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rGOOSEFEM/test/basic/MeshQuad4.cpp
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MeshQuad4.cpp
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#include <catch2/catch.hpp>
#include <xtensor/xrandom.hpp>
#include <xtensor/xmath.hpp>
#include <GooseFEM/GooseFEM.h>
#define ISCLOSE(a,b) REQUIRE_THAT((a), Catch::WithinAbs((b), 1.e-12));
TEST_CASE("GooseFEM::MeshQuad4", "MeshQuad4.h")
{
SECTION("Regular")
{
xt::xtensor<double, 2> coor_ = {{0., 0.}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.},
{0., 1.}, {1., 1.}, {2., 1.}, {3., 1.}, {4., 1.}, {5., 1.},
{0., 2.}, {1., 2.}, {2., 2.}, {3., 2.}, {4., 2.}, {5., 2.},
{0., 3.}, {1., 3.}, {2., 3.}, {3., 3.}, {4., 3.}, {5., 3.}};
xt::xtensor<double, 2> conn_ = {{0, 1, 7, 6},
{1, 2, 8, 7},
{2, 3, 9, 8},
{3, 4, 10, 9},
{4, 5, 11, 10},
{6, 7, 13, 12},
{7, 8, 14, 13},
{8, 9, 15, 14},
{9, 10, 16, 15},
{10, 11, 17, 16},
{12, 13, 19, 18},
{13, 14, 20, 19},
{14, 15, 21, 20},
{15, 16, 22, 21},
{16, 17, 23, 22}};
size_t nelem_ = 15;
size_t nnode_ = 24;
size_t nne_ = 4;
size_t ndim_ = 2;
size_t nnodePeriodic_ = 15;
xt::xtensor<size_t, 1> nodesBottomEdge_ = {0, 1, 2, 3, 4, 5};
xt::xtensor<size_t, 1> nodesTopEdge_ = {18, 19, 20, 21, 22, 23};
xt::xtensor<size_t, 1> nodesLeftEdge_ = {0, 6, 12, 18};
xt::xtensor<size_t, 1> nodesRightEdge_ = {5, 11, 17, 23};
xt::xtensor<size_t, 1> nodesBottomOpenEdge_ = {1, 2, 3, 4};
xt::xtensor<size_t, 1> nodesTopOpenEdge_ = {19, 20, 21, 22};
xt::xtensor<size_t, 1> nodesLeftOpenEdge_ = {6, 12};
xt::xtensor<size_t, 1> nodesRightOpenEdge_ = {11, 17};
size_t nodesBottomLeftCorner_ = 0;
size_t nodesBottomRightCorner_ = 5;
size_t nodesTopLeftCorner_ = 18;
size_t nodesTopRightCorner_ = 23;
size_t nodesLeftBottomCorner_ = 0;
size_t nodesLeftTopCorner_ = 18;
size_t nodesRightBottomCorner_ = 5;
size_t nodesRightTopCorner_ = 23;
xt::xtensor<size_t, 2> dofs_ = {{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {10, 11},
{12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23},
{24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {34, 35},
{36, 37}, {38, 39}, {40, 41}, {42, 43}, {44, 45}, {46, 47}};
xt::xtensor<size_t, 2> nodesPeriodic_ = {
{0, 5}, {0, 23}, {0, 18}, {1, 19}, {2, 20}, {3, 21}, {4, 22}, {6, 11}, {12, 17}};
size_t nodesOrigin_ = 0;
xt::xtensor<size_t, 2> dofsPeriodic_ = {
{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {0, 1}, {10, 11}, {12, 13},
{14, 15}, {16, 17}, {18, 19}, {10, 11}, {20, 21}, {22, 23}, {24, 25}, {26, 27},
{28, 29}, {20, 21}, {0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {0, 1}};
GooseFEM::Mesh::Quad4::Regular mesh(5, 3);
xt::xtensor<double, 2> coor = mesh.coor();
xt::xtensor<size_t, 2> conn = mesh.conn();
size_t nelem = mesh.nelem();
size_t nnode = mesh.nnode();
size_t nne = mesh.nne();
size_t ndim = mesh.ndim();
size_t nnodePeriodic = mesh.nnode() - mesh.nodesPeriodic().shape(0);
xt::xtensor<size_t, 1> nodesBottomEdge = mesh.nodesBottomEdge();
xt::xtensor<size_t, 1> nodesTopEdge = mesh.nodesTopEdge();
xt::xtensor<size_t, 1> nodesLeftEdge = mesh.nodesLeftEdge();
xt::xtensor<size_t, 1> nodesRightEdge = mesh.nodesRightEdge();
xt::xtensor<size_t, 1> nodesBottomOpenEdge = mesh.nodesBottomOpenEdge();
xt::xtensor<size_t, 1> nodesTopOpenEdge = mesh.nodesTopOpenEdge();
xt::xtensor<size_t, 1> nodesLeftOpenEdge = mesh.nodesLeftOpenEdge();
xt::xtensor<size_t, 1> nodesRightOpenEdge = mesh.nodesRightOpenEdge();
size_t nodesBottomLeftCorner = mesh.nodesBottomLeftCorner();
size_t nodesBottomRightCorner = mesh.nodesBottomRightCorner();
size_t nodesTopLeftCorner = mesh.nodesTopLeftCorner();
size_t nodesTopRightCorner = mesh.nodesTopRightCorner();
size_t nodesLeftBottomCorner = mesh.nodesLeftBottomCorner();
size_t nodesLeftTopCorner = mesh.nodesLeftTopCorner();
size_t nodesRightBottomCorner = mesh.nodesRightBottomCorner();
size_t nodesRightTopCorner = mesh.nodesRightTopCorner();
xt::xtensor<size_t, 2> dofs = mesh.dofs();
xt::xtensor<size_t, 2> nodesPeriodic = mesh.nodesPeriodic();
size_t nodesOrigin = mesh.nodesOrigin();
xt::xtensor<size_t, 2> dofsPeriodic = mesh.dofsPeriodic();
REQUIRE(nelem == nelem_);
REQUIRE(nnode == nnode_);
REQUIRE(nne == nne_);
REQUIRE(ndim == ndim_);
REQUIRE(nnodePeriodic == nnodePeriodic_);
REQUIRE(nodesBottomLeftCorner == nodesBottomLeftCorner_);
REQUIRE(nodesBottomRightCorner == nodesBottomRightCorner_);
REQUIRE(nodesTopLeftCorner == nodesTopLeftCorner_);
REQUIRE(nodesTopRightCorner == nodesTopRightCorner_);
REQUIRE(nodesLeftBottomCorner == nodesLeftBottomCorner_);
REQUIRE(nodesLeftTopCorner == nodesLeftTopCorner_);
REQUIRE(nodesRightBottomCorner == nodesRightBottomCorner_);
REQUIRE(nodesRightTopCorner == nodesRightTopCorner_);
REQUIRE(nodesOrigin == nodesOrigin_);
REQUIRE(xt::allclose(coor, coor_));
REQUIRE(xt::all(xt::equal(conn, conn_)));
REQUIRE(xt::all(xt::equal(nodesBottomEdge, nodesBottomEdge_)));
REQUIRE(xt::all(xt::equal(nodesTopEdge, nodesTopEdge_)));
REQUIRE(xt::all(xt::equal(nodesLeftEdge, nodesLeftEdge_)));
REQUIRE(xt::all(xt::equal(nodesRightEdge, nodesRightEdge_)));
REQUIRE(xt::all(xt::equal(nodesBottomOpenEdge, nodesBottomOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesTopOpenEdge, nodesTopOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesLeftOpenEdge, nodesLeftOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesRightOpenEdge, nodesRightOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesPeriodic, nodesPeriodic_)));
REQUIRE(xt::all(xt::equal(dofsPeriodic, dofsPeriodic_)));
}
SECTION("FineLayer")
{
xt::xtensor<double, 2> coor_ = {
{0., 0.}, {3., 0.}, {6., 0.}, {9., 0.}, {0., 3.}, {3., 3.}, {6., 3.}, {9., 3.},
{0., 6.}, {3., 6.}, {6., 6.}, {9., 6.}, {1., 7.}, {2., 7.}, {4., 7.}, {5., 7.},
{7., 7.}, {8., 7.}, {0., 8.}, {1., 8.}, {2., 8.}, {3., 8.}, {4., 8.}, {5., 8.},
{6., 8.}, {7., 8.}, {8., 8.}, {9., 8.}, {0., 9.}, {1., 9.}, {2., 9.}, {3., 9.},
{4., 9.}, {5., 9.}, {6., 9.}, {7., 9.}, {8., 9.}, {9., 9.}, {0., 10.}, {1., 10.},
{2., 10.}, {3., 10.}, {4., 10.}, {5., 10.}, {6., 10.}, {7., 10.}, {8., 10.}, {9., 10.},
{0., 11.}, {1., 11.}, {2., 11.}, {3., 11.}, {4., 11.}, {5., 11.}, {6., 11.}, {7., 11.},
{8., 11.}, {9., 11.}, {0., 12.}, {1., 12.}, {2., 12.}, {3., 12.}, {4., 12.}, {5., 12.},
{6., 12.}, {7., 12.}, {8., 12.}, {9., 12.}, {0., 13.}, {1., 13.}, {2., 13.}, {3., 13.},
{4., 13.}, {5., 13.}, {6., 13.}, {7., 13.}, {8., 13.}, {9., 13.}, {1., 14.}, {2., 14.},
{4., 14.}, {5., 14.}, {7., 14.}, {8., 14.}, {0., 15.}, {3., 15.}, {6., 15.}, {9., 15.},
{0., 18.}, {3., 18.}, {6., 18.}, {9., 18.}, {0., 21.}, {3., 21.}, {6., 21.}, {9., 21.}};
xt::xtensor<double, 2> conn_ = {
{0, 1, 5, 4}, {1, 2, 6, 5}, {2, 3, 7, 6}, {4, 5, 9, 8},
{5, 6, 10, 9}, {6, 7, 11, 10}, {8, 9, 13, 12}, {9, 21, 20, 13},
{12, 13, 20, 19}, {8, 12, 19, 18}, {9, 10, 15, 14}, {10, 24, 23, 15},
{14, 15, 23, 22}, {9, 14, 22, 21}, {10, 11, 17, 16}, {11, 27, 26, 17},
{16, 17, 26, 25}, {10, 16, 25, 24}, {18, 19, 29, 28}, {19, 20, 30, 29},
{20, 21, 31, 30}, {21, 22, 32, 31}, {22, 23, 33, 32}, {23, 24, 34, 33},
{24, 25, 35, 34}, {25, 26, 36, 35}, {26, 27, 37, 36}, {28, 29, 39, 38},
{29, 30, 40, 39}, {30, 31, 41, 40}, {31, 32, 42, 41}, {32, 33, 43, 42},
{33, 34, 44, 43}, {34, 35, 45, 44}, {35, 36, 46, 45}, {36, 37, 47, 46},
{38, 39, 49, 48}, {39, 40, 50, 49}, {40, 41, 51, 50}, {41, 42, 52, 51},
{42, 43, 53, 52}, {43, 44, 54, 53}, {44, 45, 55, 54}, {45, 46, 56, 55},
{46, 47, 57, 56}, {48, 49, 59, 58}, {49, 50, 60, 59}, {50, 51, 61, 60},
{51, 52, 62, 61}, {52, 53, 63, 62}, {53, 54, 64, 63}, {54, 55, 65, 64},
{55, 56, 66, 65}, {56, 57, 67, 66}, {58, 59, 69, 68}, {59, 60, 70, 69},
{60, 61, 71, 70}, {61, 62, 72, 71}, {62, 63, 73, 72}, {63, 64, 74, 73},
{64, 65, 75, 74}, {65, 66, 76, 75}, {66, 67, 77, 76}, {68, 69, 78, 84},
{69, 70, 79, 78}, {70, 71, 85, 79}, {78, 79, 85, 84}, {71, 72, 80, 85},
{72, 73, 81, 80}, {73, 74, 86, 81}, {80, 81, 86, 85}, {74, 75, 82, 86},
{75, 76, 83, 82}, {76, 77, 87, 83}, {82, 83, 87, 86}, {84, 85, 89, 88},
{85, 86, 90, 89}, {86, 87, 91, 90}, {88, 89, 93, 92}, {89, 90, 94, 93},
{90, 91, 95, 94}};
size_t nelem_ = 81;
size_t nnode_ = 96;
size_t nne_ = 4;
size_t ndim_ = 2;
size_t shape_x_ = 9;
size_t shape_y_ = 21;
xt::xtensor<size_t, 1> elementsMiddleLayer_ = {36, 37, 38, 39, 40, 41, 42, 43, 44};
xt::xtensor<size_t, 1> nodesBottomEdge_ = {0, 1, 2, 3};
xt::xtensor<size_t, 1> nodesTopEdge_ = {92, 93, 94, 95};
xt::xtensor<size_t, 1> nodesLeftEdge_ = {0, 4, 8, 18, 28, 38, 48, 58, 68, 84, 88, 92};
xt::xtensor<size_t, 1> nodesRightEdge_ = {3, 7, 11, 27, 37, 47, 57, 67, 77, 87, 91, 95};
xt::xtensor<size_t, 1> nodesBottomOpenEdge_ = {1, 2};
xt::xtensor<size_t, 1> nodesTopOpenEdge_ = {93, 94};
xt::xtensor<size_t, 1> nodesLeftOpenEdge_ = {4, 8, 18, 28, 38, 48, 58, 68, 84, 88};
xt::xtensor<size_t, 1> nodesRightOpenEdge_ = {7, 11, 27, 37, 47, 57, 67, 77, 87, 91};
size_t nodesBottomLeftCorner_ = 0;
size_t nodesBottomRightCorner_ = 3;
size_t nodesTopLeftCorner_ = 92;
size_t nodesTopRightCorner_ = 95;
size_t nodesLeftBottomCorner_ = 0;
size_t nodesLeftTopCorner_ = 92;
size_t nodesRightBottomCorner_ = 3;
size_t nodesRightTopCorner_ = 95;
xt::xtensor<size_t, 2> dofs_ = {
{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13},
{14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {26, 27},
{28, 29}, {30, 31}, {32, 33}, {34, 35}, {36, 37}, {38, 39}, {40, 41},
{42, 43}, {44, 45}, {46, 47}, {48, 49}, {50, 51}, {52, 53}, {54, 55},
{56, 57}, {58, 59}, {60, 61}, {62, 63}, {64, 65}, {66, 67}, {68, 69},
{70, 71}, {72, 73}, {74, 75}, {76, 77}, {78, 79}, {80, 81}, {82, 83},
{84, 85}, {86, 87}, {88, 89}, {90, 91}, {92, 93}, {94, 95}, {96, 97},
{98, 99}, {100, 101}, {102, 103}, {104, 105}, {106, 107}, {108, 109}, {110, 111},
{112, 113}, {114, 115}, {116, 117}, {118, 119}, {120, 121}, {122, 123}, {124, 125},
{126, 127}, {128, 129}, {130, 131}, {132, 133}, {134, 135}, {136, 137}, {138, 139},
{140, 141}, {142, 143}, {144, 145}, {146, 147}, {148, 149}, {150, 151}, {152, 153},
{154, 155}, {156, 157}, {158, 159}, {160, 161}, {162, 163}, {164, 165}, {166, 167},
{168, 169}, {170, 171}, {172, 173}, {174, 175}, {176, 177}, {178, 179}, {180, 181},
{182, 183}, {184, 185}, {186, 187}, {188, 189}, {190, 191}};
xt::xtensor<size_t, 2> nodesPeriodic_ = {{0, 3},
{0, 95},
{0, 92},
{1, 93},
{2, 94},
{4, 7},
{8, 11},
{18, 27},
{28, 37},
{38, 47},
{48, 57},
{58, 67},
{68, 77},
{84, 87},
{88, 91}};
size_t nodesOrigin_ = 0;
xt::xtensor<size_t, 2> dofsPeriodic_ = {
{0, 1}, {2, 3}, {4, 5}, {0, 1}, {6, 7}, {8, 9}, {10, 11},
{6, 7}, {12, 13}, {14, 15}, {16, 17}, {12, 13}, {18, 19}, {20, 21},
{22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {34, 35},
{36, 37}, {38, 39}, {40, 41}, {42, 43}, {44, 45}, {46, 47}, {30, 31},
{48, 49}, {50, 51}, {52, 53}, {54, 55}, {56, 57}, {58, 59}, {60, 61},
{62, 63}, {64, 65}, {48, 49}, {66, 67}, {68, 69}, {70, 71}, {72, 73},
{74, 75}, {76, 77}, {78, 79}, {80, 81}, {82, 83}, {66, 67}, {84, 85},
{86, 87}, {88, 89}, {90, 91}, {92, 93}, {94, 95}, {96, 97}, {98, 99},
{100, 101}, {84, 85}, {102, 103}, {104, 105}, {106, 107}, {108, 109}, {110, 111},
{112, 113}, {114, 115}, {116, 117}, {118, 119}, {102, 103}, {120, 121}, {122, 123},
{124, 125}, {126, 127}, {128, 129}, {130, 131}, {132, 133}, {134, 135}, {136, 137},
{120, 121}, {138, 139}, {140, 141}, {142, 143}, {144, 145}, {146, 147}, {148, 149},
{150, 151}, {152, 153}, {154, 155}, {150, 151}, {156, 157}, {158, 159}, {160, 161},
{156, 157}, {0, 1}, {2, 3}, {4, 5}, {0, 1}};
GooseFEM::Mesh::Quad4::FineLayer mesh(9, 18);
xt::xtensor<double, 2> coor = mesh.coor();
xt::xtensor<size_t, 2> conn = mesh.conn();
size_t nelem = mesh.nelem();
size_t nnode = mesh.nnode();
size_t nne = mesh.nne();
size_t ndim = mesh.ndim();
size_t shape_x = mesh.nelx();
size_t shape_y = mesh.nely();
xt::xtensor<size_t, 1> elementsMiddleLayer = mesh.elementsMiddleLayer();
xt::xtensor<size_t, 1> nodesBottomEdge = mesh.nodesBottomEdge();
xt::xtensor<size_t, 1> nodesTopEdge = mesh.nodesTopEdge();
xt::xtensor<size_t, 1> nodesLeftEdge = mesh.nodesLeftEdge();
xt::xtensor<size_t, 1> nodesRightEdge = mesh.nodesRightEdge();
xt::xtensor<size_t, 1> nodesBottomOpenEdge = mesh.nodesBottomOpenEdge();
xt::xtensor<size_t, 1> nodesTopOpenEdge = mesh.nodesTopOpenEdge();
xt::xtensor<size_t, 1> nodesLeftOpenEdge = mesh.nodesLeftOpenEdge();
xt::xtensor<size_t, 1> nodesRightOpenEdge = mesh.nodesRightOpenEdge();
size_t nodesBottomLeftCorner = mesh.nodesBottomLeftCorner();
size_t nodesBottomRightCorner = mesh.nodesBottomRightCorner();
size_t nodesTopLeftCorner = mesh.nodesTopLeftCorner();
size_t nodesTopRightCorner = mesh.nodesTopRightCorner();
size_t nodesLeftBottomCorner = mesh.nodesLeftBottomCorner();
size_t nodesLeftTopCorner = mesh.nodesLeftTopCorner();
size_t nodesRightBottomCorner = mesh.nodesRightBottomCorner();
size_t nodesRightTopCorner = mesh.nodesRightTopCorner();
xt::xtensor<size_t, 2> dofs = mesh.dofs();
xt::xtensor<size_t, 2> nodesPeriodic = mesh.nodesPeriodic();
size_t nodesOrigin = mesh.nodesOrigin();
xt::xtensor<size_t, 2> dofsPeriodic = mesh.dofsPeriodic();
REQUIRE(nelem == nelem_);
REQUIRE(nnode == nnode_);
REQUIRE(nne == nne_);
REQUIRE(ndim == ndim_);
REQUIRE(shape_x == shape_x_);
REQUIRE(shape_y == shape_y_);
REQUIRE(nodesBottomLeftCorner == nodesBottomLeftCorner_);
REQUIRE(nodesBottomRightCorner == nodesBottomRightCorner_);
REQUIRE(nodesTopLeftCorner == nodesTopLeftCorner_);
REQUIRE(nodesTopRightCorner == nodesTopRightCorner_);
REQUIRE(nodesLeftBottomCorner == nodesLeftBottomCorner_);
REQUIRE(nodesLeftTopCorner == nodesLeftTopCorner_);
REQUIRE(nodesRightBottomCorner == nodesRightBottomCorner_);
REQUIRE(nodesRightTopCorner == nodesRightTopCorner_);
REQUIRE(nodesOrigin == nodesOrigin_);
REQUIRE(xt::allclose(coor, coor_));
REQUIRE(xt::all(xt::equal(elementsMiddleLayer, elementsMiddleLayer_)));
REQUIRE(xt::all(xt::equal(conn, conn_)));
REQUIRE(xt::all(xt::equal(nodesBottomEdge, nodesBottomEdge_)));
REQUIRE(xt::all(xt::equal(nodesTopEdge, nodesTopEdge_)));
REQUIRE(xt::all(xt::equal(nodesLeftEdge, nodesLeftEdge_)));
REQUIRE(xt::all(xt::equal(nodesRightEdge, nodesRightEdge_)));
REQUIRE(xt::all(xt::equal(nodesBottomOpenEdge, nodesBottomOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesTopOpenEdge, nodesTopOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesLeftOpenEdge, nodesLeftOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesRightOpenEdge, nodesRightOpenEdge_)));
REQUIRE(xt::all(xt::equal(nodesPeriodic, nodesPeriodic_)));
REQUIRE(xt::all(xt::equal(dofsPeriodic, dofsPeriodic_)));
}
SECTION("Map::RefineRegular")
{
GooseFEM::Mesh::Quad4::Regular mesh(5, 4);
GooseFEM::Mesh::Quad4::Map::RefineRegular refine(mesh, 5, 3);
xt::xtensor<double, 1> a = xt::random::rand<double>({mesh.nelem()});
auto a_ = refine.mapToCoarse(refine.mapToFine(a));
REQUIRE(xt::allclose(a, xt::mean(a_, {1})));
xt::xtensor<double, 2> b =
xt::random::rand<double>(std::array<size_t, 2>{mesh.nelem(), 4ul});
auto b_ = refine.mapToCoarse(refine.mapToFine(b));
REQUIRE(xt::allclose(xt::mean(b, {1}), xt::mean(b_, {1})));
xt::xtensor<double, 4> c =
xt::random::rand<double>(std::array<size_t, 4>{mesh.nelem(), 4ul, 3ul, 3ul});
auto c_ = refine.mapToCoarse(refine.mapToFine(c));
REQUIRE(xt::allclose(xt::mean(c, {1}), xt::mean(c_, {1})));
}
SECTION("Map::FineLayer2Regular")
{
GooseFEM::Mesh::Quad4::FineLayer mesh(5, 5);
GooseFEM::Mesh::Quad4::Map::FineLayer2Regular map(mesh);
xt::xtensor<double, 1> a = xt::random::rand<double>({mesh.nelem()});
auto a_ = map.mapToRegular(a);
REQUIRE(xt::allclose(a, a_));
xt::xtensor<double, 2> b =
xt::random::rand<double>(std::array<size_t, 2>{mesh.nelem(), 4ul});
auto b_ = map.mapToRegular(b);
REQUIRE(xt::allclose(b, b_));
xt::xtensor<double, 4> c =
xt::random::rand<double>(std::array<size_t, 4>{mesh.nelem(), 4ul, 3ul, 3ul});
auto c_ = map.mapToRegular(c);
REQUIRE(xt::allclose(c, c_));
}
}
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