The multilevel solver of Elmer is an efficient N log(N) solution algorithm for large elliptic problems (more than 50000 degrees of freedom, say).

The figure shows the total solution time (maximum of five separate runs) of the Poisson equation on a L-shaped domain (homogeneous Dirichlet boundary conditions and constant source term). The problem was discretized by standard linear triangular finite elements and solved on a SGI Origin 2000 machine (cedar.csc.fi) using the multigrid solver of Elmer. According to the graph, the total solution time grows as N log(N) (= almost linearly) with respect to the size of the system. Before 50000 degrees of freedom, the PCG solver is more efficient.