An adaptive hierarchical matrix on point iterative Poisson solver

• Main Authors: Nik Mazlan, Nik Amir Syafiq, Othman, Mohamed, Senu, Norazak
• Format: Article
• Language: English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/52329/1/10.%20Nik%20n%20MO.pdf; http://psasir.upm.edu.my/id/eprint/52329/; http://einspem.upm.edu.my/journal/fullpaper/vol10no3/10.%20Nik%20n%20MO.pdf

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.