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UnitTestMasterElements.C
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UnitTestMasterElements.C
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#include <gtest/gtest.h>
#include <limits>
#include <stk_util/parallel/Parallel.hpp>
#include <stk_mesh/base/MetaData.hpp>
#include <stk_mesh/base/BulkData.hpp>
#include <stk_mesh/base/Bucket.hpp>
#include <stk_mesh/base/CoordinateSystems.hpp>
#include <stk_mesh/base/FieldBase.hpp>
#include <stk_mesh/base/Field.hpp>
#include <stk_mesh/base/GetEntities.hpp>
#include <master_element/MasterElement.h>
#include <master_element/MasterElementFactory.h>
#include <master_element/Quad42DCVFEM.h>
#include <master_element/Pyr5CVFEM.h>
#include <master_element/TensorOps.h>
#include <memory>
#include <random>
#include "UnitTestUtils.h"
namespace {
TEST(pyramid, is_in_element)
{
std::array<double,15> coords = {{
4.2, 4.2, 4.2, 4.2, 3.5,
5.6, 7.0, 7.0, 5.6, 6.3,
2.8, 2.8, 1.4, 1.4, 2.1
}};
std::array<double,3> point = {{3.5, 6.5, 1.5}};
std::array<double,3> mePt;
auto dist = sierra::nalu::PyrSCS().isInElement(coords.data(), point.data(), mePt.data());
ASSERT_TRUE(std::isfinite(dist));
}
using VectorFieldType = stk::mesh::Field<double, stk::mesh::Cartesian>;
//-------------------------------------------------------------------------
double linear_scalar_value(int dim, double a, const double* b, const double* x)
{
if (dim == 2u) {
return (a + b[0] * x[0] + b[1] * x[1]);
}
return (a + b[0] * x[0] + b[1] * x[1] + b[2] * x[2]);
}
//-------------------------------------------------------------------------
struct LinearField
{
LinearField(int in_dim, double in_a, const double* in_b) : dim(in_dim), a(in_a) {
b[0] = in_b[0];
b[1] = in_b[1];
if (dim == 3) b[2] = in_b[2];
}
double operator()(const double* x) { return linear_scalar_value(dim, a, b, x); }
const int dim;
const double a;
double b[3];
};
LinearField make_random_linear_field(int dim, std::mt19937& rng)
{
std::uniform_real_distribution<double> coeff(-1.0, 1.0);
std::vector<double> coeffs(dim);
double a = coeff(rng);
for (int j = 0; j < dim; ++j) {
coeffs[j] = coeff(rng);
}
return LinearField(dim, a, coeffs.data());
}
//-------------------------------------------------------------------------
void check_interpolation_at_ips(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
// Check that we can interpolate a random 3D polynomial
// to the integration points
int dim = me.nDim_;
std::mt19937 rng;
rng.seed(0);
auto linField = make_random_linear_field(dim,rng);
const auto& intgLoc = me.integration_locations();
std::vector<double> polyResult(me.num_integration_points());
for (int j = 0; j < me.num_integration_points(); ++j) {
polyResult[j] = linField(&intgLoc[j*dim]);
}
std::vector<double> ws_field(me.nodesPerElement_);
for (int j = 0; j < me.nodesPerElement_; ++j) {
ws_field[j] = linField(stk::mesh::field_data(coordField, node_rels[j]));
}
std::vector<double> meResult(me.num_integration_points(), 0.0);
std::vector<double> meShapeFunctions(me.nodesPerElement_ * me.num_integration_points());
me.shape_fcn(meShapeFunctions.data());
for (int j = 0; j < me.num_integration_points(); ++j) {
for (int i = 0; i < me.nodesPerElement_; ++i) {
meResult[j] += meShapeFunctions[j*me.nodesPerElement_+i] * ws_field[i];
}
}
for (unsigned j = 0 ; j < meResult.size(); ++j) {
EXPECT_NEAR(meResult[j], polyResult[j], tol);
}
}
//-------------------------------------------------------------------------
void check_derivatives_at_ips(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
// Check that we can interpolate a random 3D linear field
int dim = me.nDim_;
std::mt19937 rng;
rng.seed(0);
auto linField = make_random_linear_field(dim,rng);
std::vector<double> polyResult(me.num_integration_points() * dim);
for (int j = 0; j < me.num_integration_points(); ++j) {
for (int d = 0; d < dim; ++d) {
polyResult[j*dim+d] = linField.b[d];
}
}
std::vector<double> ws_field(me.nodesPerElement_);
std::vector<double> ws_coords(me.nodesPerElement_ * dim);
for (int j = 0; j < me.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; ++d) {
ws_coords[j*dim+d] = coords[d];
}
ws_field[j] = linField(coords);
}
std::vector<double> meResult(me.num_integration_points() * dim, 0.0);
std::vector<double> meGrad(me.num_integration_points() * me.nodesPerElement_ * dim);
std::vector<double> meDeriv(me.num_integration_points() * me.nodesPerElement_ * dim);
std::vector<double> meDetj(me.num_integration_points());
double error = 0.0;
me.grad_op(1, ws_coords.data(), meGrad.data(), meDeriv.data(), meDetj.data(), &error);
EXPECT_EQ(error, 0.0);
for (int j = 0; j < me.num_integration_points(); ++j) {
for (int i = 0; i < me.nodesPerElement_; ++i) {
for (int d = 0; d < dim; ++d) {
meResult[j*dim+d] += meGrad[j*me.nodesPerElement_*dim + i * dim + d] * ws_field[i];
}
}
}
// detj should be unity to floating point error
for (unsigned j = 0 ; j < meDetj.size(); ++j) {
EXPECT_NEAR(1, meDetj[j], tol) ;
}
// derivative should be exact to floating point error
for (unsigned j = 0 ; j < meResult.size(); ++j) {
EXPECT_NEAR(meResult[j], polyResult[j], tol);
}
}
//-------------------------------------------------------------------------
void check_scv_shifted_ips_are_nodal(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& meSV)
{
// check that the subcontrol volume ips are at the nodes for the shifted ips
int dim = meSV.nDim_;
std::vector<double> ws_coords(meSV.nodesPerElement_ * dim);
for (int j = 0; j < meSV.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; ++d) {
ws_coords[j*dim+d] = coords[d];
}
}
const int nint = meSV.num_integration_points()*meSV.nDim_;
const double* shiftedIps = meSV.integration_location_shift();
EXPECT_EQ(ws_coords.size(), static_cast<unsigned>(nint)) << "P1 test";
for (int j = 0; j < nint; ++j) {
EXPECT_NEAR(ws_coords[j], shiftedIps[j], tol);
}
}
//-------------------------------------------------------------------------
void check_volume_integration(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& meSV)
{
int dim = meSV.nDim_;
std::vector<double> ws_coords_mapped(meSV.nodesPerElement_ * dim, 0.0);
std::vector<double> ws_coords(meSV.nodesPerElement_ * dim, 0.0);
std::mt19937 rng;
rng.seed(0);
auto QR = unit_test_utils::random_linear_transformation(dim, 1.0, rng);
for (int j = 0; j < meSV.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
if (dim == 3) {
sierra::nalu::matvec33(QR.data(), coords, &ws_coords_mapped[j*dim]);
}
else {
sierra::nalu::matvec22(QR.data(), coords, &ws_coords_mapped[j*dim]);
}
for (int k = 0; k < dim; ++k) {
ws_coords[j*dim+k] = coords[k];
}
}
const double detQR = (dim == 3) ? sierra::nalu::determinant33(QR.data()) : sierra::nalu::determinant22(QR.data());
ASSERT_TRUE(detQR > 1.0e-15);
double error = 0;
std::vector<double> volume_integration_weights(meSV.num_integration_points());
meSV.determinant(1, ws_coords.data(), volume_integration_weights.data(), &error);
ASSERT_DOUBLE_EQ(error, 0);
std::vector<double> skewed_volume_integration_weights(meSV.num_integration_points());
meSV.determinant(1, ws_coords_mapped.data(), skewed_volume_integration_weights.data(), &error);
ASSERT_DOUBLE_EQ(error, 0);
for (int k = 0; k < meSV.num_integration_points(); ++k) {
EXPECT_NEAR(detQR*volume_integration_weights[k], skewed_volume_integration_weights[k], tol);
}
}
//-------------------------------------------------------------------------
#if 0
void check_exposed_face_shifted_ips_are_nodal(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& meSS)
{
// check that the subcontrol volume ips are at the nodes for the shifted ips
const int dim = meSS.nDim_;
std::vector<std::vector<double>> coordList(meSS.nodesPerElement_);
for (int j = 0; j < meSS.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
coordList.at(j).resize(dim);
for (int d = 0; d < dim; ++d) {
coordList.at(j).at(d) = coords[d];
}
}
const double* shiftedIps = meSS.integration_exp_face_shift();
int index = 0;
const int nint = shiftedIps.size()/dim;
std::vector<std::vector<double>> shiftedIpList(nint);
for (int j = 0; j < nint; ++j) {
shiftedIpList.at(j).resize(dim);
for (int d = 0; d < dim; ++d) {
shiftedIpList.at(j).at(d) = shiftedIps[index];
++index;
}
}
auto is_same_vector = [] (const std::vector<double>& u, const std::vector<double>& v, double tol) {
if (u.size() != v.size()) {
return false;
}
for (unsigned j = 0; j < u.size(); ++j) {
if (std::abs(u[j] - v[j]) > tol) {
return false;
}
}
return true;
};
std::vector<int> countSame(shiftedIpList.size(),0);
for (unsigned i = 0; i < shiftedIpList.size(); ++i) {
for (unsigned j = 0; j < coordList.size(); ++j) {
if (is_same_vector(coordList.at(j), shiftedIpList.at(i), tol)) {
++countSame.at(i);
}
}
}
for (unsigned j = 0; j <countSame.size(); ++j) {
if (countSame.at(j) != 1 && dim == 3) {
std::cout << "iploc: " << shiftedIpList.at(j)[0] << ", "
<< shiftedIpList.at(j)[1] << ", "
<< shiftedIpList.at(j)[2] << std::endl;
}
EXPECT_EQ(countSame.at(j), 1);
}
}
#endif
//-------------------------------------------------------------------------
void check_is_in_element(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
// Check that the isoparametric coordinates are the same as the physical point
// for the reference element
int dim = me.nDim_;
std::mt19937 rng;
rng.seed(0);
// randomly select a point within (boxmin, boxmax)^3 \subset reference element domain
const double boxmin = 0.125;
const double boxmax = 0.25;
std::uniform_real_distribution<double> coeff(boxmin, boxmax);
std::vector<double> random_pt(dim);
for (int j = 0; j < dim; ++j) {
random_pt[j] = coeff(rng);
}
// is in element uses a different stride for the coordinate data
// compared to the gradient computation
std::vector<double> ws_field(me.nodesPerElement_);
std::vector<double> ws_coords(me.nodesPerElement_ * dim);
// Hex8/Quad4's is_in_element and interpolatePoint routines use a different,
// but self-consistent reference element compared to the core shape functions
// and derivatives
bool isHexSCS = dynamic_cast<sierra::nalu::HexSCS*>(&me) != nullptr;
bool isQuadSCS = dynamic_cast<sierra::nalu::Quad42DSCS*>(&me) != nullptr;
double fac = (isHexSCS || isQuadSCS) ? 2.0 : 1.0;
for (int j = 0; j < me.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; ++d) {
ws_coords[d * me.nodesPerElement_ + j] = fac*coords[d];
}
}
std::vector<double> mePt(dim);
auto dist = me.isInElement(ws_coords.data(), random_pt.data(), mePt.data());
EXPECT_LT(dist, 1.0+tol);
for (int d = 0; d < dim; ++d) {
EXPECT_NEAR(random_pt[d], mePt[d], tol);
}
}
//-------------------------------------------------------------------------
void check_is_not_in_element(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
// check that we correctly report that a point outside of an element is
// outside of the element
int dim = me.nDim_;
// choose a point not in the element
std::vector<double> exterior_pt = { 100, 100, 100 };
std::vector<double> ws_field(me.nodesPerElement_);
std::vector<double> ws_coords(me.nodesPerElement_ * dim);
for (int j = 0; j < me.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; ++d) {
ws_coords[d * me.nodesPerElement_ + j] = coords[d];
}
}
std::vector<double> mePt(dim);
double dist = me.isInElement(ws_coords.data(), exterior_pt.data(), mePt.data());
EXPECT_GT(dist, 1 + tol);
}
//-------------------------------------------------------------------------
void check_particle_interp(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
// Check that, for a distorted element, we can find and interpolate values to
// a random located point inside of the element
int dim = me.nDim_;
std::mt19937 rng;
rng.seed(0);
auto linField = make_random_linear_field(dim,rng);
// randomly select a point within (boxmin, boxmax)^3 \subset reference element domain
const double boxmin = 0.125;
const double boxmax = 0.25;
std::uniform_real_distribution<double> coeff(boxmin, boxmax);
std::vector<double> random_pt(dim);
for (int j = 0; j < dim; ++j) {
random_pt[j] = coeff(rng);
}
std::vector<double> coeffs(dim);
for (int j = 0; j < dim; ++j) {
coeffs[j] = coeff(rng);
}
// randomly perturb each of the coordinates of by a factor of delta
// the element still needs to actually contain the box, (boxmin, boxmax)^3
const double delta = 0.25;
std::uniform_real_distribution<double> coord_perturb(-delta/2, delta/2);
// is in element uses a different stride for the coordinate data
// compared to the gradient computation
std::vector<double> ws_field(me.nodesPerElement_);
std::vector<double> ws_coords(me.nodesPerElement_ * dim);
std::vector<double> perturbed_coords(dim);
for (int j = 0; j < me.nodesPerElement_; ++j) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; ++d) {
perturbed_coords[d] = coords[d] + coord_perturb(rng);
ws_coords[d * me.nodesPerElement_ + j] = perturbed_coords[d];
}
ws_field[j] = linField(perturbed_coords.data());
}
std::vector<double> mePt(dim);
double dist = me.isInElement(ws_coords.data(), random_pt.data(), mePt.data());
EXPECT_LT(dist, 1.0+tol);
double meInterp = 0.0;
me.interpolatePoint(1, mePt.data(), ws_field.data(), &meInterp);
double exactVal = linField(random_pt.data());
EXPECT_NEAR(meInterp, exactVal, tol);
}
/** Check implementation of general_shape_fcn for a given MasterElement
*
*/
void
check_general_shape_fcn(
const stk::mesh::Entity* node_rels,
const VectorFieldType& coordField,
sierra::nalu::MasterElement& me)
{
const int dim = me.nDim_;
std::random_device rd{};
std::mt19937 rng{rd()};
// 1. Generate a random point within the element
const double boxmin = 0.125;
const double boxmax = 0.25;
std::uniform_real_distribution<double> coeff(boxmin, boxmax);
std::vector<double> nodal_coords(dim);
for (int d = 0; d < dim; d++)
nodal_coords[d] = coeff(rng);
// 2. Extract iso-parametric coordinates for this random point w.r.t element
// see check_is_in_element for an explanation of the factor
bool isHexSCS = dynamic_cast<sierra::nalu::HexSCS*>(&me) != nullptr;
bool isQuadSCS = dynamic_cast<sierra::nalu::Quad42DSCS*>(&me) != nullptr;
double fac = (isHexSCS || isQuadSCS) ? 2.0 : 1.0;
std::vector<double> elem_coords(me.nodesPerElement_ * dim);
for (int j = 0; j < me.nodesPerElement_; j++) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; d++)
elem_coords[d * me.nodesPerElement_ + j] = fac * coords[d];
}
std::vector<double> isopar_coords(dim);
auto dist = me.isInElement(
elem_coords.data(), nodal_coords.data(), isopar_coords.data());
// Catch any issues with random coordinates before general_shape_fcn check
EXPECT_LT(dist, 1.0 + tol);
//
// 3. Finally, check general shape fcn
//
auto linField = make_random_linear_field(dim, rng);
double polyResult = linField(nodal_coords.data());
// The linear field at the nodes of the reference element
std::vector<double> elem_field(me.nodesPerElement_);
std::vector<double> ws_coord(dim);
for (int j = 0; j < me.nodesPerElement_; j++) {
const double* coords = stk::mesh::field_data(coordField, node_rels[j]);
for (int d = 0; d < dim; d++) {
ws_coord[d] = fac * coords[d];
}
elem_field[j] = linField(ws_coord.data());
}
std::vector<double> gen_shape_fcn(me.nodesPerElement_);
me.general_shape_fcn(1, isopar_coords.data(), gen_shape_fcn.data());
double meResult = 0.0;
for (int j = 0; j < me.nodesPerElement_; j++) {
meResult += gen_shape_fcn[j] * elem_field[j];
}
EXPECT_NEAR(meResult, polyResult, tol);
}
}
class MasterElement : public ::testing::Test
{
protected:
MasterElement() : comm(MPI_COMM_WORLD) {}
void choose_topo(stk::topology topo)
{
meta = std::unique_ptr<stk::mesh::MetaData>(new stk::mesh::MetaData(topo.dimension()));
bulk = std::unique_ptr<stk::mesh::BulkData>(new stk::mesh::BulkData(*meta, comm));
elem = unit_test_utils::create_one_reference_element(*bulk, topo);
meSS = sierra::nalu::MasterElementRepo::get_surface_master_element(topo);
meSV = sierra::nalu::MasterElementRepo::get_volume_master_element(topo);
}
void scs_interpolation(stk::topology topo) {
choose_topo(topo);
check_interpolation_at_ips(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
void scv_interpolation(stk::topology topo) {
choose_topo(topo);
check_interpolation_at_ips(bulk->begin_nodes(elem), coordinate_field(), *meSV);
}
void volume_integration(stk::topology topo) {
choose_topo(topo);
check_volume_integration(bulk->begin_nodes(elem), coordinate_field(), *meSV);
}
void scs_derivative(stk::topology topo) {
choose_topo(topo);
check_derivatives_at_ips(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
void is_not_in_element(stk::topology topo) {
choose_topo(topo);
check_is_not_in_element(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
void scv_shifted_ips_are_nodal(stk::topology topo) {
choose_topo(topo);
check_scv_shifted_ips_are_nodal(bulk->begin_nodes(elem), coordinate_field(), *meSV);
}
// void exposed_face_shifted_ips_are_nodal(stk::topology topo) {
// choose_topo(topo);
// check_exposed_face_shifted_ips_are_nodal(bulk->begin_nodes(elem), coordinate_field(), *meSS);
// }
void is_in_element(stk::topology topo) {
choose_topo(topo);
check_is_in_element(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
void particle_interpolation(stk::topology topo) {
choose_topo(topo);
check_particle_interp(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
void general_shape_fcn(stk::topology topo) {
choose_topo(topo);
check_general_shape_fcn(bulk->begin_nodes(elem), coordinate_field(), *meSS);
}
const VectorFieldType& coordinate_field() const {
return *static_cast<const VectorFieldType*>(meta->coordinate_field());
}
stk::ParallelMachine comm;
std::unique_ptr<stk::mesh::MetaData> meta;
std::unique_ptr<stk::mesh::BulkData> bulk;
stk::mesh::Entity elem;
sierra::nalu::MasterElement* meSS;
sierra::nalu::MasterElement* meSV;
};
#define TEST_F_ALL_TOPOS(x, y) \
TEST_F(x, tri##_##y) { y(stk::topology::TRI_3_2D); } \
TEST_F(x, quad4##_##y) { y(stk::topology::QUAD_4_2D); } \
TEST_F(x, quad9##_##y) { y(stk::topology::QUAD_9_2D); } \
TEST_F(x, tet##_##y) { y(stk::topology::TET_4); } \
TEST_F(x, pyr##_##y) { y(stk::topology::PYRAMID_5); } \
TEST_F(x, wedge##_##y) { y(stk::topology::WEDGE_6); } \
TEST_F(x, hex8##_##y) { y(stk::topology::HEX_8); } \
TEST_F(x, hex27##_##y) { y(stk::topology::HEX_27); }
#define TEST_F_ALL_P1_TOPOS(x, y) \
TEST_F(x, tri##_##y) { y(stk::topology::TRI_3_2D); } \
TEST_F(x, quad4##_##y) { y(stk::topology::QUAD_4_2D); } \
TEST_F(x, tet##_##y) { y(stk::topology::TET_4); } \
TEST_F(x, wedge##_##y) { y(stk::topology::WEDGE_6); } \
TEST_F(x, pyr##_##y) { y(stk::topology::PYRAMID_5); } \
TEST_F(x, hex8##_##y) { y(stk::topology::HEX_8); }
// Patch tests
TEST_F_ALL_TOPOS(MasterElement, scs_interpolation)
TEST_F_ALL_TOPOS(MasterElement, scs_derivative)
TEST_F_ALL_TOPOS(MasterElement, scv_interpolation)
TEST_F_ALL_TOPOS(MasterElement, volume_integration)
TEST_F_ALL_TOPOS(MasterElement, is_in_element)
// Pyramid works. Doesn't work for higher-order elements sicne they have more ips than nodes
TEST_F_ALL_P1_TOPOS(MasterElement, scv_shifted_ips_are_nodal)
//TEST_F_ALL_P1_TOPOS(MasterElement, exposed_face_shifted_ips_are_nodal)
// works fore everything
TEST_F_ALL_TOPOS(MasterElement, is_not_in_element)
TEST_F_ALL_TOPOS(MasterElement, particle_interpolation)
TEST_F_ALL_P1_TOPOS(MasterElement, general_shape_fcn)