Finite Element Assembly Using an Embedded Domain Specific Language

Listing 1

Implementation of the assembly procedure for the Poisson problem.

(1) // The unknown function. The first template argument is a constant to distinguish each

     variable at compile time

(2) FieldVariable<0, ScalarField> f("f", solution_tag());

(3) // The source term, to be set at runtime using an initial condition

(4) FieldVariable<1, ScalarField> g("g", "source_term");

(5)

(6) // Action handling the assembly

(7) Handle<ProtoAction> assembly = create_component<ProtoAction>("Assembly");

(8) // Set the expression

(9) assembly->set_expression(elements_expression

(10) (

(11)  mesh::LagrangeP1::CellTypes(), // All first order Lagrange elements

(12)  group

(13)  (

(14)   _A = _0, _a = _0,// The element matrix and RHS vector, initialized to 0

(15)   element_quadrature // Integration over the element

(16)   (

(17)    _A(f) += transpose(nabla(f)) * nabla(f),

(18)    _a[f] += transpose(N(g))*g

(19)   ),

(20)   system_matrix += _A, // Assemble into the global linear system

(21)   system_rhs += _a

(22)   )

(23) ));