Phương pháp số hiệu quả trong giải phương trình Poisson: Các chiến lược tối ưu hóa thời gian tính toán

Abstract

Poisson’s equation is a second-order partial differential equation which is used to compute the electric potential based on the charge density of a system. In numerical study, the finite difference method is widely used to simplify the equations. Gauss-Seidel, Jacobi and SOR methods are three common iterative methods for solving Poisson’s equation. Choosing suitable values of maximum error or parallelizing the code for running on a supercomputer can drastically reduce computation time in order to optimize the code for complicated systems.