广西科技大学学报2026，Vol.37Issue(4)：1-7,7.DOI:10.16375/j.cnki.cn45-1395/t.2026.04.001
一种快速多极虚拟间接边界元法的预处理方法
A preconditioning method for the fast multi-pole virtual indirect boundary element method
摘要
Abstract
The fast multi-pole virtual indirect boundary element method(FMVIBEM)is an efficient numerical approach for solving large-scale acoustic problems.However,when employing the generalized minimal residual method(GMRES)to iteratively solve large-scale linear systems,the FMVIBEM exhibits poor solution characteristics,resulting in slow convergence rates.To accelerate the iterative convergence,a preconditioning matrix construction method was proposed based on the optimization of grid layer partitioning between virtual and real boundaries.By appropriately adjusting the grid layers of real and virtual boundaries,zero elements on the main diagonal of the nearfield matrix were eliminated,thereby constructing a preconditioning matrix with a low condition number.Combined with left-preconditioning techniques,this approach significantly improved the convergence rate of the iterative algorithm.Numerical simulations demonstrate that the proposed preconditioning matrix design method offers remarkable computational efficiency advantages in three-dimensional acoustic computations,particularly exhibiting more pronounced convergence acceleration effects in high frequency acoustic problems.关键词
虚拟间接边界元法/快速多极算法/广义最小残差法/预处理/条件数优化/高频Key words
virtual indirect boundary element method/fast multi-pole algorithm/generalized minimal residual method/preconditioning/condition number optimization/high frequency分类
数理科学引用本文复制引用
钱萧仰,向宇..一种快速多极虚拟间接边界元法的预处理方法[J].广西科技大学学报,2026,37(4):1-7,7.基金项目
国家自然科学基金项目(12364055)资助 （12364055）
