Hypergraph Grammar based Linear Computational Cost Solver for Three Dimensional Grids with Point Singularities

In this paper we present a hypergraph grammar based multi-frontal solver for three dimensional grids with point singularities. We show experimentally that the computational cost of the resulting solver algorithm is linear with respect to the number of degrees of freedom. We also propose a reutilization algorithm that enables to reuse LU factorizations over unrefined parts of the mesh when new local refinements are executed by the hypergraph grammar productions.