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Intrepid
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00001 // @HEADER 00002 // ************************************************************************ 00003 // 00004 // Intrepid Package 00005 // Copyright (2007) Sandia Corporation 00006 // 00007 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive 00008 // license for use of this work by or on behalf of the U.S. Government. 00009 // 00010 // This library is free software; you can redistribute it and/or modify 00011 // it under the terms of the GNU Lesser General Public License as 00012 // published by the Free Software Foundation; either version 2.1 of the 00013 // License, or (at your option) any later version. 00014 // 00015 // This library is distributed in the hope that it will be useful, but 00016 // WITHOUT ANY WARRANTY; without even the implied warranty of 00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00018 // Lesser General Public License for more details. 00019 // 00020 // You should have received a copy of the GNU Lesser General Public 00021 // License along with this library; if not, write to the Free Software 00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 00023 // USA 00024 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) or 00025 // Denis Ridzal (dridzal@sandia.gov). 00026 // 00027 // ************************************************************************ 00028 // @HEADER 00029 00035 namespace Intrepid { 00036 00037 00038 template<class Scalar, class ArrayScalar> 00039 Basis_HGRAD_HEX_C2_FEM<Scalar,ArrayScalar>::Basis_HGRAD_HEX_C2_FEM() 00040 { 00041 this -> basisCardinality_ = 27; 00042 this -> basisDegree_ = 2; 00043 this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ); 00044 this -> basisType_ = BASIS_FEM_DEFAULT; 00045 this -> basisCoordinates_ = COORDINATES_CARTESIAN; 00046 this -> basisTagsAreSet_ = false; 00047 } 00048 00049 00050 00051 template<class Scalar, class ArrayScalar> 00052 void Basis_HGRAD_HEX_C2_FEM<Scalar, ArrayScalar>::initializeTags() { 00053 00054 // Basis-dependent intializations 00055 int tagSize = 4; // size of DoF tag, i.e., number of fields in the tag 00056 int posScDim = 0; // position in the tag, counting from 0, of the subcell dim 00057 int posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal 00058 int posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell 00059 00060 // An array with local DoF tags assigned to basis functions, in the order of their local enumeration 00061 int tags[] = { 0, 0, 0, 1, // Nodes 0 to 7 follow vertex order of the topology 00062 0, 1, 0, 1, 00063 0, 2, 0, 1, 00064 0, 3, 0, 1, 00065 0, 4, 0, 1, 00066 0, 5, 0, 1, 00067 0, 6, 0, 1, 00068 0, 7, 0, 1, 00069 1, 0, 0, 1, // Node 8 -> edge 0 00070 1, 1, 0, 1, // Node 9 -> edge 1 00071 1, 2, 0, 1, // Node 10 -> edge 2 00072 1, 3, 0, 1, // Node 11 -> edge 3 00073 1, 8, 0, 1, // Node 12 -> edge 8 00074 1, 9, 0, 1, // Node 13 -> edge 9 00075 1,10, 0, 1, // Node 14 -> edge 10 00076 1,11, 0, 1, // Node 15 -> edge 11 00077 1, 4, 0, 1, // Node 16 -> edge 4 00078 1, 5, 0, 1, // Node 17 -> edge 5 00079 1, 6, 0, 1, // Node 18 -> edge 6 00080 1, 7, 0, 1, // Node 19 -> edge 7 00081 3, 0, 0, 1, // Node 20 -> Hexahedron 00082 2, 4, 0, 1, // Node 21 -> face 4 00083 2, 5, 0, 1, // Node 22 -> face 5 00084 2, 3, 0, 1, // Node 23 -> face 3 00085 2, 1, 0, 1, // Node 24 -> face 1 00086 2, 0, 0, 1, // Node 25 -> face 0 00087 2, 2, 0, 1, // Node 26 -> face 2 00088 }; 00089 00090 // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays: 00091 Intrepid::setOrdinalTagData(this -> tagToOrdinal_, 00092 this -> ordinalToTag_, 00093 tags, 00094 this -> basisCardinality_, 00095 tagSize, 00096 posScDim, 00097 posScOrd, 00098 posDfOrd); 00099 } 00100 00101 00102 00103 template<class Scalar, class ArrayScalar> 00104 void Basis_HGRAD_HEX_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar & outputValues, 00105 const ArrayScalar & inputPoints, 00106 const EOperator operatorType) const { 00107 00108 // Verify arguments 00109 #ifdef HAVE_INTREPID_DEBUG 00110 Intrepid::getValues_HGRAD_Args<Scalar, ArrayScalar>(outputValues, 00111 inputPoints, 00112 operatorType, 00113 this -> getBaseCellTopology(), 00114 this -> getCardinality() ); 00115 #endif 00116 00117 // Number of evaluation points = dim 0 of inputPoints 00118 int dim0 = inputPoints.dimension(0); 00119 00120 // Temporaries: (x,y,z) coordinates of the evaluation point 00121 Scalar x = 0.0; 00122 Scalar y = 0.0; 00123 Scalar z = 0.0; 00124 00125 switch (operatorType) { 00126 00127 case OPERATOR_VALUE: 00128 for (int i0 = 0; i0 < dim0; i0++) { 00129 x = inputPoints(i0, 0); 00130 y = inputPoints(i0, 1); 00131 z = inputPoints(i0, 2); 00132 00133 // outputValues is a rank-2 array with dimensions (basisCardinality_, dim0) 00134 outputValues( 0, i0) = 0.125*(-1. + x)*x*(-1. + y)*y*(-1. + z)*z; 00135 outputValues( 1, i0) = 0.125*x*(1.+ x)*(-1. + y)*y*(-1. + z)*z; 00136 outputValues( 2, i0) = 0.125*x*(1.+ x)*y*(1.+ y)*(-1. + z)*z; 00137 outputValues( 3, i0) = 0.125*(-1. + x)*x*y*(1.+ y)*(-1. + z)*z; 00138 outputValues( 4, i0) = 0.125*(-1. + x)*x*(-1. + y)*y*z*(1.+ z); 00139 outputValues( 5, i0) = 0.125*x*(1.+ x)*(-1. + y)*y*z*(1.+ z); 00140 outputValues( 6, i0) = 0.125*x*(1.+ x)*y*(1.+ y)*z*(1.+ z); 00141 outputValues( 7, i0) = 0.125*(-1. + x)*x*y*(1.+ y)*z*(1.+ z); 00142 outputValues( 8, i0) = 0.25*(1. - x)*(1. + x)*(-1. + y)*y*(-1. + z)*z; 00143 outputValues( 9, i0) = 0.25*x*(1.+ x)*(1. - y)*(1. + y)*(-1. + z)*z; 00144 outputValues(10, i0) = 0.25*(1. - x)*(1. + x)*y*(1.+ y)*(-1. + z)*z; 00145 outputValues(11, i0) = 0.25*(-1. + x)*x*(1. - y)*(1. + y)*(-1. + z)*z; 00146 outputValues(12, i0) = 0.25*(-1. + x)*x*(-1. + y)*y*(1. - z)*(1. + z); 00147 outputValues(13, i0) = 0.25*x*(1.+ x)*(-1. + y)*y*(1. - z)*(1. + z); 00148 outputValues(14, i0) = 0.25*x*(1.+ x)*y*(1.+ y)*(1. - z)*(1. + z); 00149 outputValues(15, i0) = 0.25*(-1. + x)*x*y*(1.+ y)*(1. - z)*(1. + z); 00150 outputValues(16, i0) = 0.25*(1. - x)*(1. + x)*(-1. + y)*y*z*(1.+ z); 00151 outputValues(17, i0) = 0.25*x*(1.+ x)*(1. - y)*(1. + y)*z*(1.+ z); 00152 outputValues(18, i0) = 0.25*(1. - x)*(1. + x)*y*(1.+ y)*z*(1.+ z); 00153 outputValues(19, i0) = 0.25*(-1. + x)*x*(1. - y)*(1. + y)*z*(1.+ z); 00154 outputValues(20, i0) = (1. - x)*(1. + x)*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00155 outputValues(21, i0) = 0.5*(1. - x)*(1. + x)*(1. - y)*(1. + y)*(-1. + z)*z; 00156 outputValues(22, i0) = 0.5*(1. - x)*(1. + x)*(1. - y)*(1. + y)*z*(1.+ z); 00157 outputValues(23, i0) = 0.5*(-1. + x)*x*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00158 outputValues(24, i0) = 0.5*x*(1.+ x)*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00159 outputValues(25, i0) = 0.5*(1. - x)*(1. + x)*(-1. + y)*y*(1. - z)*(1. + z); 00160 outputValues(26, i0) = 0.5*(1. - x)*(1. + x)*y*(1.+ y)*(1. - z)*(1. + z); 00161 } 00162 break; 00163 00164 case OPERATOR_GRAD: 00165 case OPERATOR_D1: 00166 for (int i0 = 0; i0 < dim0; i0++) { 00167 x = inputPoints(i0,0); 00168 y = inputPoints(i0,1); 00169 z = inputPoints(i0,2); 00170 00171 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim) 00172 outputValues(0, i0, 0) = (-0.125 + 0.25*x)*(-1. + y)*y*(-1. + z)*z; 00173 outputValues(0, i0, 1) = (-1. + x)*x*(-0.125 + 0.25*y)*(-1. + z)*z; 00174 outputValues(0, i0, 2) = (-1. + x)*x*(-1. + y)*y*(-0.125 + 0.25*z); 00175 00176 outputValues(1, i0, 0) = (0.125 + 0.25*x)*(-1. + y)*y*(-1. + z)*z; 00177 outputValues(1, i0, 1) = x*(1. + x)*(-0.125 + 0.25*y)*(-1. + z)*z; 00178 outputValues(1, i0, 2) = x*(1. + x)*(-1. + y)*y*(-0.125 + 0.25*z); 00179 00180 outputValues(2, i0, 0) = (0.125 + 0.25*x)*y*(1. + y)*(-1. + z)*z; 00181 outputValues(2, i0, 1) = x*(1. + x)*(0.125 + 0.25*y)*(-1. + z)*z; 00182 outputValues(2, i0, 2) = x*(1. + x)*y*(1. + y)*(-0.125 + 0.25*z); 00183 00184 outputValues(3, i0, 0) = (-0.125 + 0.25*x)*y*(1. + y)*(-1. + z)*z; 00185 outputValues(3, i0, 1) = (-1. + x)*x*(0.125 + 0.25*y)*(-1. + z)*z; 00186 outputValues(3, i0, 2) = (-1. + x)*x*y*(1. + y)*(-0.125 + 0.25*z); 00187 00188 outputValues(4, i0, 0) = (-0.125 + 0.25*x)*(-1. + y)*y*z*(1. + z); 00189 outputValues(4, i0, 1) = (-1. + x)*x*(-0.125 + 0.25*y)*z*(1. + z); 00190 outputValues(4, i0, 2) = (-1. + x)*x*(-1. + y)*y*(0.125 + 0.25*z); 00191 00192 outputValues(5, i0, 0) = (0.125 + 0.25*x)*(-1. + y)*y*z*(1. + z); 00193 outputValues(5, i0, 1) = x*(1. + x)*(-0.125 + 0.25*y)*z*(1. + z); 00194 outputValues(5, i0, 2) = x*(1. + x)*(-1. + y)*y*(0.125 + 0.25*z); 00195 00196 outputValues(6, i0, 0) = (0.125 + 0.25*x)*y*(1. + y)*z*(1. + z); 00197 outputValues(6, i0, 1) = x*(1. + x)*(0.125 + 0.25*y)*z*(1. + z); 00198 outputValues(6, i0, 2) = x*(1. + x)*y*(1. + y)*(0.125 + 0.25*z); 00199 00200 outputValues(7, i0, 0) = (-0.125 + 0.25*x)*y*(1. + y)*z*(1. + z); 00201 outputValues(7, i0, 1) = (-1. + x)*x*(0.125 + 0.25*y)*z*(1. + z); 00202 outputValues(7, i0, 2) = (-1. + x)*x*y*(1. + y)*(0.125 + 0.25*z); 00203 00204 outputValues(8, i0, 0) = -0.5*x*(-1. + y)*y*(-1. + z)*z; 00205 outputValues(8, i0, 1) = (1. - x)*(1. + x)*(-0.25 + 0.5*y)*(-1. + z)*z; 00206 outputValues(8, i0, 2) = (1. - x)*(1. + x)*(-1. + y)*y*(-0.25 + 0.5*z); 00207 00208 outputValues(9, i0, 0) = (0.25 + 0.5*x)*(1. - y)*(1. + y)*(-1. + z)*z; 00209 outputValues(9, i0, 1) = x*(1. + x)*(-0.5*y)*(-1. + z)*z; 00210 outputValues(9, i0, 2) = x*(1. + x)*(1. - y)*(1. + y)*(-0.25 + 0.5*z); 00211 00212 outputValues(10,i0, 0) = -0.5*x*y*(1. + y)*(-1. + z)*z; 00213 outputValues(10,i0, 1) = (1. - x)*(1. + x)*(0.25 + 0.5*y)*(-1. + z)*z; 00214 outputValues(10,i0, 2) = (1. - x)*(1. + x)*y*(1. + y)*(-0.25 + 0.5*z); 00215 00216 outputValues(11,i0, 0) = (-0.25 + 0.5*x)*(1. - y)*(1. + y)*(-1. + z)*z; 00217 outputValues(11,i0, 1) = (-1. + x)*x*(-0.5*y)*(-1. + z)*z; 00218 outputValues(11,i0, 2) = (-1. + x)*x*(1. - y)*(1. + y)*(-0.25 + 0.5*z); 00219 00220 outputValues(12,i0, 0) = (-0.25 + 0.5*x)*(-1. + y)*y*(1. - z)*(1. + z); 00221 outputValues(12,i0, 1) = (-1. + x)*x*(-0.25 + 0.5*y)*(1. - z)*(1. + z); 00222 outputValues(12,i0, 2) = (-1. + x)*x*(-1. + y)*y*(-0.5*z); 00223 00224 outputValues(13,i0, 0) = (0.25 + 0.5*x)*(-1. + y)*y*(1. - z)*(1. + z); 00225 outputValues(13,i0, 1) = x*(1. + x)*(-0.25 + 0.5*y)*(1. - z)*(1. + z); 00226 outputValues(13,i0, 2) = x*(1. + x)*(-1. + y)*y*(-0.5*z); 00227 00228 outputValues(14,i0, 0) = (0.25 + 0.5*x)*y*(1. + y)*(1. - z)*(1. + z); 00229 outputValues(14,i0, 1) = x*(1. + x)*(0.25 + 0.5*y)*(1. - z)*(1. + z); 00230 outputValues(14,i0, 2) = x*(1. + x)*y*(1. + y)*(-0.5*z); 00231 00232 outputValues(15,i0, 0) = (-0.25 + 0.5*x)*y*(1. + y)*(1. - z)*(1. + z); 00233 outputValues(15,i0, 1) = (-1. + x)*x*(0.25 + 0.5*y)*(1. - z)*(1. + z); 00234 outputValues(15,i0, 2) = (-1. + x)*x*y*(1. + y)*(-0.5*z); 00235 00236 outputValues(16,i0, 0) = -0.5*x*(-1. + y)*y*z*(1. + z); 00237 outputValues(16,i0, 1) = (1. - x)*(1. + x)*(-0.25 + 0.5*y)*z*(1. + z); 00238 outputValues(16,i0, 2) = (1. - x)*(1. + x)*(-1. + y)*y*(0.25 + 0.5*z); 00239 00240 outputValues(17,i0, 0) = (0.25 + 0.5*x)*(1. - y)*(1. + y)*z*(1. + z); 00241 outputValues(17,i0, 1) = x*(1. + x)*(-0.5*y)*z*(1. + z); 00242 outputValues(17,i0, 2) = x*(1. + x)*(1. - y)*(1. + y)*(0.25 + 0.5*z); 00243 00244 outputValues(18,i0, 0) = -0.5*x*y*(1. + y)*z*(1. + z); 00245 outputValues(18,i0, 1) = (1. - x)*(1. + x)*(0.25 + 0.5*y)*z*(1. + z); 00246 outputValues(18,i0, 2) = (1. - x)*(1. + x)*y*(1. + y)*(0.25 + 0.5*z); 00247 00248 outputValues(19,i0, 0) = (-0.25 + 0.5*x)*(1. - y)*(1. + y)*z*(1. + z); 00249 outputValues(19,i0, 1) = (-1. + x)*x*(-0.5*y)*z*(1. + z); 00250 outputValues(19,i0, 2) = (-1. + x)*x*(1. - y)*(1. + y)*(0.25 + 0.5*z); 00251 00252 outputValues(20,i0, 0) = -2.*x*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00253 outputValues(20,i0, 1) = (1. - x)*(1. + x)*(-2.*y)*(1. - z)*(1. + z); 00254 outputValues(20,i0, 2) = (1. - x)*(1. + x)*(1. - y)*(1. + y)*(-2.*z); 00255 00256 outputValues(21,i0, 0) = -x*(1. - y)*(1. + y)*(-1. + z)*z; 00257 outputValues(21,i0, 1) = (1. - x)*(1. + x)*(-y)*(-1. + z)*z; 00258 outputValues(21,i0, 2) = (1. - x)*(1. + x)*(1. - y)*(1. + y)*(-0.5 + z); 00259 00260 outputValues(22,i0, 0) = -x*(1. - y)*(1. + y)*z*(1. + z); 00261 outputValues(22,i0, 1) = (1. - x)*(1. + x)*(-y)*z*(1. + z); 00262 outputValues(22,i0, 2) = (1. - x)*(1. + x)*(1. - y)*(1. + y)*(0.5 + z); 00263 00264 outputValues(23,i0, 0) = (-0.5 + x)*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00265 outputValues(23,i0, 1) = (-1. + x)*x*(-y)*(1. - z)*(1. + z); 00266 outputValues(23,i0, 2) = (-1. + x)*x*(1. - y)*(1. + y)*(-z); 00267 00268 outputValues(24,i0, 0) = (0.5 + x)*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00269 outputValues(24,i0, 1) = x*(1. + x)*(-y)*(1. - z)*(1. + z); 00270 outputValues(24,i0, 2) = x*(1. + x)*(1. - y)*(1. + y)*(-z); 00271 00272 outputValues(25,i0, 0) = -x*(-1. + y)*y*(1. - z)*(1. + z); 00273 outputValues(25,i0, 1) = (1. - x)*(1. + x)*(-0.5 + y)*(1. - z)*(1. + z); 00274 outputValues(25,i0, 2) = (1. - x)*(1. + x)*(-1. + y)*y*(-z); 00275 00276 outputValues(26,i0, 0) = -x*y*(1. + y)*(1. - z)*(1. + z); 00277 outputValues(26,i0, 1) = (1. - x)*(1. + x)*(0.5 + y)*(1. - z)*(1. + z); 00278 outputValues(26,i0, 2) = (1. - x)*(1. + x)*y*(1. + y)*(-z); 00279 } 00280 break; 00281 00282 case OPERATOR_CURL: 00283 TEST_FOR_EXCEPTION( (operatorType == OPERATOR_CURL), std::invalid_argument, 00284 ">>> ERROR (Basis_HGRAD_HEX_C2_FEM): CURL is invalid operator for rank-0 (scalar) functions in 3D"); 00285 break; 00286 00287 case OPERATOR_DIV: 00288 TEST_FOR_EXCEPTION( (operatorType == OPERATOR_DIV), std::invalid_argument, 00289 ">>> ERROR (Basis_HGRAD_HEX_C2_FEM): DIV is invalid operator for rank-0 (scalar) functions in 3D"); 00290 break; 00291 00292 case OPERATOR_D2: 00293 for (int i0 = 0; i0 < dim0; i0++) { 00294 x = inputPoints(i0,0); 00295 y = inputPoints(i0,1); 00296 z = inputPoints(i0,2); 00297 00298 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, D2Cardinality = 6) 00299 outputValues(0, i0, 0) = 0.25*(-1. + y)*y*(-1. + z)*z; 00300 outputValues(0, i0, 1) = (-0.125 + y*(0.25 - 0.25*z) + x*(0.25 + y*(-0.5 + 0.5*z) - 0.25*z) + 0.125*z)*z; 00301 outputValues(0, i0, 2) = y*(-0.125 + x*(0.25 + y*(-0.25 + 0.5*z) - 0.5*z) + y*(0.125 - 0.25*z) + 0.25*z); 00302 outputValues(0, i0, 3) = 0.25*(-1. + x)*x*(-1. + z)*z; 00303 outputValues(0, i0, 4) = x*(-0.125 + y*(0.25 - 0.5*z) + x*(0.125 + y*(-0.25 + 0.5*z) - 0.25*z) + 0.25*z); 00304 outputValues(0, i0, 5) = 0.25*(-1. + x)*x*(-1. + y)*y; 00305 00306 outputValues(1, i0, 0) = 0.25*(-1. + y)*y*(-1. + z)*z; 00307 outputValues(1, i0, 1) = (0.125 + x*(0.25 + y*(-0.5 + 0.5*z) - 0.25*z) + y*(-0.25 + 0.25*z) - 0.125*z)*z; 00308 outputValues(1, i0, 2) = y*(0.125 + x*(0.25 + y*(-0.25 + 0.5*z) - 0.5*z) + y*(-0.125 + 0.25*z) - 0.25*z); 00309 outputValues(1, i0, 3) = 0.25*x*(1 + x)*(-1. + z)*z; 00310 outputValues(1, i0, 4) = x*(1. + x)*(0.125 + y*(-0.25 + 0.5*z) - 0.25*z); 00311 outputValues(1, i0, 5) = 0.25*x*(1 + x)*(-1. + y)*y; 00312 00313 outputValues(2, i0, 0) = 0.25*y*(1 + y)*(-1. + z)*z; 00314 outputValues(2, i0, 1) = (0.125 + x*(0.25 + 0.5*y) + 0.25*y)*(-1. + z)*z; 00315 outputValues(2, i0, 2) = y*(1. + y)*(-0.125 + x*(-0.25 + 0.5*z) + 0.25*z); 00316 outputValues(2, i0, 3) = 0.25*x*(1 + x)*(-1. + z)*z; 00317 outputValues(2, i0, 4) = x*(1. + x)*(-0.125 + y*(-0.25 + 0.5*z) + 0.25*z); 00318 outputValues(2, i0, 5) = 0.25*x*(1 + x)*y*(1 + y); 00319 00320 outputValues(3, i0, 0) = 0.25*y*(1 + y)*(-1. + z)*z; 00321 outputValues(3, i0, 1) = (0.125 + y*(0.25 - 0.25*z) + x*(-0.25 + y*(-0.5 + 0.5*z) + 0.25*z) - 0.125*z)*z; 00322 outputValues(3, i0, 2) = y*(1. + y)*(0.125 + x*(-0.25 + 0.5*z) - 0.25*z); 00323 outputValues(3, i0, 3) = 0.25*(-1. + x)*x*(-1. + z)*z; 00324 outputValues(3, i0, 4) = x*(0.125 + y*(0.25 - 0.5*z) + x*(-0.125 + y*(-0.25 + 0.5*z) + 0.25*z) - 0.25*z); 00325 outputValues(3, i0, 5) = 0.25*(-1. + x)*x*y*(1 + y); 00326 00327 outputValues(4, i0, 0) = 0.25*(-1. + y)*y*z*(1 + z); 00328 outputValues(4, i0, 1) = (0.125 + x*(-0.25 + 0.5*y) - 0.25*y)*z*(1. + z); 00329 outputValues(4, i0, 2) = y*(0.125 + x*(-0.25 + y*(0.25 + 0.5*z) - 0.5*z) + y*(-0.125 - 0.25*z) + 0.25*z); 00330 outputValues(4, i0, 3) = 0.25*(-1. + x)*x*z*(1 + z); 00331 outputValues(4, i0, 4) = x*(0.125 + y*(-0.25 - 0.5*z) + x*(-0.125 + y*(0.25 + 0.5*z) - 0.25*z) + 0.25*z); 00332 outputValues(4, i0, 5) = 0.25*(-1. + x)*x*(-1. + y)*y; 00333 00334 outputValues(5, i0, 0) = 0.25*(-1. + y)*y*z*(1 + z); 00335 outputValues(5, i0, 1) = (-0.125 + x*(-0.25 + 0.5*y) + 0.25*y)*z*(1. + z); 00336 outputValues(5, i0, 2) = (-1. + y)*y*(0.125 + x*(0.25 + 0.5*z) + 0.25*z); 00337 outputValues(5, i0, 3) = 0.25*x*(1 + x)*z*(1 + z); 00338 outputValues(5, i0, 4) = x*(1. + x)*(-0.125 + y*(0.25 + 0.5*z) - 0.25*z); 00339 outputValues(5, i0, 5) = 0.25*x*(1 + x)*(-1. + y)*y; 00340 00341 outputValues(6, i0, 0) = 0.25*y*(1 + y)*z*(1 + z); 00342 outputValues(6, i0, 1) = (0.125 + x*(0.25 + 0.5*y) + 0.25*y)*z*(1. + z); 00343 outputValues(6, i0, 2) = y*(1. + y)*(0.125 + x*(0.25 + 0.5*z) + 0.25*z); 00344 outputValues(6, i0, 3) = 0.25*x*(1 + x)*z*(1 + z); 00345 outputValues(6, i0, 4) = x*(1. + x)*(0.125 + y*(0.25 + 0.5*z) + 0.25*z); 00346 outputValues(6, i0, 5) = 0.25*x*(1 + x)*y*(1 + y); 00347 00348 outputValues(7, i0, 0) = 0.25*y*(1 + y)*z*(1 + z); 00349 outputValues(7, i0, 1) = (-0.125 + x*(0.25 + 0.5*y) - 0.25*y)*z*(1. + z); 00350 outputValues(7, i0, 2) = y*(1. + y)*(-0.125 + x*(0.25 + 0.5*z) - 0.25*z); 00351 outputValues(7, i0, 3) = 0.25*(-1. + x)*x*z*(1 + z); 00352 outputValues(7, i0, 4) = (-1. + x)*x*(0.125 + y*(0.25 + 0.5*z) + 0.25*z); 00353 outputValues(7, i0, 5) = 0.25*(-1. + x)*x*y*(1 + y); 00354 00355 outputValues(8, i0, 0) = -0.5*(-1. + y)*y*(-1. + z)*z; 00356 outputValues(8, i0, 1) = (0. + x*(-0.5 + y))*z + (x*(0.5 - y) )*(z*z); 00357 outputValues(8, i0, 2) = (y*y)*(x*(0.5 - z) ) + y*(x*(-0.5 + z)); 00358 outputValues(8, i0, 3) = 0.5*(1. - x)*(1. + x)*(-1. + z)*z; 00359 outputValues(8, i0, 4) = 0.25 + (x*x)*(-0.25 + y*(0.5 - z) + 0.5*z) - 0.5*z + y*(-0.5 + z); 00360 outputValues(8, i0, 5) = 0.5*(1. - x)*(1. + x)*(-1. + y)*y; 00361 00362 outputValues(9, i0, 0) = 0.5*(1. - y)*(1. + y)*(-1. + z)*z; 00363 outputValues(9, i0, 1) = (0.5*y + x*(y))*z + (x*(-y) - 0.5*y)*(z*z); 00364 outputValues(9, i0, 2) = -0.25 + (y*y)*(0.25 - 0.5*z) + 0.5*z + x*(-0.5 + (y*y)*(0.5 - z) + z); 00365 outputValues(9, i0, 3) = -0.5*x*(1 + x)*(-1. + z)*z; 00366 outputValues(9, i0, 4) = x*(y*(0.5 - z) ) + (x*x)*(y*(0.5 - z) ); 00367 outputValues(9, i0, 5) = 0.5*x*(1 + x)*(1. - y)*(1. + y); 00368 00369 outputValues(10,i0, 0) = -0.5*y*(1 + y)*(-1. + z)*z; 00370 outputValues(10,i0, 1) = (0. + x*(0.5 + y))*z + (x*(-0.5 - y) )*(z*z); 00371 outputValues(10,i0, 2) = y*(x*(0.5 - z) ) + (y*y)*(x*(0.5 - z) ); 00372 outputValues(10,i0, 3) = 0.5*(1. - x)*(1. + x)*(-1. + z)*z; 00373 outputValues(10,i0, 4) = -0.25 + (x*x)*(0.25 + y*(0.5 - z) - 0.5*z) + 0.5*z + y*(-0.5 + z); 00374 outputValues(10,i0, 5) = 0.5*(1. - x)*(1. + x)*y*(1 + y); 00375 00376 outputValues(11,i0, 0) = 0.5*(1. - y)*(1. + y)*(-1. + z)*z; 00377 outputValues(11,i0, 1) = (-0.5*y + x*(y))*z + (x*(-y) + 0.5*y)*(z*z); 00378 outputValues(11,i0, 2) = 0.25 + (y*y)*(-0.25 + 0.5*z) - 0.5*z + x*(-0.5 + (y*y)*(0.5 - z) + z); 00379 outputValues(11,i0, 3) = -0.5*(-1. + x)*x*(-1. + z)*z; 00380 outputValues(11,i0, 4) = (x*x)*(y*(0.5 - z) ) + x*(y*(-0.5 + z)); 00381 outputValues(11,i0, 5) = 0.5*(-1. + x)*x*(1. - y)*(1. + y); 00382 00383 outputValues(12,i0, 0) = 0.5*(-1. + y)*y*(1. - z)*(1. + z); 00384 outputValues(12,i0, 1) = 0.25 - 0.25*(z*z) + y*(-0.5 + 0.5*(z*z)) + x*(-0.5 + 0.5*(z*z) + y*(1. - (z*z))); 00385 outputValues(12,i0, 2) = (y*y)*(x*(-z) + 0.5*z) + y*(-0.5*z + x*(z)); 00386 outputValues(12,i0, 3) = 0.5*(-1. + x)*x*(1. - z)*(1. + z); 00387 outputValues(12,i0, 4) = (x*x)*(y*(-z) + 0.5*z) + x*(-0.5*z + y*(z)); 00388 outputValues(12,i0, 5) = -0.5*(-1. + x)*x*(-1. + y)*y; 00389 00390 outputValues(13,i0, 0) = 0.5*(-1. + y)*y*(1. - z)*(1. + z); 00391 outputValues(13,i0, 1) = -0.25 + 0.25*(z*z) + y*(0.5 - 0.5*(z*z)) + x*(-0.5 + 0.5*(z*z) + y*(1. - (z*z))); 00392 outputValues(13,i0, 2) = (y*y)*(x*(-z) - 0.5*z) + y*(0.5*z + x*(z)); 00393 outputValues(13,i0, 3) = 0.5*x*(1 + x)*(1. - z)*(1. + z); 00394 outputValues(13,i0, 4) = x*(y*(-z) + 0.5*z) + (x*x)*(y*(-z) + 0.5*z); 00395 outputValues(13,i0, 5) = -0.5*x*(1 + x)*(-1. + y)*y; 00396 00397 outputValues(14,i0, 0) = 0.5*y*(1 + y)*(1. - z)*(1. + z); 00398 outputValues(14,i0, 1) = 0.25 - 0.25*(z*z) + y*(0.5 - 0.5*(z*z)) + x*(0.5 - 0.5*(z*z) + y*(1. - (z*z))); 00399 outputValues(14,i0, 2) = y*(x*(-z) - 0.5*z) + (y*y)*(x*(-z) - 0.5*z); 00400 outputValues(14,i0, 3) = 0.5*x*(1 + x)*(1. - z)*(1. + z); 00401 outputValues(14,i0, 4) = x*(y*(-z) - 0.5*z) + (x*x)*(y*(-z) - 0.5*z); 00402 outputValues(14,i0, 5) = -0.5*x*(1 + x)*y*(1 + y); 00403 00404 outputValues(15,i0, 0) = 0.5*y*(1 + y)*(1. - z)*(1. + z); 00405 outputValues(15,i0, 1) = -0.25 + 0.25*(z*z) + y*(-0.5 + 0.5*(z*z)) + x*(0.5 - 0.5*(z*z) + y*(1. - (z*z))); 00406 outputValues(15,i0, 2) = y*(x*(-z) + 0.5*z) + (y*y)*(x*(-z) + 0.5*z); 00407 outputValues(15,i0, 3) = 0.5*(-1. + x)*x*(1. - z)*(1. + z); 00408 outputValues(15,i0, 4) = (x*x)*(y*(-z) - 0.5*z) + x*(0.5*z + y*(z)); 00409 outputValues(15,i0, 5) = -0.5*(-1. + x)*x*y*(1 + y); 00410 00411 outputValues(16,i0, 0) = -0.5*(-1. + y)*y*z*(1 + z); 00412 outputValues(16,i0, 1) = (x*(0.5 - y) )*z + (x*(0.5 - y) )*(z*z); 00413 outputValues(16,i0, 2) = (y*y)*(x*(-0.5 - z) ) + y*(x*(0.5 + z)); 00414 outputValues(16,i0, 3) = 0.5*(1. - x)*(1. + x)*z*(1 + z); 00415 outputValues(16,i0, 4) = -0.25 + (x*x)*(0.25 + y*(-0.5 - z) + 0.5*z) - 0.5*z + y*(0.5 + z); 00416 outputValues(16,i0, 5) = 0.5*(1. - x)*(1. + x)*(-1. + y)*y; 00417 00418 outputValues(17,i0, 0) = 0.5*(1. - y)*(1. + y)*z*(1 + z); 00419 outputValues(17,i0, 1) = (x*(-y) - 0.5*y)*z + (x*(-y) - 0.5*y)*(z*z); 00420 outputValues(17,i0, 2) = 0.25 + (y*y)*(-0.25 - 0.5*z) + 0.5*z + x*(0.5 + (y*y)*(-0.5 - z) + z); 00421 outputValues(17,i0, 3) = -0.5*x*(1 + x)*z*(1 + z); 00422 outputValues(17,i0, 4) = x*(y*(-0.5 - z) ) + (x*x)*(y*(-0.5 - z) ); 00423 outputValues(17,i0, 5) = 0.5*x*(1 + x)*(1. - y)*(1. + y); 00424 00425 outputValues(18,i0, 0) = -0.5*y*(1 + y)*z*(1 + z); 00426 outputValues(18,i0, 1) = (x*(-0.5 - y) )*z + (x*(-0.5 - y) )*(z*z); 00427 outputValues(18,i0, 2) = y*(x*(-0.5 - z) ) + (y*y)*(x*(-0.5 - z) ); 00428 outputValues(18,i0, 3) = 0.5*(1. - x)*(1. + x)*z*(1 + z); 00429 outputValues(18,i0, 4) = 0.25 + (x*x)*(-0.25 + y*(-0.5 - z) - 0.5*z) + 0.5*z + y*(0.5 + z); 00430 outputValues(18,i0, 5) = 0.5*(1. - x)*(1. + x)*y*(1 + y); 00431 00432 outputValues(19,i0, 0) = 0.5*(1. - y)*(1. + y)*z*(1 + z); 00433 outputValues(19,i0, 1) = (x*(-y) + 0.5*y)*z + (x*(-y) + 0.5*y)*(z*z); 00434 outputValues(19,i0, 2) = -0.25 + (y*y)*(0.25 + 0.5*z) - 0.5*z + x*(0.5 + (y*y)*(-0.5 - z) + z); 00435 outputValues(19,i0, 3) = -0.5*(-1. + x)*x*z*(1 + z); 00436 outputValues(19,i0, 4) = (x*x)*(y*(-0.5 - z) ) + x*(y*(0.5 + z)); 00437 outputValues(19,i0, 5) = 0.5*(-1. + x)*x*(1. - y)*(1. + y); 00438 00439 outputValues(20,i0, 0) = -2.*(1. - y)*(1. + y)*(1. - z)*(1. + z); 00440 outputValues(20,i0, 1) = -4.*x*y*(-1. + z*z); 00441 outputValues(20,i0, 2) = x*((y*y)*(-4.*z) + 4.*z); 00442 outputValues(20,i0, 3) = -2.*(1. - x)*(1. + x)*(1. - z)*(1. + z); 00443 outputValues(20,i0, 4) = (x*x)*(y*(-4.*z) ) + y*(4.*z); 00444 outputValues(20,i0, 5) = -2.*(1. - x)*(1. + x)*(1. - y)*(1. + y); 00445 00446 outputValues(21,i0, 0) = -(1. - y)*(1. + y)*(-1. + z)*z; 00447 outputValues(21,i0, 1) = (x*(-2.*y) )*z + (0. + x*(2.*y))*(z*z); 00448 outputValues(21,i0, 2) = x*(1. - 2.*z + (y*y)*(-1. + 2.*z)); 00449 outputValues(21,i0, 3) = -(1. - x)*(1. + x)*(-1. + z)*z; 00450 outputValues(21,i0, 4) = y*(1. - 2.*z) + (x*x)*(y*(-1. + 2.*z)); 00451 outputValues(21,i0, 5) = (1. - x)*(1. + x)*(1. - y)*(1. + y); 00452 00453 outputValues(22,i0, 0) = -(1. - y)*(1. + y)*z*(1 + z); 00454 outputValues(22,i0, 1) = (0. + x*(2.*y))*z + (0. + x*(2.*y))*(z*z); 00455 outputValues(22,i0, 2) = x*(-1. - 2.*z + (y*y)*(1. + 2.*z)); 00456 outputValues(22,i0, 3) = -(1. - x)*(1. + x)*z*(1 + z); 00457 outputValues(22,i0, 4) = y*(-1. - 2.*z) + (x*x)*(y*(1. + 2.*z)); 00458 outputValues(22,i0, 5) = (1. - x)*(1. + x)*(1. - y)*(1. + y); 00459 00460 outputValues(23,i0, 0) = (1. - y)*(1. + y)*(1. - z)*(1. + z); 00461 outputValues(23,i0, 1) = (-1. + 2.*x)*y*(-1. + z*z); 00462 outputValues(23,i0, 2) = (-1. + 2.*x)*(-1. + y*y)*z; 00463 outputValues(23,i0, 3) =-(-1. + x)*x*(1. - z)*(1. + z); 00464 outputValues(23,i0, 4) = 2.*(-1. + x)*x*y*z; 00465 outputValues(23,i0, 5) =-(-1. + x)*x*(1. - y)*(1. + y); 00466 00467 outputValues(24,i0, 0) = (1. - y)*(1. + y)*(1. - z)*(1. + z); 00468 outputValues(24,i0, 1) = (1. + 2.*x)*y*(-1. + z*z); 00469 outputValues(24,i0, 2) = (1. + 2.*x)*(-1. + y*y)*z; 00470 outputValues(24,i0, 3) = x*(1. + x)*(-1. + z)*(1. + z); 00471 outputValues(24,i0, 4) = 2.*x*(1. + x)*y*z; 00472 outputValues(24,i0, 5) = x*(1. + x)*(-1. + y)*(1. + y); 00473 00474 outputValues(25,i0, 0) = -(-1. + y)*y*(1. - z)*(1. + z); 00475 outputValues(25,i0, 1) = x*(-1. + 2.*y)*(-1. + z*z); 00476 outputValues(25,i0, 2) = 2.*x*(-1. + y)*y*z; 00477 outputValues(25,i0, 3) = (1. - x)*(1. + x)*(1. - z)*(1. + z); 00478 outputValues(25,i0, 4) = (-1. + x*x)*(-1. + 2.*y)*z; 00479 outputValues(25,i0, 5) =-(1. - x)*(1. + x)*(-1. + y)*y; 00480 00481 outputValues(26,i0, 0) = y*(1. + y)*(-1. + z)*(1. + z); 00482 outputValues(26,i0, 1) = x*(1. + 2.*y)*(-1. + z*z); 00483 outputValues(26,i0, 2) = 2.*x*y*(1. + y)*z; 00484 outputValues(26,i0, 3) = (-1. + x)*(1. + x)*(-1. + z)*(1. + z); 00485 outputValues(26,i0, 4) = (-1. + x*x)*(1. + 2.*y)*z; 00486 outputValues(26,i0, 5) = (-1. + x)*(1. + x)*y*(1. + y); 00487 } 00488 break; 00489 00490 case OPERATOR_D3: 00491 for (int i0 = 0; i0 < dim0; i0++) { 00492 x = inputPoints(i0,0); 00493 y = inputPoints(i0,1); 00494 z = inputPoints(i0,2); 00495 00496 outputValues(0,i0, 0) = 0.; 00497 outputValues(0,i0, 1) = ((-1.+ 2.*y)*(-1.+ z)*z)/4.; 00498 outputValues(0,i0, 2) = ((-1.+ y)*y*(-1.+ 2.*z))/4.; 00499 outputValues(0,i0, 3) = ((-1.+ 2.*x)*(-1.+ z)*z)/4.; 00500 outputValues(0,i0, 4) = ((-1.+ 2.*x)*(-1.+ 2.*y)*(-1.+ 2.*z))/8.; 00501 outputValues(0,i0, 5) = ((-1.+ 2.*x)*(-1.+ y)*y)/4.; 00502 outputValues(0,i0, 6) = 0.; 00503 outputValues(0,i0, 7) = ((-1.+ x)*x*(-1.+ 2.*z))/4.; 00504 outputValues(0,i0, 8) = ((-1.+ x)*x*(-1.+ 2.*y))/4.; 00505 outputValues(0,i0, 9) = 0.; 00506 00507 outputValues(1, i0, 0) = 0.; 00508 outputValues(1, i0, 1) = ((-1.+ 2.*y)*(-1.+ z)*z)/4.; 00509 outputValues(1, i0, 2) = ((-1.+ y)*y*(-1.+ 2.*z))/4.; 00510 outputValues(1, i0, 3) = ((1.+ 2.*x)*(-1.+ z)*z)/4.; 00511 outputValues(1, i0, 4) = ((1.+ 2.*x)*(-1.+ 2.*y)*(-1.+ 2.*z))/8.; 00512 outputValues(1, i0, 5) = ((1.+ 2.*x)*(-1.+ y)*y)/4.; 00513 outputValues(1, i0, 6) = 0.; 00514 outputValues(1, i0, 7) = (x*(1.+ x)*(-1.+ 2.*z))/4.; 00515 outputValues(1, i0, 8) = (x*(1.+ x)*(-1.+ 2.*y))/4.; 00516 outputValues(1, i0, 9) = 0.; 00517 00518 outputValues(2, i0, 0) = 0.; 00519 outputValues(2, i0, 1) = ((1.+ 2.*y)*(-1.+ z)*z)/4.; 00520 outputValues(2, i0, 2) = (y*(1.+ y)*(-1.+ 2.*z))/4.; 00521 outputValues(2, i0, 3) = ((1.+ 2.*x)*(-1.+ z)*z)/4.; 00522 outputValues(2, i0, 4) = ((1.+ 2.*x)*(1.+ 2.*y)*(-1.+ 2.*z))/8.; 00523 outputValues(2, i0, 5) = ((1.+ 2.*x)*y*(1.+ y))/4.; 00524 outputValues(2, i0, 6) = 0.; 00525 outputValues(2, i0, 7) = (x*(1.+ x)*(-1.+ 2.*z))/4.; 00526 outputValues(2, i0, 8) = (x*(1.+ x)*(1.+ 2.*y))/4.; 00527 outputValues(2, i0, 9) = 0.; 00528 00529 outputValues(3, i0, 0) = 0.; 00530 outputValues(3, i0, 1) = ((1.+ 2.*y)*(-1.+ z)*z)/4.; 00531 outputValues(3, i0, 2) = (y*(1.+ y)*(-1.+ 2.*z))/4.; 00532 outputValues(3, i0, 3) = ((-1.+ 2.*x)*(-1.+ z)*z)/4.; 00533 outputValues(3, i0, 4) = ((-1.+ 2.*x)*(1.+ 2.*y)*(-1.+ 2.*z))/8.; 00534 outputValues(3, i0, 5) = ((-1.+ 2.*x)*y*(1.+ y))/4.; 00535 outputValues(3, i0, 6) = 0.; 00536 outputValues(3, i0, 7) = ((-1.+ x)*x*(-1.+ 2.*z))/4.; 00537 outputValues(3, i0, 8) = ((-1.+ x)*x*(1.+ 2.*y))/4.; 00538 outputValues(3, i0, 9) = 0.; 00539 00540 outputValues(4, i0, 0) = 0.; 00541 outputValues(4, i0, 1) = ((-1.+ 2.*y)*z*(1.+ z))/4.; 00542 outputValues(4, i0, 2) = ((-1.+ y)*y*(1.+ 2.*z))/4.; 00543 outputValues(4, i0, 3) = ((-1.+ 2.*x)*z*(1.+ z))/4.; 00544 outputValues(4, i0, 4) = ((-1.+ 2.*x)*(-1.+ 2.*y)*(1.+ 2.*z))/8.; 00545 outputValues(4, i0, 5) = ((-1.+ 2.*x)*(-1.+ y)*y)/4.; 00546 outputValues(4, i0, 6) = 0.; 00547 outputValues(4, i0, 7) = ((-1.+ x)*x*(1.+ 2.*z))/4.; 00548 outputValues(4, i0, 8) = ((-1.+ x)*x*(-1.+ 2.*y))/4.; 00549 outputValues(4, i0, 9) = 0.; 00550 00551 outputValues(5, i0, 0) = 0.; 00552 outputValues(5, i0, 1) = ((-1.+ 2.*y)*z*(1.+ z))/4.; 00553 outputValues(5, i0, 2) = ((-1.+ y)*y*(1.+ 2.*z))/4.; 00554 outputValues(5, i0, 3) = ((1.+ 2.*x)*z*(1.+ z))/4.; 00555 outputValues(5, i0, 4) = ((1.+ 2.*x)*(-1.+ 2.*y)*(1.+ 2.*z))/8.; 00556 outputValues(5, i0, 5) = ((1.+ 2.*x)*(-1.+ y)*y)/4.; 00557 outputValues(5, i0, 6) = 0.; 00558 outputValues(5, i0, 7) = (x*(1.+ x)*(1.+ 2.*z))/4.; 00559 outputValues(5, i0, 8) = (x*(1.+ x)*(-1.+ 2.*y))/4.; 00560 outputValues(5, i0, 9) = 0.; 00561 00562 outputValues(6, i0, 0) = 0.; 00563 outputValues(6, i0, 1) = ((1.+ 2.*y)*z*(1.+ z))/4.; 00564 outputValues(6, i0, 2) = (y*(1.+ y)*(1.+ 2.*z))/4.; 00565 outputValues(6, i0, 3) = ((1.+ 2.*x)*z*(1.+ z))/4.; 00566 outputValues(6, i0, 4) = ((1.+ 2.*x)*(1.+ 2.*y)*(1.+ 2.*z))/8.; 00567 outputValues(6, i0, 5) = ((1.+ 2.*x)*y*(1.+ y))/4.; 00568 outputValues(6, i0, 6) = 0.; 00569 outputValues(6, i0, 7) = (x*(1.+ x)*(1.+ 2.*z))/4.; 00570 outputValues(6, i0, 8) = (x*(1.+ x)*(1.+ 2.*y))/4.; 00571 outputValues(6, i0, 9) = 0.; 00572 00573 outputValues(7, i0, 0) = 0.; 00574 outputValues(7, i0, 1) = ((1.+ 2.*y)*z*(1.+ z))/4.; 00575 outputValues(7, i0, 2) = (y*(1.+ y)*(1.+ 2.*z))/4.; 00576 outputValues(7, i0, 3) = ((-1.+ 2.*x)*z*(1.+ z))/4.; 00577 outputValues(7, i0, 4) = ((-1.+ 2.*x)*(1.+ 2.*y)*(1.+ 2.*z))/8.; 00578 outputValues(7, i0, 5) = ((-1.+ 2.*x)*y*(1.+ y))/4.; 00579 outputValues(7, i0, 6) = 0.; 00580 outputValues(7, i0, 7) = ((-1.+ x)*x*(1.+ 2.*z))/4.; 00581 outputValues(7, i0, 8) = ((-1.+ x)*x*(1.+ 2.*y))/4.; 00582 outputValues(7, i0, 9) = 0.; 00583 00584 outputValues(8, i0, 0) = 0.; 00585 outputValues(8, i0, 1) = -((-1.+ 2.*y)*(-1.+ z)*z)/2.; 00586 outputValues(8, i0, 2) = -((-1.+ y)*y*(-1.+ 2.*z))/2.; 00587 outputValues(8, i0, 3) = -(x*(-1.+ z)*z); 00588 outputValues(8, i0, 4) = -(x*(-1.+ 2.*y)*(-1.+ 2.*z))/2.; 00589 outputValues(8, i0, 5) = -(x*(-1.+ y)*y); 00590 outputValues(8, i0, 6) = 0.; 00591 outputValues(8, i0, 7) = -((-1.+ (x*x))*(-1.+ 2.*z))/2.; 00592 outputValues(8, i0, 8) = -((-1.+ (x*x))*(-1.+ 2.*y))/2.; 00593 outputValues(8, i0, 9) = 0.; 00594 00595 outputValues(9, i0, 0) = 0.; 00596 outputValues(9, i0, 1) = -(y*(-1.+ z)*z); 00597 outputValues(9, i0, 2) = -((-1.+ (y*y))*(-1.+ 2.*z))/2.; 00598 outputValues(9, i0, 3) = -((1.+ 2.*x)*(-1.+ z)*z)/2.; 00599 outputValues(9, i0, 4) = -((1.+ 2.*x)*y*(-1.+ 2.*z))/2.; 00600 outputValues(9, i0, 5) = -((1.+ 2.*x)*(-1.+ (y*y)))/2.; 00601 outputValues(9, i0, 6) = 0.; 00602 outputValues(9, i0, 7) = -(x*(1.+ x)*(-1.+ 2.*z))/2.; 00603 outputValues(9, i0, 8) = -(x*(1.+ x)*y); 00604 outputValues(9, i0, 9) = 0.; 00605 00606 outputValues(10,i0, 0) = 0.; 00607 outputValues(10,i0, 1) = -((1.+ 2.*y)*(-1.+ z)*z)/2.; 00608 outputValues(10,i0, 2) = -(y*(1.+ y)*(-1.+ 2.*z))/2.; 00609 outputValues(10,i0, 3) = -(x*(-1.+ z)*z); 00610 outputValues(10,i0, 4) = -(x*(1.+ 2.*y)*(-1.+ 2.*z))/2.; 00611 outputValues(10,i0, 5) = -(x*y*(1.+ y)); 00612 outputValues(10,i0, 6) = 0.; 00613 outputValues(10,i0, 7) = -((-1.+ (x*x))*(-1.+ 2.*z))/2.; 00614 outputValues(10,i0, 8) = -((-1.+ (x*x))*(1.+ 2.*y))/2.; 00615 outputValues(10,i0, 9) = 0.; 00616 00617 outputValues(11,i0, 0) = 0.; 00618 outputValues(11,i0, 1) = -(y*(-1.+ z)*z); 00619 outputValues(11,i0, 2) = -((-1.+ (y*y))*(-1.+ 2.*z))/2.; 00620 outputValues(11,i0, 3) = -((-1.+ 2.*x)*(-1.+ z)*z)/2.; 00621 outputValues(11,i0, 4) = -((-1.+ 2.*x)*y*(-1.+ 2.*z))/2.; 00622 outputValues(11,i0, 5) = -((-1.+ 2.*x)*(-1.+ (y*y)))/2.; 00623 outputValues(11,i0, 6) = 0.; 00624 outputValues(11,i0, 7) = -((-1.+ x)*x*(-1.+ 2.*z))/2.; 00625 outputValues(11,i0, 8) = -((-1.+ x)*x*y); 00626 outputValues(11,i0, 9) = 0.; 00627 00628 outputValues(12,i0, 0) = 0.; 00629 outputValues(12,i0, 1) = -((-1.+ 2.*y)*(-1.+ (z*z)))/2.; 00630 outputValues(12,i0, 2) = -((-1.+ y)*y*z); 00631 outputValues(12,i0, 3) = -((-1.+ 2.*x)*(-1.+ (z*z)))/2.; 00632 outputValues(12,i0, 4) = -((-1.+ 2.*x)*(-1.+ 2.*y)*z)/2.; 00633 outputValues(12,i0, 5) = -((-1.+ 2.*x)*(-1.+ y)*y)/2.; 00634 outputValues(12,i0, 6) = 0.; 00635 outputValues(12,i0, 7) = -((-1.+ x)*x*z); 00636 outputValues(12,i0, 8) = -((-1.+ x)*x*(-1.+ 2.*y))/2.; 00637 outputValues(12,i0, 9) = 0.; 00638 00639 outputValues(13,i0, 0) = 0.; 00640 outputValues(13,i0, 1) = -((-1.+ 2.*y)*(-1.+ (z*z)))/2.; 00641 outputValues(13,i0, 2) = -((-1.+ y)*y*z); 00642 outputValues(13,i0, 3) = -((1.+ 2.*x)*(-1.+ (z*z)))/2.; 00643 outputValues(13,i0, 4) = -((1.+ 2.*x)*(-1.+ 2.*y)*z)/2.; 00644 outputValues(13,i0, 5) = -((1.+ 2.*x)*(-1.+ y)*y)/2.; 00645 outputValues(13,i0, 6) = 0.; 00646 outputValues(13,i0, 7) = -(x*(1.+ x)*z); 00647 outputValues(13,i0, 8) = -(x*(1.+ x)*(-1.+ 2.*y))/2.; 00648 outputValues(13,i0, 9) = 0.; 00649 00650 outputValues(14,i0, 0) = 0.; 00651 outputValues(14,i0, 1) = -((1.+ 2.*y)*(-1.+ (z*z)))/2.; 00652 outputValues(14,i0, 2) = -(y*(1.+ y)*z); 00653 outputValues(14,i0, 3) = -((1.+ 2.*x)*(-1.+ (z*z)))/2.; 00654 outputValues(14,i0, 4) = -((1.+ 2.*x)*(1.+ 2.*y)*z)/2.; 00655 outputValues(14,i0, 5) = -((1.+ 2.*x)*y*(1.+ y))/2.; 00656 outputValues(14,i0, 6) = 0.; 00657 outputValues(14,i0, 7) = -(x*(1.+ x)*z); 00658 outputValues(14,i0, 8) = -(x*(1.+ x)*(1.+ 2.*y))/2.; 00659 outputValues(14,i0, 9) = 0.; 00660 00661 outputValues(15,i0, 0) = 0.; 00662 outputValues(15,i0, 1) = -((1.+ 2.*y)*(-1.+ (z*z)))/2.; 00663 outputValues(15,i0, 2) = -(y*(1.+ y)*z); 00664 outputValues(15,i0, 3) = -((-1.+ 2.*x)*(-1.+ (z*z)))/2.; 00665 outputValues(15,i0, 4) = -((-1.+ 2.*x)*(1.+ 2.*y)*z)/2.; 00666 outputValues(15,i0, 5) = -((-1.+ 2.*x)*y*(1.+ y))/2.; 00667 outputValues(15,i0, 6) = 0.; 00668 outputValues(15,i0, 7) = -((-1.+ x)*x*z); 00669 outputValues(15,i0, 8) = -((-1.+ x)*x*(1.+ 2.*y))/2.; 00670 outputValues(15,i0, 9) = 0.; 00671 00672 outputValues(16,i0, 0) = 0.; 00673 outputValues(16,i0, 1) = -((-1.+ 2.*y)*z*(1.+ z))/2.; 00674 outputValues(16,i0, 2) = -((-1.+ y)*y*(1.+ 2.*z))/2.; 00675 outputValues(16,i0, 3) = -(x*z*(1.+ z)); 00676 outputValues(16,i0, 4) = -(x*(-1.+ 2.*y)*(1.+ 2.*z))/2.; 00677 outputValues(16,i0, 5) = -(x*(-1.+ y)*y); 00678 outputValues(16,i0, 6) = 0.; 00679 outputValues(16,i0, 7) = -((-1.+ (x*x))*(1.+ 2.*z))/2.; 00680 outputValues(16,i0, 8) = -((-1.+ (x*x))*(-1.+ 2.*y))/2.; 00681 outputValues(16,i0, 9) = 0.; 00682 00683 outputValues(17,i0, 0) = 0.; 00684 outputValues(17,i0, 1) = -(y*z*(1.+ z)); 00685 outputValues(17,i0, 2) = -((-1.+ (y*y))*(1.+ 2.*z))/2.; 00686 outputValues(17,i0, 3) = -((1.+ 2.*x)*z*(1.+ z))/2.; 00687 outputValues(17,i0, 4) = -((1.+ 2.*x)*y*(1.+ 2.*z))/2.; 00688 outputValues(17,i0, 5) = -((1.+ 2.*x)*(-1.+ (y*y)))/2.; 00689 outputValues(17,i0, 6) = 0.; 00690 outputValues(17,i0, 7) = -(x*(1.+ x)*(1.+ 2.*z))/2.; 00691 outputValues(17,i0, 8) = -(x*(1.+ x)*y); 00692 outputValues(17,i0, 9) = 0.; 00693 00694 outputValues(18,i0, 0) = 0.; 00695 outputValues(18,i0, 1) = -((1.+ 2.*y)*z*(1.+ z))/2.; 00696 outputValues(18,i0, 2) = -(y*(1.+ y)*(1.+ 2.*z))/2.; 00697 outputValues(18,i0, 3) = -(x*z*(1.+ z)); 00698 outputValues(18,i0, 4) = -(x*(1.+ 2.*y)*(1.+ 2.*z))/2.; 00699 outputValues(18,i0, 5) = -(x*y*(1.+ y)); 00700 outputValues(18,i0, 6) = 0.; 00701 outputValues(18,i0, 7) = -((-1.+ (x*x))*(1.+ 2.*z))/2.; 00702 outputValues(18,i0, 8) = -((-1.+ (x*x))*(1.+ 2.*y))/2.; 00703 outputValues(18,i0, 9) = 0.; 00704 00705 outputValues(19,i0, 0) = 0.; 00706 outputValues(19,i0, 1) = -(y*z*(1.+ z)); 00707 outputValues(19,i0, 2) = -((-1.+ (y*y))*(1.+ 2.*z))/2.; 00708 outputValues(19,i0, 3) = -((-1.+ 2.*x)*z*(1.+ z))/2.; 00709 outputValues(19,i0, 4) = -((-1.+ 2.*x)*y*(1.+ 2.*z))/2.; 00710 outputValues(19,i0, 5) = -((-1.+ 2.*x)*(-1.+ (y*y)))/2.; 00711 outputValues(19,i0, 6) = 0.; 00712 outputValues(19,i0, 7) = -((-1.+ x)*x*(1.+ 2.*z))/2.; 00713 outputValues(19,i0, 8) = -((-1.+ x)*x*y); 00714 outputValues(19,i0, 9) = 0.; 00715 00716 outputValues(20,i0, 0) = 0.; 00717 outputValues(20,i0, 1) = -4*y*(-1.+ (z*z)); 00718 outputValues(20,i0, 2) = -4*(-1.+ (y*y))*z; 00719 outputValues(20,i0, 3) = -4*x*(-1.+ (z*z)); 00720 outputValues(20,i0, 4) = -8*x*y*z; 00721 outputValues(20,i0, 5) = -4*x*(-1.+ (y*y)); 00722 outputValues(20,i0, 6) = 0.; 00723 outputValues(20,i0, 7) = -4*(-1.+ (x*x))*z; 00724 outputValues(20,i0, 8) = -4*(-1.+ (x*x))*y; 00725 outputValues(20,i0, 9) = 0.; 00726 00727 outputValues(21,i0, 0) = 0.; 00728 outputValues(21,i0, 1) = 2.*y*(-1.+ z)*z; 00729 outputValues(21,i0, 2) = (-1.+ (y*y))*(-1.+ 2.*z); 00730 outputValues(21,i0, 3) = 2.*x*(-1.+ z)*z; 00731 outputValues(21,i0, 4) = 2.*x*y*(-1.+ 2.*z); 00732 outputValues(21,i0, 5) = 2.*x*(-1.+ (y*y)); 00733 outputValues(21,i0, 6) = 0.; 00734 outputValues(21,i0, 7) = (-1.+ (x*x))*(-1.+ 2.*z); 00735 outputValues(21,i0, 8) = 2.*(-1.+ (x*x))*y; 00736 outputValues(21,i0, 9) = 0.; 00737 00738 outputValues(22,i0, 0) = 0.; 00739 outputValues(22,i0, 1) = 2.*y*z*(1.+ z); 00740 outputValues(22,i0, 2) = (-1.+ (y*y))*(1.+ 2.*z); 00741 outputValues(22,i0, 3) = 2.*x*z*(1.+ z); 00742 outputValues(22,i0, 4) = 2.*x*y*(1.+ 2.*z); 00743 outputValues(22,i0, 5) = 2.*x*(-1.+ (y*y)); 00744 outputValues(22,i0, 6) = 0.; 00745 outputValues(22,i0, 7) = (-1.+ (x*x))*(1.+ 2.*z); 00746 outputValues(22,i0, 8) = 2.*(-1.+ (x*x))*y; 00747 outputValues(22,i0, 9) = 0.; 00748 00749 outputValues(23,i0, 0) = 0.; 00750 outputValues(23,i0, 1) = 2.*y*(-1.+ (z*z)); 00751 outputValues(23,i0, 2) = 2.*(-1.+ (y*y))*z; 00752 outputValues(23,i0, 3) = (-1.+ 2.*x)*(-1.+ (z*z)); 00753 outputValues(23,i0, 4) = 2.*(-1.+ 2.*x)*y*z; 00754 outputValues(23,i0, 5) = (-1.+ 2.*x)*(-1.+ (y*y)); 00755 outputValues(23,i0, 6) = 0.; 00756 outputValues(23,i0, 7) = 2.*(-1.+ x)*x*z; 00757 outputValues(23,i0, 8) = 2.*(-1.+ x)*x*y; 00758 outputValues(23,i0, 9) = 0.; 00759 00760 outputValues(24,i0, 0) = 0.; 00761 outputValues(24,i0, 1) = 2.*y*(-1.+ (z*z)); 00762 outputValues(24,i0, 2) = 2.*(-1.+ (y*y))*z; 00763 outputValues(24,i0, 3) = (1.+ 2.*x)*(-1.+ (z*z)); 00764 outputValues(24,i0, 4) = 2.*(1.+ 2.*x)*y*z; 00765 outputValues(24,i0, 5) = (1.+ 2.*x)*(-1.+ (y*y)); 00766 outputValues(24,i0, 6) = 0.; 00767 outputValues(24,i0, 7) = 2.*x*(1.+ x)*z; 00768 outputValues(24,i0, 8) = 2.*x*(1.+ x)*y; 00769 outputValues(24,i0, 9) = 0.; 00770 00771 outputValues(25,i0, 0) = 0.; 00772 outputValues(25,i0, 1) = (-1.+ 2.*y)*(-1.+ (z*z)); 00773 outputValues(25,i0, 2) = 2.*(-1.+ y)*y*z; 00774 outputValues(25,i0, 3) = 2.*x*(-1.+ (z*z)); 00775 outputValues(25,i0, 4) = 2.*x*(-1.+ 2.*y)*z; 00776 outputValues(25,i0, 5) = 2.*x*(-1.+ y)*y; 00777 outputValues(25,i0, 6) = 0.; 00778 outputValues(25,i0, 7) = 2.*(-1.+ (x*x))*z; 00779 outputValues(25,i0, 8) = (-1.+ (x*x))*(-1.+ 2.*y); 00780 outputValues(25,i0, 9) = 0.; 00781 00782 outputValues(26,i0, 0) = 0.; 00783 outputValues(26,i0, 1) = (1.+ 2.*y)*(-1.+ (z*z)); 00784 outputValues(26,i0, 2) = 2.*y*(1.+ y)*z; 00785 outputValues(26,i0, 3) = 2.*x*(-1.+ (z*z)); 00786 outputValues(26,i0, 4) = 2.*x*(1.+ 2.*y)*z; 00787 outputValues(26,i0, 5) = 2.*x*y*(1.+ y); 00788 outputValues(26,i0, 6) = 0.; 00789 outputValues(26,i0, 7) = 2.*(-1.+ (x*x))*z; 00790 outputValues(26,i0, 8) = (-1.+ (x*x))*(1.+ 2.*y); 00791 outputValues(26,i0, 9) = 0.; 00792 } 00793 break; 00794 00795 case OPERATOR_D4: 00796 { 00797 // Non-zero entries have Dk (derivative cardinality) indices {3,4,5,7,8,12}, all other entries are 0. 00798 // Intitialize array by zero and then fill only non-zero entries. 00799 int DkCardinality = Intrepid::getDkCardinality(operatorType, this -> basisCellTopology_.getDimension() ); 00800 for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) { 00801 for (int i0 = 0; i0 < dim0; i0++) { 00802 for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){ 00803 outputValues(dofOrd, i0, dkOrd) = 0.0; 00804 } 00805 } 00806 } 00807 00808 for (int i0 = 0; i0 < dim0; i0++) { 00809 x = inputPoints(i0,0); 00810 y = inputPoints(i0,1); 00811 z = inputPoints(i0,2); 00812 00813 outputValues(0, i0, 3) = ((-1.+ z)*z)/2.; 00814 outputValues(0, i0, 4) = ((-1.+ 2.*y)*(-1.+ 2.*z))/4.; 00815 outputValues(0, i0, 5) = ((-1.+ y)*y)/2.; 00816 outputValues(0, i0, 7) = ((-1.+ 2.*x)*(-1.+ 2.*z))/4.; 00817 outputValues(0, i0, 8) = ((-1.+ 2.*x)*(-1.+ 2.*y))/4.; 00818 outputValues(0, i0, 12)= ((-1.+ x)*x)/2.; 00819 00820 outputValues(1, i0, 3) = ((-1.+ z)*z)/2.; 00821 outputValues(1, i0, 4) = ((-1.+ 2.*y)*(-1.+ 2.*z))/4.; 00822 outputValues(1, i0, 5) = ((-1.+ y)*y)/2.; 00823 outputValues(1, i0, 7) = ((1. + 2.*x)*(-1.+ 2.*z))/4.; 00824 outputValues(1, i0, 8) = ((1. + 2.*x)*(-1.+ 2.*y))/4.; 00825 outputValues(1, i0, 12)= (x*(1. + x))/2.; 00826 00827 outputValues(2, i0, 3) = ((-1.+ z)*z)/2.; 00828 outputValues(2, i0, 4) = ((1. + 2.*y)*(-1.+ 2.*z))/4.; 00829 outputValues(2, i0, 5) = (y*(1. + y))/2.; 00830 outputValues(2, i0, 7) = ((1. + 2.*x)*(-1.+ 2.*z))/4.; 00831 outputValues(2, i0, 8) = ((1. + 2.*x)*(1. + 2.*y))/4.; 00832 outputValues(2, i0, 12)= (x*(1. + x))/2.; 00833 00834 outputValues(3, i0, 3) = ((-1.+ z)*z)/2.; 00835 outputValues(3, i0, 4) = ((1. + 2.*y)*(-1.+ 2.*z))/4.; 00836 outputValues(3, i0, 5) = (y*(1. + y))/2.; 00837 outputValues(3, i0, 7) = ((-1.+ 2.*x)*(-1.+ 2.*z))/4.; 00838 outputValues(3, i0, 8) = ((-1.+ 2.*x)*(1. + 2.*y))/4.; 00839 outputValues(3, i0, 12)= ((-1.+ x)*x)/2.; 00840 00841 outputValues(4, i0, 3) = (z*(1. + z))/2.; 00842 outputValues(4, i0, 4) = ((-1.+ 2.*y)*(1. + 2.*z))/4.; 00843 outputValues(4, i0, 5) = ((-1.+ y)*y)/2.; 00844 outputValues(4, i0, 7) = ((-1.+ 2.*x)*(1. + 2.*z))/4.; 00845 outputValues(4, i0, 8) = ((-1.+ 2.*x)*(-1.+ 2.*y))/4.; 00846 outputValues(4, i0, 12)= ((-1.+ x)*x)/2.; 00847 00848 outputValues(5, i0, 3) = (z*(1. + z))/2.; 00849 outputValues(5, i0, 4) = ((-1.+ 2.*y)*(1. + 2.*z))/4.; 00850 outputValues(5, i0, 5) = ((-1.+ y)*y)/2.; 00851 outputValues(5, i0, 7) = ((1. + 2.*x)*(1. + 2.*z))/4.; 00852 outputValues(5, i0, 8) = ((1. + 2.*x)*(-1.+ 2.*y))/4.; 00853 outputValues(5, i0, 12)= (x*(1. + x))/2.; 00854 00855 outputValues(6, i0, 3) = (z*(1. + z))/2.; 00856 outputValues(6, i0, 4) = ((1. + 2.*y)*(1. + 2.*z))/4.; 00857 outputValues(6, i0, 5) = (y*(1. + y))/2.; 00858 outputValues(6, i0, 7) = ((1. + 2.*x)*(1. + 2.*z))/4.; 00859 outputValues(6, i0, 8) = ((1. + 2.*x)*(1. + 2.*y))/4.; 00860 outputValues(6, i0, 12)= (x*(1. + x))/2.; 00861 00862 outputValues(7, i0, 3) = (z*(1. + z))/2.; 00863 outputValues(7, i0, 4) = ((1. + 2.*y)*(1. + 2.*z))/4.; 00864 outputValues(7, i0, 5) = (y*(1. + y))/2.; 00865 outputValues(7, i0, 7) = ((-1.+ 2.*x)*(1. + 2.*z))/4.; 00866 outputValues(7, i0, 8) = ((-1.+ 2.*x)*(1. + 2.*y))/4.; 00867 outputValues(7, i0, 12)= ((-1.+ x)*x)/2.; 00868 00869 outputValues(8, i0, 3) = -((-1.+ z)*z); 00870 outputValues(8, i0, 4) = -0.5 + y + z - 2.*y*z; 00871 outputValues(8, i0, 5) = -((-1.+ y)*y); 00872 outputValues(8, i0, 7) = x - 2.*x*z; 00873 outputValues(8, i0, 8) = x - 2.*x*y; 00874 outputValues(8, i0, 12)= 1. - x*x; 00875 00876 outputValues(9, i0, 3) = -((-1.+ z)*z); 00877 outputValues(9, i0, 4) = y - 2.*y*z; 00878 outputValues(9, i0, 5) = 1 - y*y; 00879 outputValues(9, i0, 7) = 0.5 + x - z - 2.*x*z; 00880 outputValues(9, i0, 8) = -((1. + 2.*x)*y); 00881 outputValues(9, i0, 12)= -(x*(1. + x)); 00882 00883 outputValues(10,i0, 3) = -((-1.+ z)*z); 00884 outputValues(10,i0, 4) = 0.5 + y - z - 2.*y*z; 00885 outputValues(10,i0, 5) = -(y*(1. + y)); 00886 outputValues(10,i0, 7) = x - 2.*x*z; 00887 outputValues(10,i0, 8) = -(x*(1. + 2.*y)); 00888 outputValues(10,i0, 12)= 1. - x*x; 00889 00890 outputValues(11,i0, 3) = -((-1.+ z)*z); 00891 outputValues(11,i0, 4) = y - 2.*y*z; 00892 outputValues(11,i0, 5) = 1. - y*y; 00893 outputValues(11,i0, 7) = -0.5 + x + z - 2.*x*z; 00894 outputValues(11,i0, 8) = y - 2.*x*y; 00895 outputValues(11,i0, 12)= -((-1.+ x)*x); 00896 00897 outputValues(12,i0, 3) = 1. - z*z; 00898 outputValues(12,i0, 4) = z - 2.*y*z; 00899 outputValues(12,i0, 5) = -((-1.+ y)*y); 00900 outputValues(12,i0, 7) = z - 2.*x*z; 00901 outputValues(12,i0, 8) = -0.5 + x + y - 2.*x*y; 00902 outputValues(12,i0, 12)= -((-1.+ x)*x); 00903 00904 outputValues(13,i0, 3) = 1. - z*z; 00905 outputValues(13,i0, 4) = z - 2.*y*z; 00906 outputValues(13,i0, 5) = -((-1.+ y)*y); 00907 outputValues(13,i0, 7) = -((1. + 2.*x)*z); 00908 outputValues(13,i0, 8) = 0.5 + x - y - 2.*x*y; 00909 outputValues(13,i0, 12)= -(x*(1. + x)); 00910 00911 outputValues(14,i0, 3) = 1. - z*z; 00912 outputValues(14,i0, 4) = -((1. + 2.*y)*z); 00913 outputValues(14,i0, 5) = -(y*(1. + y)); 00914 outputValues(14,i0, 7) = -((1. + 2.*x)*z); 00915 outputValues(14,i0, 8) = -((1. + 2.*x)*(1. + 2.*y))/2.; 00916 outputValues(14,i0, 12)= -(x*(1. + x)); 00917 00918 outputValues(15,i0, 3) = 1. - z*z; 00919 outputValues(15,i0, 4) = -((1. + 2.*y)*z); 00920 outputValues(15,i0, 5) = -(y*(1. + y)); 00921 outputValues(15,i0, 7) = z - 2.*x*z; 00922 outputValues(15,i0, 8) = 0.5 + y - x*(1. + 2.*y); 00923 outputValues(15,i0, 12)= -((-1.+ x)*x); 00924 00925 outputValues(16,i0, 3) = -(z*(1. + z)); 00926 outputValues(16,i0, 4) = 0.5 + z - y*(1. + 2.*z); 00927 outputValues(16,i0, 5) = -((-1.+ y)*y); 00928 outputValues(16,i0, 7) = -(x*(1. + 2.*z)); 00929 outputValues(16,i0, 8) = x - 2.*x*y; 00930 outputValues(16,i0, 12)= 1. - x*x; 00931 00932 outputValues(17,i0, 3) = -(z*(1. + z)); 00933 outputValues(17,i0, 4) = -(y*(1. + 2.*z)); 00934 outputValues(17,i0, 5) = 1. - y*y; 00935 outputValues(17,i0, 7) = -((1. + 2.*x)*(1. + 2.*z))/2.; 00936 outputValues(17,i0, 8) = -((1. + 2.*x)*y); 00937 outputValues(17,i0, 12)= -(x*(1. + x)); 00938 00939 outputValues(18,i0, 3) = -(z*(1. + z)); 00940 outputValues(18,i0, 4) = -((1. + 2.*y)*(1. + 2.*z))/2.; 00941 outputValues(18,i0, 5) = -(y*(1. + y)); 00942 outputValues(18,i0, 7) = -(x*(1. + 2.*z)); 00943 outputValues(18,i0, 8) = -(x*(1. + 2.*y)); 00944 outputValues(18,i0, 12)= 1. - x*x; 00945 00946 outputValues(19,i0, 3) = -(z*(1. + z)); 00947 outputValues(19,i0, 4) = -(y*(1. + 2.*z)); 00948 outputValues(19,i0, 5) = 1. - y*y; 00949 outputValues(19,i0, 7) = 0.5 + z - x*(1. + 2.*z); 00950 outputValues(19,i0, 8) = y - 2.*x*y; 00951 outputValues(19,i0, 12)= -((-1.+ x)*x); 00952 00953 outputValues(20,i0, 3) = 4. - 4.*z*z; 00954 outputValues(20,i0, 4) = -8.*y*z; 00955 outputValues(20,i0, 5) = 4. - 4.*y*y; 00956 outputValues(20,i0, 7) = -8.*x*z; 00957 outputValues(20,i0, 8) = -8.*x*y; 00958 outputValues(20,i0, 12)= 4. - 4.*x*x; 00959 00960 outputValues(21,i0, 3) = 2.*(-1.+ z)*z; 00961 outputValues(21,i0, 4) = 2.*y*(-1.+ 2.*z); 00962 outputValues(21,i0, 5) = 2.*(-1.+ y*y); 00963 outputValues(21,i0, 7) = 2.*x*(-1.+ 2.*z); 00964 outputValues(21,i0, 8) = 4.*x*y; 00965 outputValues(21,i0, 12)= 2.*(-1.+ x*x); 00966 00967 outputValues(22,i0, 3) = 2.*z*(1. + z); 00968 outputValues(22,i0, 4) = 2.*(y + 2.*y*z); 00969 outputValues(22,i0, 5) = 2.*(-1.+ y*y); 00970 outputValues(22,i0, 7) = 2.*(x + 2.*x*z); 00971 outputValues(22,i0, 8) = 4.*x*y; 00972 outputValues(22,i0, 12)= 2.*(-1.+ x*x); 00973 00974 outputValues(23,i0, 3) = 2.*(-1.+ z*z); 00975 outputValues(23,i0, 4) = 4.*y*z; 00976 outputValues(23,i0, 5) = 2.*(-1.+ y*y); 00977 outputValues(23,i0, 7) = 2.*(-1.+ 2.*x)*z; 00978 outputValues(23,i0, 8) = 2.*(-1.+ 2.*x)*y; 00979 outputValues(23,i0, 12)= 2.*(-1.+ x)*x; 00980 00981 outputValues(24,i0, 3) = 2.*(-1.+ z*z); 00982 outputValues(24,i0, 4) = 4.*y*z; 00983 outputValues(24,i0, 5) = 2.*(-1.+ y*y); 00984 outputValues(24,i0, 7) = 2.*(z + 2.*x*z); 00985 outputValues(24,i0, 8) = 2.*(y + 2.*x*y); 00986 outputValues(24,i0, 12)= 2.*x*(1. + x); 00987 00988 outputValues(25,i0, 3) = 2.*(-1.+ z*z); 00989 outputValues(25,i0, 4) = 2.*(-1.+ 2.*y)*z; 00990 outputValues(25,i0, 5) = 2.*(-1.+ y)*y; 00991 outputValues(25,i0, 7) = 4.*x*z; 00992 outputValues(25,i0, 8) = 2.*x*(-1.+ 2.*y); 00993 outputValues(25,i0, 12)= 2.*(-1.+ x*x); 00994 00995 outputValues(26,i0, 3) = 2.*(-1.+ z*z); 00996 outputValues(26,i0, 4) = 2.*(z + 2.*y*z); 00997 outputValues(26,i0, 5) = 2.*y*(1. + y); 00998 outputValues(26,i0, 7) = 4.*x*z; 00999 outputValues(26,i0, 8) = 2.*(x + 2.*x*y); 01000 outputValues(26,i0, 12)= 2.*(-1.+ x*x); 01001 } 01002 } 01003 break; 01004 01005 case OPERATOR_D5: 01006 case OPERATOR_D6: 01007 TEST_FOR_EXCEPTION( true, std::invalid_argument, 01008 ">>> ERROR (Basis_HGRAD_HEX_C2_FEM): operator not supported"); 01009 break; 01010 01011 case OPERATOR_D7: 01012 case OPERATOR_D8: 01013 case OPERATOR_D9: 01014 case OPERATOR_D10: 01015 { 01016 // outputValues is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality) 01017 int DkCardinality = Intrepid::getDkCardinality(operatorType, 01018 this -> basisCellTopology_.getDimension() ); 01019 for(int dofOrd = 0; dofOrd < this -> basisCardinality_; dofOrd++) { 01020 for (int i0 = 0; i0 < dim0; i0++) { 01021 for(int dkOrd = 0; dkOrd < DkCardinality; dkOrd++){ 01022 outputValues(dofOrd, i0, dkOrd) = 0.0; 01023 } 01024 } 01025 } 01026 } 01027 break; 01028 01029 default: 01030 TEST_FOR_EXCEPTION( !( Intrepid::isValidOperator(operatorType) ), std::invalid_argument, 01031 ">>> ERROR (Basis_HGRAD_HEX_C2_FEM): Invalid operator type"); 01032 } 01033 } 01034 01035 01036 01037 template<class Scalar, class ArrayScalar> 01038 void Basis_HGRAD_HEX_C2_FEM<Scalar, ArrayScalar>::getValues(ArrayScalar& outputValues, 01039 const ArrayScalar & inputPoints, 01040 const ArrayScalar & cellVertices, 01041 const EOperator operatorType) const { 01042 TEST_FOR_EXCEPTION( (true), std::logic_error, 01043 ">>> ERROR (Basis_HGRAD_HEX_C2_FEM): FEM Basis calling an FVD member function"); 01044 } 01045 01046 template<class Scalar, class ArrayScalar> 01047 void Basis_HGRAD_HEX_C2_FEM<Scalar, ArrayScalar>::getDofCoords(ArrayScalar & DofCoords) const { 01048 #ifdef HAVE_INTREPID_DEBUG 01049 // Verify rank of output array. 01050 TEST_FOR_EXCEPTION( !(DofCoords.rank() == 2), std::invalid_argument, 01051 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C2_FEM::getDofCoords) rank = 2 required for DofCoords array"); 01052 // Verify 0th dimension of output array. 01053 TEST_FOR_EXCEPTION( !( DofCoords.dimension(0) == this -> basisCardinality_ ), std::invalid_argument, 01054 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C2_FEM::getDofCoords) mismatch in number of DoF and 0th dimension of DofCoords array"); 01055 // Verify 1st dimension of output array. 01056 TEST_FOR_EXCEPTION( !( DofCoords.dimension(1) == (int)(this -> basisCellTopology_.getDimension()) ), std::invalid_argument, 01057 ">>> ERROR: (Intrepid::Basis_HGRAD_HEX_C2_FEM::getDofCoords) incorrect reference cell (1st) dimension in DofCoords array"); 01058 #endif 01059 01060 DofCoords(0,0) = -1.0; DofCoords(0,1) = -1.0; DofCoords(0,2) = -1.0; 01061 DofCoords(1,0) = 1.0; DofCoords(1,1) = -1.0; DofCoords(1,2) = -1.0; 01062 DofCoords(2,0) = 1.0; DofCoords(2,1) = 1.0; DofCoords(2,2) = -1.0; 01063 DofCoords(3,0) = -1.0; DofCoords(3,1) = 1.0; DofCoords(3,2) = -1.0; 01064 DofCoords(4,0) = -1.0; DofCoords(4,1) = -1.0; DofCoords(4,2) = 1.0; 01065 DofCoords(5,0) = 1.0; DofCoords(5,1) = -1.0; DofCoords(5,2) = 1.0; 01066 DofCoords(6,0) = 1.0; DofCoords(6,1) = 1.0; DofCoords(6,2) = 1.0; 01067 DofCoords(7,0) = -1.0; DofCoords(7,1) = 1.0; DofCoords(7,2) = 1.0; 01068 01069 DofCoords(8,0) = 0.0; DofCoords(8,1) = -1.0; DofCoords(8,2) = -1.0; 01070 DofCoords(9,0) = 1.0; DofCoords(9,1) = 0.0; DofCoords(9,2) = -1.0; 01071 DofCoords(10,0) = 0.0; DofCoords(10,1) = 1.0; DofCoords(10,2) = -1.0; 01072 DofCoords(11,0) = -1.0; DofCoords(11,1) = 0.0; DofCoords(11,2) = -1.0; 01073 DofCoords(12,0) = -1.0; DofCoords(12,1) = -1.0; DofCoords(12,2) = 0.0; 01074 DofCoords(13,0) = 1.0; DofCoords(13,1) = -1.0; DofCoords(13,2) = 0.0; 01075 DofCoords(14,0) = 1.0; DofCoords(14,1) = 1.0; DofCoords(14,2) = 0.0; 01076 DofCoords(15,0) = -1.0; DofCoords(15,1) = 1.0; DofCoords(15,2) = 0.0; 01077 DofCoords(16,0) = 0.0; DofCoords(16,1) = -1.0; DofCoords(16,2) = 1.0; 01078 DofCoords(17,0) = 1.0; DofCoords(17,1) = 0.0; DofCoords(17,2) = 1.0; 01079 DofCoords(18,0) = 0.0; DofCoords(18,1) = 1.0; DofCoords(18,2) = 1.0; 01080 DofCoords(19,0) = -1.0; DofCoords(19,1) = 0.0; DofCoords(19,2) = 1.0; 01081 01082 DofCoords(20,0) = 0.0; DofCoords(20,1) = 0.0; DofCoords(20,2) = 0.0; 01083 01084 DofCoords(21,0) = 0.0; DofCoords(21,1) = 0.0; DofCoords(21,2) = -1.0; 01085 DofCoords(22,0) = 0.0; DofCoords(22,1) = 0.0; DofCoords(22,2) = 1.0; 01086 DofCoords(23,0) = -1.0; DofCoords(23,1) = 0.0; DofCoords(23,2) = 0.0; 01087 DofCoords(24,0) = 1.0; DofCoords(24,1) = 0.0; DofCoords(24,2) = 0.0; 01088 DofCoords(25,0) = 0.0; DofCoords(25,1) = -1.0; DofCoords(25,2) = 0.0; 01089 DofCoords(26,0) = 0.0; DofCoords(26,1) = 1.0; DofCoords(26,2) = 0.0; 01090 } 01091 01092 }// namespace Intrepid
1.7.4