Malaysian Journal of Mathematical Sciences, September 2016, Vol. 10, No. 3
An Adaptive Hierarchical Matrix on Point Iterative Poisson Solver
Nik Amir Syafiq, Mohamed Othman, and Norazak Senu
Corresponding Email: mothman@upm.edu.my
Received date: -
Accepted date: -
Abstract:
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.
Keywords: Adaptive Hierarchical Matrix, Point Iterative Solver, Poisson Equation, Finite Difference Approximation
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