Decomposition Method for Complex 3D Problems in Electron Optics

Abstract

Abstract:The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM (Finite Difference Method) and FEM (Finite Element Method) mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM (Boundary Element Method) based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU (Central Processor Unit) desktop computer. New algorithm is iterative one, but exponential convergence for the Schwartz's algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code "POISSON-3".