libMesh
exact_solution.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2003 Benjamin S. Kirk
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 
19 
20 // C++ Includes
21 #include <math.h>
22 
23 // Mesh library includes
24 #include "libmesh/libmesh_common.h"
25 
26 // Bring in everything from the libMesh namespace
27 using namespace libMesh;
28 
29 
30 
31 
32 
37  const Real y,
38  const Real t)
39 {
40  const Real xo = 0.2;
41  const Real yo = 0.2;
42  const Real u = 0.8;
43  const Real v = 0.8;
44 
45  const Real num =
46  pow(x - u*t - xo, 2.) +
47  pow(y - v*t - yo, 2.);
48 
49  const Real den =
50  0.01*(4.*t + 1.);
51 
52  return exp(-num/den)/(4.*t + 1.);
53 }
Real exact_solution(const Real x, const Real y, const Real z=0.)
This is the exact solution that we are trying to obtain.
The libMesh namespace provides an interface to certain functionality in the library.
PetscErrorCode Vec x
double pow(double a, int b)
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real