neumann-laplace.cc

The Poisson problem with Neumann boundary conditions.

The Poisson problem with Neumann boundary conditions

#include "rheolef.h"
using namespace rheolef;
using namespace std;
size_t d;
Float f (const point& x) { return 1; }
Float g (const point& x) { return -0.5/d; }
int main(int argc, char**argv) {
  environment rheolef (argc, argv);
  geo omega (argv[1]);
  d = omega.dimension();
  space Xh (omega, argv[2]);
  trial u (Xh); test v (Xh);
  form  a  = integrate (dot(grad(u),grad(v)));
  field b  = integrate(v);
  field lh = integrate (f*v) + integrate ("boundary", g*v); 
  form  A = {{   a,      b},
             { trans(b), 0}};
  field Bh = {   lh,     0};
  field Uh (Bh.get_space(), 0); 
  A.set_symmetry(true);
  problem p (A);
  p.solve (Bh, Uh);
  dout << Uh[0];
}