Intrepid: http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/src/Shared/Intrepid

00001 
00002 //
00003 // File: Intrepid_Polylib.hpp
00004 //
00005 // For more information, please see: http://www.nektar.info
00006 //
00007 // The MIT License
00008 //
00009 // Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
00010 // Department of Aeronautics, Imperial College London (UK), and Scientific
00011 // Computing and Imaging Institute, University of Utah (USA).
00012 //
00013 // License for the specific language governing rights and limitations under
00014 // Permission is hereby granted, free of charge, to any person obtaining a
00015 // copy of this software and associated documentation files (the "Software"),
00016 // to deal in the Software without restriction, including without limitation
00017 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
00018 // and/or sell copies of the Software, and to permit persons to whom the
00019 // Software is furnished to do so, subject to the following conditions:
00020 //
00021 // The above copyright notice and this permission notice shall be included
00022 // in all copies or substantial portions of the Software.
00023 //
00024 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
00025 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
00026 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
00027 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
00028 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
00029 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
00030 // DEALINGS IN THE SOFTWARE.
00031 //
00032 // Description:
00033 // This file is redistributed with the Intrepid package. It should be used
00034 // in accordance with the above MIT license, at the request of the authors.
00035 // This file is NOT covered by the usual Intrepid/Trilinos LGPL license.
00036 //
00037 // Origin: Nektar++ library, http://www.nektar.info, downloaded on
00038 //         March 10, 2009.
00039 //
00041 
00042 
00050 #ifndef INTREPID_POLYLIB_HPP
00051 #define INTREPID_POLYLIB_HPP
00052 
00053 #include "Intrepid_ConfigDefs.hpp"
00054 #include "Intrepid_Types.hpp"
00055 #include "Teuchos_TestForException.hpp"
00056 
00057 namespace Intrepid {
00058 
00152   enum EIntrepidPLPoly {
00153     PL_GAUSS=0,
00154     PL_GAUSS_RADAU_LEFT,
00155     PL_GAUSS_RADAU_RIGHT,
00156     PL_GAUSS_LOBATTO,
00157     PL_MAX
00158   };
00159 
00160   inline EIntrepidPLPoly & operator++(EIntrepidPLPoly &type) {
00161     return type = static_cast<EIntrepidPLPoly>(type+1);
00162   }
00163 
00164   inline EIntrepidPLPoly operator++(EIntrepidPLPoly &type, int) {
00165     EIntrepidPLPoly oldval = type;
00166     ++type;
00167     return oldval;
00168   }
00169 
00170 
00178   class IntrepidPolylib {
00179 
00180     public:
00181 
00182     /* Points and weights */
00183 
00191     template<class Scalar>
00192     static void   zwgj   (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
00193 
00194 
00202     template<class Scalar>
00203     static void   zwgrjm (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
00204 
00205 
00213     template<class Scalar>
00214     static void   zwgrjp (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
00215 
00216 
00224     template<class Scalar>
00225     static void   zwglj  (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
00226 
00227 
00228 
00229     /* Derivative operators */
00230 
00239     template<class Scalar>
00240     static void   Dgj    (Scalar *D,  const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
00241 
00242 
00251     template<class Scalar>
00252     static void   Dgrjm  (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
00253 
00254 
00263     template<class Scalar>
00264     static void   Dgrjp  (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
00265 
00266 
00275     template<class Scalar>
00276     static void   Dglj   (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
00277 
00278 
00279 
00280     /* Lagrangian interpolants */
00281 
00301     template<class Scalar>
00302     static Scalar hgj     (const int i, const Scalar z, const Scalar *zgj,
00303                            const int np, const Scalar alpha, const Scalar beta);
00304 
00305 
00325     template<class Scalar>
00326     static Scalar hgrjm   (const int i, const Scalar z, const Scalar *zgrj,
00327                            const int np, const Scalar alpha, const Scalar beta);
00328 
00329 
00349     template<class Scalar>
00350     static Scalar hgrjp   (const int i, const Scalar z, const Scalar *zgrj,
00351                            const int np, const Scalar alpha, const Scalar beta);
00352 
00353 
00373     template<class Scalar>
00374     static Scalar hglj    (const int i, const Scalar z, const Scalar *zglj,
00375                            const int np, const Scalar alpha, const Scalar beta);
00376 
00377 
00378 
00379     /* Interpolation operators */
00380 
00391     template<class Scalar>
00392     static void  Imgj  (Scalar *im, const Scalar *zgj, const Scalar *zm, const int nz,
00393                         const int mz, const Scalar alpha, const Scalar beta);
00394 
00395 
00406     template<class Scalar>
00407     static void  Imgrjm(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
00408                         const int mz, const Scalar alpha, const Scalar beta);
00409 
00410 
00421     template<class Scalar>
00422     static void  Imgrjp(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
00423                         const int mz, const Scalar alpha, const Scalar beta);
00424 
00425 
00436     template<class Scalar>
00437     static void  Imglj (Scalar *im, const Scalar *zglj, const Scalar *zm, const int nz,
00438                         const int mz, const Scalar alpha, const Scalar beta);
00439 
00440 
00441     /* Polynomial functions */
00442 
00482     template<class Scalar>
00483     static void jacobfd (const int np, const Scalar *z, Scalar *poly_in, Scalar *polyd,
00484                          const int n, const Scalar alpha, const Scalar beta);
00485 
00486 
00500     template<class Scalar>
00501     static void jacobd  (const int np, const Scalar *z, Scalar *polyd, const int n,
00502                          const Scalar alpha, const Scalar beta);
00503 
00504 
00505 
00506     /* Helper functions. */
00507 
00514     template<class Scalar>
00515     static void   Jacobz (const int n, Scalar *z, const Scalar alpha, const Scalar beta);
00516 
00517 
00540     template<class Scalar>
00541     static void   JacZeros (const int n, Scalar *a, const Scalar alpha, const Scalar beta);
00542 
00543 
00567     template<class Scalar>
00568     static void   TriQL    (const int n, Scalar *d, Scalar *e);
00569 
00570 
00580     template<class Scalar>
00581     static Scalar gammaF (const Scalar x);
00582 
00583 
00584   }; // class IntrepidPolylib
00585 
00586 } // end of Intrepid namespace
00587 
00588 // include templated definitions
00589 #include <Intrepid_PolylibDef.hpp>
00590 
00591 #endif
http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/src/Shared/Intrepid_Polylib.hpp
