Graph Grammar Based Direct Solver for Hp-adaptive Finite Element Method with Point Singularities

In this paper we present a graph grammar based direct solver algorithm for hp-adaptive finite element method simulations with point singularities. The solver algorithm is obtained by representing computational mesh as a graph and prescribing the solver algorithm by graph grammar productions. Classical direct solvers deliver O(Np4+N1.5) computational cost for regular 2D grids, and O(Np6+N2) for regular 3D grids, where N denotes number of degrees of freedom and p denotes the polynomial order of approximation. The solver presented in this paper delivers linear computational cost for uniform polynomial order of approximation p. For non-uniform polynomial order the computational cost is almost linear