A Linear Complexity Direct Solver for H-adaptive Grids with Point Singularities

In this paper we present a theoretical proof of linear computational cost and complexity for a recently developed direct solver driven by hypergraph grammar productions. The solver is specialized for computational meshes with point singularities in two and three dimensions. Linear complexity is achieved due to utilizing the special structure of such grids. We describe the algorithm and estimate the exact computational cost on an example of a two-dimensional mesh containing a single point singularity. We extend this reasoning to the three dimensional meshes.