一种快速多极虚拟间接边界元法的预处理方法OA

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.