neumann_dg.cc

The Helmholtz problem with Neumann boundary conditions by the discontinuous Galerkin method.

The Helmholtz problem with Neumann boundary conditions by the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sinusprod_helmholtz.h"
int main(int argc, char**argv) {
  environment rheolef (argc, argv);
  geo omega (argv[1]);
  space Xh (omega, argv[2]);
  size_t d = omega.dimension();
  size_t k = Xh.degree();
  Float beta = (k+1)*(k+d)/Float(d);
  trial u (Xh); test v (Xh);
  form  a = integrate (u*v + dot(grad_h(u),grad_h(v)))
          + integrate ("internal_sides", 
                  beta*penalty()*jump(u)*jump(v)
                - jump(u)*average(dot(grad_h(v),normal()))
                - jump(v)*average(dot(grad_h(u),normal())));
  field lh = integrate (f(d)*v) + integrate ("boundary", g(d)*v);
  field uh(Xh);
  problem p (a);
  p.solve (lh, uh);
  dout << uh;
}