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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 // Redistribution and use in source and binary forms, with or without 00011 // modification, are permitted provided that the following conditions are 00012 // met: 00013 // 00014 // 1. Redistributions of source code must retain the above copyright 00015 // notice, this list of conditions and the following disclaimer. 00016 // 00017 // 2. Redistributions in binary form must reproduce the above copyright 00018 // notice, this list of conditions and the following disclaimer in the 00019 // documentation and/or other materials provided with the distribution. 00020 // 00021 // 3. Neither the name of the Corporation nor the names of the 00022 // contributors may be used to endorse or promote products derived from 00023 // this software without specific prior written permission. 00024 // 00025 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY 00026 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 00027 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 00028 // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE 00029 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 00030 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 00031 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 00032 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 00033 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 00034 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 00035 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 00036 // 00037 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) 00038 // Denis Ridzal (dridzal@sandia.gov), or 00039 // Kara Peterson (kjpeter@sandia.gov) 00040 // 00041 // ************************************************************************ 00042 // @HEADER 00043 00049 namespace Intrepid { 00050 00051 template <class Scalar, class ArrayPoint, class ArrayWeight> 00052 CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::CubatureDirectLineGauss(const int degree) { 00053 this->degree_ = degree; 00054 this->dimension_ = 1; 00055 TEUCHOS_TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM), 00056 std::out_of_range, 00057 ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree."); 00058 } // end constructor 00059 00060 00061 00062 template <class Scalar, class ArrayPoint, class ArrayWeight> 00063 const CubatureTemplate * CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::exposeCubatureData() const { 00064 return cubature_data_; 00065 } 00066 00067 00068 00069 template <class Scalar, class ArrayPoint, class ArrayWeight> 00070 int CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getMaxAccuracy() const { 00071 return INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM; 00072 } 00073 00074 00075 00076 template <class Scalar, class ArrayPoint, class ArrayWeight> 00077 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getName() const { 00078 return cubature_name_; 00079 } // end getName 00080 00081 00082 00083 template <class Scalar, class ArrayPoint, class ArrayWeight> 00084 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_name_ = "INTREPID_CUBATURE_LINE_GAUSS"; 00085 00086 00087 //-------------------------------------------------------------------------------------// 00088 // Definition of cubature templates // 00089 //-------------------------------------------------------------------------------------// 00090 00091 /* 00092 Cubature templates for lines are defined the reference cell: 00093 00094 Line -> (-1,0,0),(1,0,0) 00095 */ 00096 00097 /* 00098 This static const member contains templates for Gauss(-Legendre) rules. 00099 */ 00100 00101 template <class Scalar, class ArrayPoint, class ArrayWeight> 00102 const CubatureTemplate CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_data_[INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM+1] = 00103 { 00104 00105 // Collection of Gauss rules on [-1,1] 00106 // The rule with array index i is exact for polynomials up to order i 00107 { 00108 1, 00109 {{0e0, 0.0, 0.0}}, 00110 {2e0} 00111 }, 00112 { 00113 1, 00114 {{0e0, 0.0, 0.0}}, 00115 {2e0} 00116 }, 00117 { 00118 2, 00119 {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0}, 00120 {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}}, 00121 {1e0, 00122 1e0} 00123 }, 00124 { 00125 2, 00126 {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0}, 00127 {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}}, 00128 {1e0, 00129 1e0} 00130 }, 00131 { 00132 3, 00133 {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0}, 00134 {0e0, 0.0, 0.0}, 00135 {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}}, 00136 {5.555555555555555555555555555555555555556e-1, 00137 8.888888888888888888888888888888888888889e-1, 00138 5.555555555555555555555555555555555555556e-1} 00139 }, 00140 { 00141 3, 00142 {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0}, 00143 {0e0, 0.0, 0.0}, 00144 {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}}, 00145 {5.555555555555555555555555555555555555556e-1, 00146 8.888888888888888888888888888888888888889e-1, 00147 5.555555555555555555555555555555555555556e-1} 00148 }, 00149 { 00150 4, 00151 {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0}, 00152 {3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00153 {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00154 {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}}, 00155 {3.478548451374538573730639492219994072353e-1, 00156 6.521451548625461426269360507780005927647e-1, 00157 6.521451548625461426269360507780005927647e-1, 00158 3.478548451374538573730639492219994072353e-1} 00159 }, 00160 { 00161 4, 00162 {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0}, 00163 {3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00164 {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0}, 00165 {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}}, 00166 {3.478548451374538573730639492219994072353e-1, 00167 6.521451548625461426269360507780005927647e-1, 00168 6.521451548625461426269360507780005927647e-1, 00169 3.478548451374538573730639492219994072353e-1} 00170 }, 00171 { 00172 5, 00173 {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0}, 00174 {5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00175 {0e0, 0.0, 0.0}, 00176 {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00177 {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}}, 00178 {2.369268850561890875142640407199173626433e-1, 00179 4.786286704993664680412915148356381929123e-1, 00180 5.688888888888888888888888888888888888889e-1, 00181 4.786286704993664680412915148356381929123e-1, 00182 2.369268850561890875142640407199173626433e-1} 00183 }, 00184 { 00185 5, 00186 {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0}, 00187 {5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00188 {0e0, 0.0, 0.0}, 00189 {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0}, 00190 {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}}, 00191 {2.369268850561890875142640407199173626433e-1, 00192 4.786286704993664680412915148356381929123e-1, 00193 5.688888888888888888888888888888888888889e-1, 00194 4.786286704993664680412915148356381929123e-1, 00195 2.369268850561890875142640407199173626433e-1} 00196 }, 00197 { 00198 6, 00199 {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0}, 00200 {6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00201 {2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00202 {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00203 {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00204 {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}}, 00205 {1.713244923791703450402961421727328935268e-1, 00206 3.607615730481386075698335138377161116615e-1, 00207 4.679139345726910473898703439895509948117e-1, 00208 4.679139345726910473898703439895509948117e-1, 00209 3.607615730481386075698335138377161116615e-1, 00210 1.713244923791703450402961421727328935268e-1} 00211 }, 00212 { 00213 6, 00214 {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0}, 00215 {6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00216 {2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00217 {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0}, 00218 {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0}, 00219 {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}}, 00220 {1.713244923791703450402961421727328935268e-1, 00221 3.607615730481386075698335138377161116615e-1, 00222 4.679139345726910473898703439895509948117e-1, 00223 4.679139345726910473898703439895509948117e-1, 00224 3.607615730481386075698335138377161116615e-1, 00225 1.713244923791703450402961421727328935268e-1} 00226 }, 00227 { 00228 7, 00229 {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0}, 00230 {7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00231 {4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00232 {0e0, 0.0, 0.0}, 00233 {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00234 {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00235 {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}}, 00236 {1.294849661688696932706114326790820183286e-1, 00237 2.797053914892766679014677714237795824869e-1, 00238 3.818300505051189449503697754889751338784e-1, 00239 4.179591836734693877551020408163265306122e-1, 00240 3.818300505051189449503697754889751338784e-1, 00241 2.797053914892766679014677714237795824869e-1, 00242 1.294849661688696932706114326790820183286e-1} 00243 }, 00244 { 00245 7, 00246 {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0}, 00247 {7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00248 {4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00249 {0e0, 0.0, 0.0}, 00250 {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0}, 00251 {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0}, 00252 {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}}, 00253 {1.294849661688696932706114326790820183286e-1, 00254 2.797053914892766679014677714237795824869e-1, 00255 3.818300505051189449503697754889751338784e-1, 00256 4.179591836734693877551020408163265306122e-1, 00257 3.818300505051189449503697754889751338784e-1, 00258 2.797053914892766679014677714237795824869e-1, 00259 1.294849661688696932706114326790820183286e-1} 00260 }, 00261 { 00262 8, 00263 {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0}, 00264 {7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00265 {5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00266 {1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00267 {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00268 {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00269 {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00270 {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}}, 00271 {1.012285362903762591525313543099621901154e-1, 00272 2.223810344533744705443559944262408844301e-1, 00273 3.137066458778872873379622019866013132603e-1, 00274 3.626837833783619829651504492771956121941e-1, 00275 3.626837833783619829651504492771956121941e-1, 00276 3.137066458778872873379622019866013132603e-1, 00277 2.223810344533744705443559944262408844301e-1, 00278 1.012285362903762591525313543099621901154e-1} 00279 }, 00280 { 00281 8, 00282 {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0}, 00283 {7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00284 {5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00285 {1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00286 {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0}, 00287 {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0}, 00288 {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0}, 00289 {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}}, 00290 {1.012285362903762591525313543099621901154e-1, 00291 2.223810344533744705443559944262408844301e-1, 00292 3.137066458778872873379622019866013132603e-1, 00293 3.626837833783619829651504492771956121941e-1, 00294 3.626837833783619829651504492771956121941e-1, 00295 3.137066458778872873379622019866013132603e-1, 00296 2.223810344533744705443559944262408844301e-1, 00297 1.012285362903762591525313543099621901154e-1} 00298 }, 00299 { 00300 9, 00301 {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0}, 00302 {8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00303 {6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00304 {3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00305 {0e0, 0.0, 0.0}, 00306 {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00307 {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00308 {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00309 {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}}, 00310 {8.127438836157441197189215811052365067566e-2, 00311 1.806481606948574040584720312429128095143e-1, 00312 2.606106964029354623187428694186328497718e-1, 00313 3.123470770400028400686304065844436655988e-1, 00314 3.302393550012597631645250692869740488788e-1, 00315 3.123470770400028400686304065844436655988e-1, 00316 2.606106964029354623187428694186328497718e-1, 00317 1.806481606948574040584720312429128095143e-1, 00318 8.127438836157441197189215811052365067566e-2} 00319 }, 00320 { 00321 9, 00322 {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0}, 00323 {8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00324 {6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00325 {3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00326 {0e0, 0.0, 0.0}, 00327 {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0}, 00328 {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0}, 00329 {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0}, 00330 {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}}, 00331 {8.127438836157441197189215811052365067566e-2, 00332 1.806481606948574040584720312429128095143e-1, 00333 2.606106964029354623187428694186328497718e-1, 00334 3.123470770400028400686304065844436655988e-1, 00335 3.302393550012597631645250692869740488788e-1, 00336 3.123470770400028400686304065844436655988e-1, 00337 2.606106964029354623187428694186328497718e-1, 00338 1.806481606948574040584720312429128095143e-1, 00339 8.127438836157441197189215811052365067566e-2} 00340 }, 00341 { 00342 10, 00343 {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0}, 00344 {8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00345 {6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00346 {4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00347 {1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00348 {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0}, 00349 {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0}, 00350 {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0}, 00351 {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0}, 00352 {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}}, 00353 {6.667134430868813759356880989333179285786e-2, 00354 1.494513491505805931457763396576973324026e-1, 00355 2.190863625159820439955349342281631924588e-1, 00356 2.692667193099963550912269215694693528598e-1, 00357 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1.7.6.1