HexLagrangeShapeTest.cpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2006 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retian certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2010) kraftche@cae.wisc.edu

  ***************************************************************** */

/** \file HexLagrangeShapeTest.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "HexLagrangeShape.hpp"
#include "TopologyInfo.hpp"
#include "MsqError.hpp"
#include "IdealElements.hpp"
#include "JacobianCalculator.hpp"

#include "UnitUtil.hpp"

#include <vector>
#include <algorithm>
#include <iostream>
#include <sstream>

using namespace MBMesquite;
using namespace std;
const double epsilon = 1e-6;
#define ASSERT_VALUES_EQUAL( v1, v2, location ) \
    ASSERT_MESSAGE( value_message( ( location ), ( v1 ), ( v2 ) ), test_value( ( v1 ), ( v2 ) ) )

static bool test_value( double v1, double v2 )
{
    return fabs( v1 - v2 ) < epsilon;
}

static inline CppUnit::Message value_message( unsigned location, double v1, double v2 )
{
    CppUnit::Message m( "equality assertion failed" );

    std::ostringstream buffer1;
    buffer1 << "Expected : " << v1;
    m.addDetail( buffer1.str() );

    std::ostringstream buffer2;
    buffer2 << "Actual   : " << v2;
    m.addDetail( buffer2.str() );

    std::ostringstream buffer3;
    buffer3 << "Location : ";
    if( location < 9 )
        buffer3 << "Corner " << location;
    else if( location < 20 )
        buffer3 << "Edge " << location - 8;
    else if( location < 26 )
        buffer3 << "Face " << location - 20;
    else if( location == 26 )
        buffer3 << "Mid-element";
    else
        buffer3 << "INVALID!!";
    m.addDetail( buffer3.str() );
    return m;
}

static bool test_value( MsqVector< 3 > v1, MsqVector< 3 > v2 )
{
    return length( v1 - v2 ) < epsilon;
}

static inline CppUnit::Message value_message( unsigned location, MsqVector< 3 > v1, MsqVector< 3 > v2 )
{
    CppUnit::Message m( "equality assertion failed" );

    std::ostringstream buffer1;
    buffer1 << "Expected : [" << v1[0] << ", " << v1[1] << ", " << v1[2] << "]";
    m.addDetail( buffer1.str() );

    std::ostringstream buffer2;
    buffer2 << "Actual   : [" << v2[0] << ", " << v2[1] << ", " << v2[2] << "]";
    m.addDetail( buffer2.str() );

    std::ostringstream buffer3;
    buffer3 << "Location : ";
    if( location < 9 )
        buffer3 << "Corner " << location;
    else if( location < 20 )
        buffer3 << "Edge " << location - 8;
    else if( location < 26 )
        buffer3 << "Face " << location - 20;
    else if( location == 26 )
        buffer3 << "Mid-element";
    else
        buffer3 << "INVALID!!";
    m.addDetail( buffer3.str() );
    return m;
}

class HexLagrangeShapeTest : public CppUnit::TestFixture
{
  private:
    CPPUNIT_TEST_SUITE( HexLagrangeShapeTest );

    CPPUNIT_TEST( test_corners_coeff );
    CPPUNIT_TEST( test_edges_coeff );
    CPPUNIT_TEST( test_faces_coeff );
    CPPUNIT_TEST( test_mid_coeff );

    CPPUNIT_TEST( test_corners_derivs );
    CPPUNIT_TEST( test_edges_derivs );
    CPPUNIT_TEST( test_faces_derivs );
    CPPUNIT_TEST( test_mid_derivs );

    CPPUNIT_TEST( test_ideal_jacobian );

    CPPUNIT_TEST_SUITE_END();

    HexLagrangeShape sf;

  public:
    void test_corner_coeff( int corner );
    void test_edge_coeff( int edge );
    void test_face_coeff( int face );
    void test_mid_coeff();

    void test_corner_derivs( int corner );
    void test_edge_derivs( int edge );
    void test_face_derivs( int face );
    void test_mid_derivs();

    NodeSet allNodes;
    void setUp()
    {
        allNodes.set_all_nodes( HEXAHEDRON );
    }

    void test_corners_coeff();
    void test_edges_coeff();
    void test_faces_coeff();

    void test_corners_derivs();
    void test_edges_derivs();
    void test_faces_derivs();

    void test_ideal_jacobian();
};

CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( HexLagrangeShapeTest, "HexLagrangeShapeTest" );
CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( HexLagrangeShapeTest, "Unit" );

// Indices
enum
{
    XI   = 0,
    ETA  = 1,
    ZETA = 2
};
// Parameter range
const double min_xi = 0;
const double max_xi = 1;
const double mid_xi = 0.5 * ( min_xi + max_xi );

// Some lagrange polynomial terms
static double l21( double xi )
{
    return ( 2 * xi - 1 ) * ( xi - 1 );
}
static double l22( double xi )
{
    return 4 * xi * ( 1 - xi );
}
static double l23( double xi )
{
    return xi * ( 2 * xi - 1 );
}
// First derivatives of lagrange polynomial terms
static double dl21( double xi )
{
    return 4 * xi - 3;
}
static double dl22( double xi )
{
    return 4 - 8 * xi;
}
static double dl23( double xi )
{
    return 4 * xi - 1;
}
// Indexible polynomail terms
typedef double ( *f_t )( double );
f_t l[4]         = { 0, &l21, &l22, &l23 };
f_t dl[4]        = { 0, &dl21, &dl22, &dl23 };
const int C[][3] = {
    { 1, 1, 1 },  //   0
    { 3, 1, 1 },  //   1
    { 3, 3, 1 },  //   2
    { 1, 3, 1 },  //   3

    { 1, 1, 3 },  //   4
    { 3, 1, 3 },  //   5
    { 3, 3, 3 },  //   6
    { 1, 3, 3 },  //   7

    { 2, 1, 1 },  //   8
    { 3, 2, 1 },  //   9
    { 2, 3, 1 },  //  10
    { 1, 2, 1 },  //  11

    { 1, 1, 2 },  //  12
    { 3, 1, 2 },  //  13
    { 3, 3, 2 },  //  14
    { 1, 3, 2 },  //  15

    { 2, 1, 3 },  //  16
    { 3, 2, 3 },  //  17
    { 2, 3, 3 },  //  18
    { 1, 2, 3 },  //  19

    { 2, 1, 2 },  //  20
    { 3, 2, 2 },  //  21
    { 2, 3, 2 },  //  22
    { 1, 2, 2 },  //  23

    { 2, 2, 1 },  //  24
    { 2, 2, 3 },  //  25

    { 2, 2, 2 }  //  26
};

const double corners[8][3] = { { min_xi, min_xi, min_xi }, { max_xi, min_xi, min_xi }, { max_xi, max_xi, min_xi },
                               { min_xi, max_xi, min_xi }, { min_xi, min_xi, max_xi }, { max_xi, min_xi, max_xi },
                               { max_xi, max_xi, max_xi }, { min_xi, max_xi, max_xi } };

static MsqVector< 3 > XI_corner( int i )
{
    return MsqVector< 3 >( corners[i] );
}

static MsqVector< 3 > XI_edge( int i )
{
    const unsigned* idx = TopologyInfo::edge_vertices( HEXAHEDRON, i );
    return 0.5 * ( XI_corner( idx[0] ) + XI_corner( idx[1] ) );
}

static MsqVector< 3 > XI_face( int i )
{
    unsigned n;
    const unsigned* idx   = TopologyInfo::face_vertices( HEXAHEDRON, i, n );
    MsqVector< 3 > result = XI_corner( idx[0] );
    for( unsigned j = 1; j < n; ++j )
        result += XI_corner( idx[j] );
    result *= 1.0 / n;
    return result;
}

static MsqVector< 3 > XI_elem()
{
    const double vals[] = { mid_xi, mid_xi, mid_xi };
    return MsqVector< 3 >( vals );
}

static double N( int i, MsqVector< 3 > xi )
{
    const int* c = C[i];
    return l[c[XI]]( xi[XI] ) * l[c[ETA]]( xi[ETA] ) * l[c[ZETA]]( xi[ZETA] );
}

static MsqVector< 3 > dN( int i, MsqVector< 3 > xi )
{
    MsqVector< 3 > result;
    const int* c = C[i];
    result[XI]   = dl[c[XI]]( xi[XI] ) * l[c[ETA]]( xi[ETA] ) * l[c[ZETA]]( xi[ZETA] );
    result[ETA]  = l[c[XI]]( xi[XI] ) * dl[c[ETA]]( xi[ETA] ) * l[c[ZETA]]( xi[ZETA] );
    result[ZETA] = l[c[XI]]( xi[XI] ) * l[c[ETA]]( xi[ETA] ) * dl[c[ZETA]]( xi[ZETA] );
    return result;
}

static void get_coeffs( MsqVector< 3 > xi, double coeffs_out[27] )
{
    for( int i = 0; i < 27; ++i )
        coeffs_out[i] = N( i, xi );
}

static void get_derivs( MsqVector< 3 > xi, MsqVector< 3 > derivs_out[27] )
{
    for( int i = 0; i < 27; ++i )
        derivs_out[i] = dN( i, xi );
}

static void check_valid_indices( const size_t* vertices, size_t num_vtx )
{
    // check valid size of list (at least fout, at most all nodes)
    CPPUNIT_ASSERT( num_vtx <= 27 );
    CPPUNIT_ASSERT( num_vtx >= 4 );
    // make sure vertex indices are valid (in [0,26])
    size_t vertcopy[27];
    std::copy( vertices, vertices + num_vtx, vertcopy );
    std::sort( vertcopy, vertcopy + num_vtx );
    CPPUNIT_ASSERT( vertcopy[num_vtx - 1] <= 26 );  // max value less than 27
                                                    // make sure there are no duplicates in the list
    const size_t* iter = std::unique( vertcopy, vertcopy + num_vtx );
    CPPUNIT_ASSERT( iter == vertcopy + num_vtx );
}

static void check_no_zeros( const MsqVector< 3 >* derivs, size_t num_vtx )
{
    for( unsigned i = 0; i < num_vtx; ++i )
    {
        CPPUNIT_ASSERT( length( derivs[i] ) > 1e-6 );
    }
}

static void compare_coefficients( const double* coeffs,
                                  const size_t* indices,
                                  size_t num_coeff,
                                  const double* expected_coeffs,
                                  unsigned loc )
{
    // find the location in the returned list for each node
    size_t revidx[27];
    double test_vals[27];
    for( size_t i = 0; i < 27; ++i )
    {
        revidx[i]    = std::find( indices, indices + num_coeff, i ) - indices;
        test_vals[i] = ( revidx[i] == num_coeff ) ? 0.0 : coeffs[revidx[i]];
    }

    // compare expected and actual coefficient values
    ASSERT_VALUES_EQUAL( expected_coeffs[0], test_vals[0], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[1], test_vals[1], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[2], test_vals[2], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[3], test_vals[3], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[4], test_vals[4], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[5], test_vals[5], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[6], test_vals[6], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[7], test_vals[7], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[8], test_vals[8], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[9], test_vals[9], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[10], test_vals[10], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[11], test_vals[11], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[12], test_vals[12], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[13], test_vals[13], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[14], test_vals[14], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[15], test_vals[15], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[16], test_vals[16], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[17], test_vals[17], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[18], test_vals[18], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[19], test_vals[19], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[20], test_vals[20], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[21], test_vals[21], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[22], test_vals[22], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[23], test_vals[23], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[24], test_vals[24], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[25], test_vals[25], loc );
    ASSERT_VALUES_EQUAL( expected_coeffs[26], test_vals[26], loc );
}

static void compare_derivatives( const size_t* vertices,
                                 size_t num_vtx,
                                 const MsqVector< 3 >* actual,
                                 const MsqVector< 3 >* expected,
                                 unsigned loc )
{
    check_valid_indices( vertices, num_vtx );
    check_no_zeros( actual, num_vtx );

    // Input has values in dxi & deta & dzeta only for nodes in 'vertices'
    // Convert to values for every possible node, with zero's for
    // nodes that are not present.
    CPPUNIT_ASSERT( num_vtx <= 9 );
    MsqVector< 3 > expanded[27];
    std::fill( expanded, expanded + 27, MsqVector< 3 >( 0.0 ) );
    for( unsigned i = 0; i < num_vtx; ++i )
    {
        CPPUNIT_ASSERT( vertices[i] <= 26 );
        expanded[vertices[i]] = actual[i];
    }

    ASSERT_VALUES_EQUAL( expected[0], expanded[0], loc );
    ASSERT_VALUES_EQUAL( expected[1], expanded[1], loc );
    ASSERT_VALUES_EQUAL( expected[2], expanded[2], loc );
    ASSERT_VALUES_EQUAL( expected[3], expanded[3], loc );
    ASSERT_VALUES_EQUAL( expected[4], expanded[4], loc );
    ASSERT_VALUES_EQUAL( expected[5], expanded[5], loc );
    ASSERT_VALUES_EQUAL( expected[6], expanded[6], loc );
    ASSERT_VALUES_EQUAL( expected[7], expanded[7], loc );
    ASSERT_VALUES_EQUAL( expected[8], expanded[8], loc );
    ASSERT_VALUES_EQUAL( expected[9], expanded[9], loc );
    ASSERT_VALUES_EQUAL( expected[10], expanded[10], loc );
    ASSERT_VALUES_EQUAL( expected[11], expanded[11], loc );
    ASSERT_VALUES_EQUAL( expected[12], expanded[12], loc );
    ASSERT_VALUES_EQUAL( expected[13], expanded[13], loc );
    ASSERT_VALUES_EQUAL( expected[14], expanded[14], loc );
    ASSERT_VALUES_EQUAL( expected[15], expanded[15], loc );
    ASSERT_VALUES_EQUAL( expected[16], expanded[16], loc );
    ASSERT_VALUES_EQUAL( expected[17], expanded[17], loc );
    ASSERT_VALUES_EQUAL( expected[18], expanded[18], loc );
    ASSERT_VALUES_EQUAL( expected[19], expanded[19], loc );
    ASSERT_VALUES_EQUAL( expected[20], expanded[20], loc );
    ASSERT_VALUES_EQUAL( expected[21], expanded[21], loc );
    ASSERT_VALUES_EQUAL( expected[22], expanded[22], loc );
    ASSERT_VALUES_EQUAL( expected[23], expanded[23], loc );
    ASSERT_VALUES_EQUAL( expected[24], expanded[24], loc );
    ASSERT_VALUES_EQUAL( expected[25], expanded[25], loc );
    ASSERT_VALUES_EQUAL( expected[26], expanded[26], loc );
}

void HexLagrangeShapeTest::test_corner_coeff( int corner )
{
    MsqPrintError err( std::cout );

    double expected[27];
    get_coeffs( XI_corner( corner ), expected );

    double coeff[100];
    size_t num_coeff = 11, indices[100];
    sf.coefficients( Sample( 0, corner ), allNodes, coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( !err );

    compare_coefficients( coeff, indices, num_coeff, expected, corner );
}

void HexLagrangeShapeTest::test_edge_coeff( int edge )
{
    MsqPrintError err( std::cout );

    double expected[27];
    get_coeffs( XI_edge( edge ), expected );

    double coeff[100];
    size_t num_coeff = 11, indices[100];
    sf.coefficients( Sample( 1, edge ), allNodes, coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( !err );

    compare_coefficients( coeff, indices, num_coeff, expected, edge + 8 );
}

void HexLagrangeShapeTest::test_face_coeff( int face )
{
    MsqPrintError err( std::cout );

    double expected[27];
    get_coeffs( XI_face( face ), expected );

    double coeff[100];
    size_t num_coeff = 11, indices[100];
    sf.coefficients( Sample( 2, face ), allNodes, coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( !err );

    compare_coefficients( coeff, indices, num_coeff, expected, face + 20 );
}

void HexLagrangeShapeTest::test_mid_coeff()
{
    MsqPrintError err( std::cout );

    double expected[27];
    get_coeffs( XI_elem(), expected );

    double coeff[100];
    size_t num_coeff = 11, indices[100];
    sf.coefficients( Sample( 3, 0 ), allNodes, coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( !err );

    compare_coefficients( coeff, indices, num_coeff, expected, 26 );
}

void HexLagrangeShapeTest::test_corner_derivs( int corner )
{
    MsqPrintError err( std::cout );

    MsqVector< 3 > expected[27];
    get_derivs( XI_corner( corner ), expected );

    size_t vertices[100], num_vtx = 23;
    MsqVector< 3 > derivs[100];
    sf.derivatives( Sample( 0, corner ), allNodes, vertices, derivs, num_vtx, err );
    CPPUNIT_ASSERT( !err );

    compare_derivatives( vertices, num_vtx, derivs, expected, corner );
}

void HexLagrangeShapeTest::test_edge_derivs( int edge )
{
    MsqPrintError err( std::cout );

    MsqVector< 3 > expected[27];
    get_derivs( XI_edge( edge ), expected );

    size_t vertices[100], num_vtx = 23;
    MsqVector< 3 > derivs[100];
    sf.derivatives( Sample( 1, edge ), allNodes, vertices, derivs, num_vtx, err );
    CPPUNIT_ASSERT( !err );

    compare_derivatives( vertices, num_vtx, derivs, expected, edge + 8 );
}

void HexLagrangeShapeTest::test_face_derivs( int face )
{
    MsqPrintError err( std::cout );

    MsqVector< 3 > expected[27];
    get_derivs( XI_face( face ), expected );

    size_t vertices[100], num_vtx = 23;
    MsqVector< 3 > derivs[100];
    sf.derivatives( Sample( 2, face ), allNodes, vertices, derivs, num_vtx, err );
    CPPUNIT_ASSERT( !err );

    compare_derivatives( vertices, num_vtx, derivs, expected, face + 20 );
}

void HexLagrangeShapeTest::test_mid_derivs()
{
    MsqPrintError err( std::cout );

    MsqVector< 3 > expected[27];
    get_derivs( XI_elem(), expected );

    size_t vertices[100], num_vtx = 23;
    MsqVector< 3 > derivs[100];
    sf.derivatives( Sample( 3, 0 ), allNodes, vertices, derivs, num_vtx, err );
    CPPUNIT_ASSERT( !err );

    compare_derivatives( vertices, num_vtx, derivs, expected, 26 );
}

void HexLagrangeShapeTest::test_corners_coeff()
{
    for( unsigned i = 0; i < 8; ++i )
        test_corner_coeff( i );
}

void HexLagrangeShapeTest::test_edges_coeff()
{
    for( unsigned i = 0; i < 12; ++i )
        test_edge_coeff( i );
}

void HexLagrangeShapeTest::test_faces_coeff()
{
    for( unsigned i = 0; i < 6; ++i )
        test_face_coeff( i );
}

void HexLagrangeShapeTest::test_corners_derivs()
{
    for( unsigned i = 0; i < 8; ++i )
        test_corner_derivs( i );
}

void HexLagrangeShapeTest::test_edges_derivs()
{
    for( unsigned i = 0; i < 12; ++i )
        test_edge_derivs( i );
}

void HexLagrangeShapeTest::test_faces_derivs()
{
    for( unsigned i = 0; i < 6; ++i )
        test_face_derivs( i );
}

void HexLagrangeShapeTest::test_ideal_jacobian()
{
    MsqError err;
    MsqMatrix< 3, 3 > J_act, J_exp( 1.0 );
    sf.ideal( Sample( 3, 0 ), J_act, err );
    ASSERT_NO_ERROR( err );

    // Matrices should be a rotation of each other.
    // First, calculate tentative rotation matrix
    MsqMatrix< 3, 3 > R = inverse( J_exp ) * J_act;
    // next check that it is a rotation
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 1.0, det( R ), 1e-6 );          // no scaling
    ASSERT_MATRICES_EQUAL( transpose( R ), inverse( R ), 1e-6 );  // orthogonal
}