());
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        if (r <= 1) {
            double_t val = std::abs(2.0 * a_f * r);
            EXPECT_NEAR(Bmag(i), val, std::abs(2 * a_f * 0.05));
        } else {
            double_t val = std::abs(a_h / r);
            EXPECT_NEAR(Bmag(i), val, std::abs(a_h* 0.05));
        }
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        double_t a = std::atan2(qp[i][0].y(), qp[i][0].x()) * 180 / M_PI + 90.0;
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        if (Bang(i) < 0.0) { Bang(i) += 360.0; };
        EXPECT_NEAR(Bang(i), a, 90 * 0.05);
    }
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}