388 lines
11 KiB
C++
388 lines
11 KiB
C++
// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
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// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
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// LICENSE and NOTICE for details. LLNL-CODE-806117.
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//
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// This file is part of the MFEM library. For more information and source code
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// availability visit https://mfem.org.
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//
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// MFEM is free software; you can redistribute it and/or modify it under the
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// terms of the BSD-3 license. We welcome feedback and contributions, see file
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// CONTRIBUTING.md for details.
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#include "mfem.hpp"
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#include "catch.hpp"
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#include <iostream>
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#include <cmath>
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using namespace mfem;
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/**
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* Utility function to generate IntegerationPoints, based on param ip
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* that are outside the unit interval. Results are placed in output
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* parameter arr.
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*
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* Note: this is defined in test_calcshape.cpp
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*/
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void GetRelatedIntegrationPoints(const IntegrationPoint& ip, int dim,
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Array<IntegrationPoint>& arr);
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/**
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* Utility function to setup IsoparametricTransformations for reference
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* elements of various types.
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*/
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void GetReferenceTransformation(const Element::Type ElemType,
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IsoparametricTransformation & T)
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{
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T.Attribute = 1;
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T.ElementNo = 0;
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switch (ElemType)
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{
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case Element::POINT :
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T.GetPointMat().SetSize(1, 1);
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T.GetPointMat()(0, 0) = 0.0;
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T.SetFE(&PointFE);
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break;
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case Element::SEGMENT :
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T.GetPointMat().SetSize(1, 2);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.SetFE(&SegmentFE);
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break;
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case Element::TRIANGLE :
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T.GetPointMat().SetSize(2, 3);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(0, 2) = 0.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.SetFE(&TriangleFE);
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break;
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case Element::QUADRILATERAL :
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T.GetPointMat().SetSize(2, 4);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(0, 2) = 1.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.GetPointMat()(0, 3) = 0.0;
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T.GetPointMat()(1, 3) = 1.0;
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T.SetFE(&QuadrilateralFE);
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break;
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case Element::TETRAHEDRON :
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T.GetPointMat().SetSize(3, 4);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(2, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(2, 1) = 0.0;
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T.GetPointMat()(0, 2) = 0.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.GetPointMat()(2, 2) = 0.0;
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T.GetPointMat()(0, 3) = 0.0;
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T.GetPointMat()(1, 3) = 0.0;
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T.GetPointMat()(2, 3) = 1.0;
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T.SetFE(&TetrahedronFE);
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break;
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case Element::HEXAHEDRON :
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T.GetPointMat().SetSize(3, 8);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(2, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(2, 1) = 0.0;
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T.GetPointMat()(0, 2) = 1.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.GetPointMat()(2, 2) = 0.0;
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T.GetPointMat()(0, 3) = 0.0;
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T.GetPointMat()(1, 3) = 1.0;
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T.GetPointMat()(2, 3) = 0.0;
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T.GetPointMat()(0, 4) = 0.0;
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T.GetPointMat()(1, 4) = 0.0;
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T.GetPointMat()(2, 4) = 1.0;
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T.GetPointMat()(0, 5) = 1.0;
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T.GetPointMat()(1, 5) = 0.0;
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T.GetPointMat()(2, 5) = 1.0;
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T.GetPointMat()(0, 6) = 1.0;
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T.GetPointMat()(1, 6) = 1.0;
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T.GetPointMat()(2, 6) = 1.0;
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T.GetPointMat()(0, 7) = 0.0;
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T.GetPointMat()(1, 7) = 1.0;
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T.GetPointMat()(2, 7) = 1.0;
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T.SetFE(&HexahedronFE);
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break;
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case Element::WEDGE :
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T.GetPointMat().SetSize(3, 6);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(2, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(2, 1) = 0.0;
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T.GetPointMat()(0, 2) = 0.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.GetPointMat()(2, 2) = 0.0;
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T.GetPointMat()(0, 3) = 0.0;
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T.GetPointMat()(1, 3) = 0.0;
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T.GetPointMat()(2, 3) = 1.0;
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T.GetPointMat()(0, 4) = 1.0;
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T.GetPointMat()(1, 4) = 0.0;
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T.GetPointMat()(2, 4) = 1.0;
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T.GetPointMat()(0, 5) = 0.0;
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T.GetPointMat()(1, 5) = 1.0;
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T.GetPointMat()(2, 5) = 1.0;
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T.SetFE(&WedgeFE);
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break;
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case Element::PYRAMID :
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T.GetPointMat().SetSize(3, 5);
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T.GetPointMat()(0, 0) = 0.0;
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T.GetPointMat()(1, 0) = 0.0;
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T.GetPointMat()(2, 0) = 0.0;
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T.GetPointMat()(0, 1) = 1.0;
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T.GetPointMat()(1, 1) = 0.0;
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T.GetPointMat()(2, 1) = 0.0;
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T.GetPointMat()(0, 2) = 1.0;
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T.GetPointMat()(1, 2) = 1.0;
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T.GetPointMat()(2, 2) = 0.0;
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T.GetPointMat()(0, 3) = 0.0;
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T.GetPointMat()(1, 3) = 1.0;
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T.GetPointMat()(2, 3) = 0.0;
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T.GetPointMat()(0, 4) = 0.0;
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T.GetPointMat()(1, 4) = 0.0;
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T.GetPointMat()(2, 4) = 1.0;
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T.SetFE(&PyramidFE);
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break;
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default:
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MFEM_ABORT("Unknown element type \"" << ElemType << "\"");
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break;
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}
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}
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/**
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* Tests fe->CalcVShape() over a grid of IntegrationPoints
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* of resolution res. Also tests at integration points
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* that are outside the element.
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*/
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void TestCalcVShape(FiniteElement* fe, ElementTransformation * T, int res)
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{
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int dim = fe->GetDim();
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int dof = fe->GetDof();
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Vector dofsx(dof);
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Vector dofsy(dof);
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Vector dofsz(dof);
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Vector v(dim);
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Vector vx(dim); vx = 0.0; vx[0] = 1.0;
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Vector vy(dim); vy = 0.0;
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if (dim > 1) { vy[1] = 1.0; }
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Vector vz(dim); vz = 0.0;
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if (dim > 2) { vz[2] = 1.0; }
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DenseMatrix weights( dof, dim );
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VectorConstantCoefficient vxCoef(vx);
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VectorConstantCoefficient vyCoef(vy);
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VectorConstantCoefficient vzCoef(vz);
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fe->Project(vxCoef, *T, dofsx);
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if (dim> 1) { fe->Project(vyCoef, *T, dofsy); }
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if (dim> 2) { fe->Project(vzCoef, *T, dofsz); }
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// Get a uniform grid or integration points
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RefinedGeometry* ref = GlobGeometryRefiner.Refine( fe->GetGeomType(), res);
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const IntegrationRule& intRule = ref->RefPts;
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int npoints = intRule.GetNPoints();
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for (int i=0; i < npoints; ++i)
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{
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// Get the current integration point from intRule
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IntegrationPoint pt = intRule.IntPoint(i);
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// Get several variants of this integration point
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// some of which are inside the element and some are outside
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Array<IntegrationPoint> ipArr;
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GetRelatedIntegrationPoints( pt, dim, ipArr );
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// For each such integration point check that the weights
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// from CalcShape() sum to one
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for (int j=0; j < ipArr.Size(); ++j)
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{
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IntegrationPoint& ip = ipArr[j];
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// Pyramid basis functions are poorly behaved outside the
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// reference pyramid
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if (fe->GetGeomType() == Geometry::PYRAMID &&
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(ip.z >= 1.0 || ip.y > 1.0 - ip.z || ip.x > 1.0 - ip.z)) { continue; }
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CAPTURE(ip.x, ip.y, ip.z);
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fe->CalcVShape(ip, weights);
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weights.MultTranspose(dofsx, v);
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REQUIRE( v[0] == Approx(1.) );
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if (dim > 1)
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{
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weights.MultTranspose(dofsy, v);
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REQUIRE( v[1] == Approx(1.) );
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}
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if (dim > 2)
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{
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weights.MultTranspose(dofsz, v);
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REQUIRE( v[2] == Approx(1.) );
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}
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}
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}
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}
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TEST_CASE("CalcVShape ND",
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"[ND_SegmentElement]"
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"[ND_TriangleElement]"
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"[ND_QuadrilateralElement]"
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"[ND_TetrahedronElement]"
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"[ND_WedgeElement]"
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"[ND_FuentesPyramidElement]"
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"[ND_HexahedronElement]")
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{
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const int maxOrder = 5;
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const int resolution = 10;
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auto order = GENERATE_COPY(range(1, maxOrder + 1));
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CAPTURE(order);
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SECTION("ND_SegmentElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::SEGMENT, T);
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ND_SegmentElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_TriangleElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::TRIANGLE, T);
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ND_TriangleElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_QuadrilateralElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::QUADRILATERAL, T);
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ND_QuadrilateralElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_TetrahedronElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::TETRAHEDRON, T);
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ND_TetrahedronElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_WedgeElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::WEDGE, T);
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ND_WedgeElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_FuentesPyramidElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::PYRAMID, T);
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ND_FuentesPyramidElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("ND_HexahedronElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::HEXAHEDRON, T);
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ND_HexahedronElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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}
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TEST_CASE("CalcVShape RT",
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"[RT_TriangleElement]"
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"[RT_QuadrilateralElement]"
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"[RT_TetrahedronElement]"
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"[RT_WedgeElement]"
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"[RT_FuentesPyramidElement]"
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"[RT_HexahedronElement]")
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{
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const int maxOrder = 5;
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const int resolution = 10;
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auto order = GENERATE_COPY(range(1, maxOrder + 1));
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CAPTURE(order);
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SECTION("RT_TriangleElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::TRIANGLE, T);
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RT_TriangleElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("RT_QuadrilateralElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::QUADRILATERAL, T);
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RT_QuadrilateralElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("RT_TetrahedronElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::TETRAHEDRON, T);
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RT_TetrahedronElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("RT_WedgeElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::WEDGE, T);
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RT_WedgeElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("RT_FuentesElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::PYRAMID, T);
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RT_FuentesPyramidElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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SECTION("RT_HexahedronElement")
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{
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IsoparametricTransformation T;
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GetReferenceTransformation(Element::HEXAHEDRON, T);
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RT_HexahedronElement fe(order);
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TestCalcVShape(&fe, &T, resolution);
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}
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}
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