SyFi - Symbolic Finite Elements

Appetizer

The following example shows the computation of the element matrix for the Poisson problem,

void compute_element_matrix(Polygon& T, int order) { 
  std::map<std::pair<int,int>, ex> A;      // matrix of expression
  std::pair<int,int> index;                // index in matrix
  LagrangeFE fe;                           // Lagrangian element of any order 
  fe.set(order);                           // set the order 
  fe.set(domain);                          // set the polygon 
  fe.compute_basis_functions();            // compute the basis functions
  for (int i=1; i<= fe.nbf() ; i++) {
    index.first = i; 
    for (int j=1; j<= fe.nbf() ; j++) {
      index.second = j; 
      ex nabla = inner(grad(fe.N(i)), grad(fe.N(j)));   // compute the integrands 
      ex Aij = T.integrate(nabla);                      // compute the weak form 
      A[index] = Aij;                                   // update element matrix
    }
  }
}

Requirement