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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 template <class Scalar, class ArrayPoint, class ArrayWeight> 00038 CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::CubatureDirectLineGauss(const int degree) { 00039 this->degree_ = degree; 00040 this->dimension_ = 1; 00041 TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM), 00042 std::out_of_range, 00043 ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree."); 00044 } // end constructor 00045 00046 00047 00048 template <class Scalar, class ArrayPoint, class ArrayWeight> 00049 const CubatureTemplate * CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::exposeCubatureData() const { 00050 return cubature_data_; 00051 } 00052 00053 00054 00055 template <class Scalar, class ArrayPoint, class ArrayWeight> 00056 int CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getMaxAccuracy() const { 00057 return INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM; 00058 } 00059 00060 00061 00062 template <class Scalar, class ArrayPoint, class ArrayWeight> 00063 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getName() const { 00064 return cubature_name_; 00065 } // end getName 00066 00067 00068 00069 template <class Scalar, class ArrayPoint, class ArrayWeight> 00070 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_name_ = "INTREPID_CUBATURE_LINE_GAUSS"; 00071 00072 00073 //-------------------------------------------------------------------------------------// 00074 // Definition of cubature templates // 00075 //-------------------------------------------------------------------------------------// 00076 00077 /* 00078 Cubature templates for lines are defined the reference cell: 00079 00080 Line -> (-1,0,0),(1,0,0) 00081 */ 00082 00083 /* 00084 This static const member contains templates for Gauss(-Legendre) rules. 00085 */ 00086 00087 template <class Scalar, class ArrayPoint, class ArrayWeight> 00088 const CubatureTemplate CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_data_[INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM+1] = 00089 { 00090 00091 // Collection of Gauss rules on [-1,1] 00092 // The rule with array index i is exact for polynomials up to order i 00093 { 00094 1, 00095 {{0e0, 0.0, 0.0}}, 00096 {2e0} 00097 }, 00098 { 00099 1, 00100 {{0e0, 0.0, 0.0}}, 00101 {2e0} 00102 }, 00103 { 00104 2, 00105 {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0}, 00106 {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}}, 00107 {1e0, 00108 1e0} 00109 }, 00110 { 00111 2, 00112 {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0}, 00113 {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}}, 00114 {1e0, 00115 1e0} 00116 }, 00117 { 00118 3, 00119 {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0}, 00120 {0e0, 0.0, 0.0}, 00121 {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}}, 00122 {5.555555555555555555555555555555555555556e-1, 00123 8.888888888888888888888888888888888888889e-1, 00124 5.555555555555555555555555555555555555556e-1} 00125 }, 00126 { 00127 3, 00128 {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0}, 00129 {0e0, 0.0, 0.0}, 00130 {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}}, 00131 {5.555555555555555555555555555555555555556e-1, 00132 8.888888888888888888888888888888888888889e-1, 00133 5.555555555555555555555555555555555555556e-1} 00134 }, 00135 { 00136 4, 00137 {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0}, 00138 {3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00139 {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00140 {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}}, 00141 {3.478548451374538573730639492219994072353e-1, 00142 6.521451548625461426269360507780005927647e-1, 00143 6.521451548625461426269360507780005927647e-1, 00144 3.478548451374538573730639492219994072353e-1} 00145 }, 00146 { 00147 4, 00148 {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0}, 00149 {3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00150 {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00151 {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}}, 00152 {3.478548451374538573730639492219994072353e-1, 00153 6.521451548625461426269360507780005927647e-1, 00154 6.521451548625461426269360507780005927647e-1, 00155 3.478548451374538573730639492219994072353e-1} 00156 }, 00157 { 00158 5, 00159 {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0}, 00160 {5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00161 {0e0, 0.0, 0.0}, 00162 {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00163 {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}}, 00164 {2.369268850561890875142640407199173626433e-1, 00165 4.786286704993664680412915148356381929123e-1, 00166 5.688888888888888888888888888888888888889e-1, 00167 4.786286704993664680412915148356381929123e-1, 00168 2.369268850561890875142640407199173626433e-1} 00169 }, 00170 { 00171 5, 00172 {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0}, 00173 {5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00174 {0e0, 0.0, 0.0}, 00175 {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00176 {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}}, 00177 {2.369268850561890875142640407199173626433e-1, 00178 4.786286704993664680412915148356381929123e-1, 00179 5.688888888888888888888888888888888888889e-1, 00180 4.786286704993664680412915148356381929123e-1, 00181 2.369268850561890875142640407199173626433e-1} 00182 }, 00183 { 00184 6, 00185 {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0}, 00186 {6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00187 {2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00188 {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00189 {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00190 {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}}, 00191 {1.713244923791703450402961421727328935268e-1, 00192 3.607615730481386075698335138377161116615e-1, 00193 4.679139345726910473898703439895509948117e-1, 00194 4.679139345726910473898703439895509948117e-1, 00195 3.607615730481386075698335138377161116615e-1, 00196 1.713244923791703450402961421727328935268e-1} 00197 }, 00198 { 00199 6, 00200 {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0}, 00201 {6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00202 {2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00203 {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00204 {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00205 {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}}, 00206 {1.713244923791703450402961421727328935268e-1, 00207 3.607615730481386075698335138377161116615e-1, 00208 4.679139345726910473898703439895509948117e-1, 00209 4.679139345726910473898703439895509948117e-1, 00210 3.607615730481386075698335138377161116615e-1, 00211 1.713244923791703450402961421727328935268e-1} 00212 }, 00213 { 00214 7, 00215 {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0}, 00216 {7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00217 {4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00218 {0e0, 0.0, 0.0}, 00219 {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00220 {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00221 {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}}, 00222 {1.294849661688696932706114326790820183286e-1, 00223 2.797053914892766679014677714237795824869e-1, 00224 3.818300505051189449503697754889751338784e-1, 00225 4.179591836734693877551020408163265306122e-1, 00226 3.818300505051189449503697754889751338784e-1, 00227 2.797053914892766679014677714237795824869e-1, 00228 1.294849661688696932706114326790820183286e-1} 00229 }, 00230 { 00231 7, 00232 {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0}, 00233 {7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00234 {4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00235 {0e0, 0.0, 0.0}, 00236 {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00237 {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00238 {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}}, 00239 {1.294849661688696932706114326790820183286e-1, 00240 2.797053914892766679014677714237795824869e-1, 00241 3.818300505051189449503697754889751338784e-1, 00242 4.179591836734693877551020408163265306122e-1, 00243 3.818300505051189449503697754889751338784e-1, 00244 2.797053914892766679014677714237795824869e-1, 00245 1.294849661688696932706114326790820183286e-1} 00246 }, 00247 { 00248 8, 00249 {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0}, 00250 {7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00251 {5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00252 {1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00253 {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00254 {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00255 {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00256 {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}}, 00257 {1.012285362903762591525313543099621901154e-1, 00258 2.223810344533744705443559944262408844301e-1, 00259 3.137066458778872873379622019866013132603e-1, 00260 3.626837833783619829651504492771956121941e-1, 00261 3.626837833783619829651504492771956121941e-1, 00262 3.137066458778872873379622019866013132603e-1, 00263 2.223810344533744705443559944262408844301e-1, 00264 1.012285362903762591525313543099621901154e-1} 00265 }, 00266 { 00267 8, 00268 {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0}, 00269 {7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00270 {5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00271 {1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00272 {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00273 {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00274 {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00275 {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}}, 00276 {1.012285362903762591525313543099621901154e-1, 00277 2.223810344533744705443559944262408844301e-1, 00278 3.137066458778872873379622019866013132603e-1, 00279 3.626837833783619829651504492771956121941e-1, 00280 3.626837833783619829651504492771956121941e-1, 00281 3.137066458778872873379622019866013132603e-1, 00282 2.223810344533744705443559944262408844301e-1, 00283 1.012285362903762591525313543099621901154e-1} 00284 }, 00285 { 00286 9, 00287 {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0}, 00288 {8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00289 {6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00290 {3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00291 {0e0, 0.0, 0.0}, 00292 {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00293 {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00294 {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00295 {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}}, 00296 {8.127438836157441197189215811052365067566e-2, 00297 1.806481606948574040584720312429128095143e-1, 00298 2.606106964029354623187428694186328497718e-1, 00299 3.123470770400028400686304065844436655988e-1, 00300 3.302393550012597631645250692869740488788e-1, 00301 3.123470770400028400686304065844436655988e-1, 00302 2.606106964029354623187428694186328497718e-1, 00303 1.806481606948574040584720312429128095143e-1, 00304 8.127438836157441197189215811052365067566e-2} 00305 }, 00306 { 00307 9, 00308 {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0}, 00309 {8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00310 {6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00311 {3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00312 {0e0, 0.0, 0.0}, 00313 {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00314 {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00315 {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00316 {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}}, 00317 {8.127438836157441197189215811052365067566e-2, 00318 1.806481606948574040584720312429128095143e-1, 00319 2.606106964029354623187428694186328497718e-1, 00320 3.123470770400028400686304065844436655988e-1, 00321 3.302393550012597631645250692869740488788e-1, 00322 3.123470770400028400686304065844436655988e-1, 00323 2.606106964029354623187428694186328497718e-1, 00324 1.806481606948574040584720312429128095143e-1, 00325 8.127438836157441197189215811052365067566e-2} 00326 }, 00327 { 00328 10, 00329 {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0}, 00330 {8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00331 {6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00332 {4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00333 {1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00334 {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00335 {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00336 {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00337 {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00338 {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}}, 00339 {6.667134430868813759356880989333179285786e-2, 00340 1.494513491505805931457763396576973324026e-1, 00341 2.190863625159820439955349342281631924588e-1, 00342 2.692667193099963550912269215694693528598e-1, 00343 2.95524224714752870173892994651338329421e-1, 00344 2.95524224714752870173892994651338329421e-1, 00345 2.692667193099963550912269215694693528598e-1, 00346 2.190863625159820439955349342281631924588e-1, 00347 1.494513491505805931457763396576973324026e-1, 00348 6.667134430868813759356880989333179285786e-2} 00349 }, 00350 { 00351 10, 00352 {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0}, 00353 {8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00354 {6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00355 {4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00356 {1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00357 {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00358 {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00359 {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00360 {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00361 {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}}, 00362 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1.7.4