Line data    Source code

       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
       3             : 
       4             : // This library is free software; you can redistribute it and/or
       5             : // modify it under the terms of the GNU Lesser General Public
       6             : // License as published by the Free Software Foundation; either
       7             : // version 2.1 of the License, or (at your option) any later version.
       8             : 
       9             : // This library is distributed in the hope that it will be useful,
      10             : // but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      12             : // Lesser General Public License for more details.
      13             : 
      14             : // You should have received a copy of the GNU Lesser General Public
      15             : // License along with this library; if not, write to the Free Software
      16             : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      17             : 
      18             : #ifndef LIBMESH_JACOBI_POLYNOMIALS_H
      19             : #define LIBMESH_JACOBI_POLYNOMIALS_H
      20             : 
      21             : // libMesh includes
      22             : #include "libmesh/libmesh_common.h" // Real
      23             : 
      24             : // C++ includes
      25             : #include <utility> // std::swap
      26             : 
      27             : namespace libMesh
      28             : {
      29             : 
      30             : namespace JacobiPolynomials
      31             : {
      32             : 
      33             : /**
      34             :  * The Jacobi polynomial value and derivative formulas are based on
      35             :  * the corresponding Wikipedia article [0]. Note that we have shifted
      36             :  * the indices used in the recurrence relation, otherwise this is
      37             :  * identical to the recurrence relation given in the article. When
      38             :  * alpha = beta = 0, the Jacobi polynomials reduce to the Legendre
      39             :  * polynomials.
      40             :  *
      41             :  * [0]: https://en.wikipedia.org/wiki/Jacobi_polynomials
      42             :  */
      43             : inline
      44        9198 : Real value(unsigned n, unsigned alpha, unsigned beta, Real x)
      45             : {
      46        9198 :   if (n == 0)
      47         186 :     return 1.;
      48             : 
      49             :   // Compute constants independent of loop index.
      50        8733 :   unsigned int ab = alpha + beta;
      51        8733 :   unsigned int a2 = alpha * alpha;
      52        8733 :   unsigned int b2 = beta * beta;
      53             : 
      54        1899 :   Real p0 = 1;
      55        8733 :   Real p1 = (alpha + 1) + (ab + 2) * 0.5 * (x - 1);
      56             : 
      57        1899 :   unsigned int i = 1;
      58       28356 :   while (i < n)
      59             :     {
      60             :       // Note: we swap before updating p1, so p0 and p1 appear in
      61             :       // opposite positions than is usual in the update formula.
      62        1935 :       std::swap(p0, p1);
      63       25428 :       p1 = (((2*i + ab + 1) *
      64       23493 :         ((2*i + ab + 2) * (2*i + ab) * x + a2 - b2)) * p0
      65       25428 :         - 2 * (i + alpha) * (i + beta) * (2*i + ab + 2) * p1) /
      66       21558 :        (2 * (i + 1) * (i + 1 + ab) * (2*i + ab));
      67             : 
      68        1935 :       ++i;
      69             :     }
      70        1899 :   return p1;
      71             : }
      72             : 
      73             : inline
      74        1875 : Real deriv(unsigned n, unsigned alpha, unsigned beta, Real x)
      75             : {
      76             :   // Call value() with elevated (alpha, beta) and decremented n.
      77        1875 :   return n == 0 ? 0 : 0.5 * (1 + alpha + beta + n) * value(n-1, alpha+1, beta+1, x);
      78             : }
      79             : 
      80             : } // namespace JacobiPolynomials
      81             : } // namespace libMesh
      82             : 
      83             : #endif // LIBMESH_JACOBI_POLYNOMIALS_H