Several Efficient Algorithms for Finding the Solution of the Three-dimensional Poisson’s Equation on Personal Computers

Abstract

The paper presents a study of efficiency of several algorithms for finding the solution of the three-dimensional (3D) Poisson’s equation on personal computers. The algorithms under investigation are CGS, TFQMR and preconditioned BiCGSTAB(3). The algorithms were incorporated into the self-consistent ensemble Monte -Carlo (EMC) method and then applied to simulate the carrier dynamics in GaAs p-i-n diodes to test their efficiency. The results showed that the running time on personal computers of the considering algorithms is reduced around eighty times compared to the fastest conventional methods. The results confirm that the methods are good choices for the solution of the 3D Poisson’s equation, not only on big platforms but also on single personal computers.