An adaptive hierarchical matrix on point iterative poisson solver

In this paper,an adaptive hierarchical matrix (h -matrix) points iterative method based solution was proposed to solve two-dimensional poisson problem with dirichlet boundary condition. the finite difference approximation was used to discretize the problem,which led to a system of linear equation. two types of admissibility conditions,standard and weak,produces two different h -matrix structures,hs- and hw- respectively. the adaption of the h -matrices to a linear system leads to the saving of memory utilization. an experiment was conducted which compares the proposed hw-matrix with the benchmarked hs-matrix. the results showed the superiority of the proposed method when comparing both h -matrix structures.