Improved Method for Solving Systems of Linear Equations in Frequency Response Problems

摘要

Vibration and acoustics problems that require solving matrix equations for many frequencies have solutions that vary very little from one frequency to the next. This suggests that an iterative method using the solution at one frequency could be used to obtain the next frequency solution. In this report, the matrix inverse at the first frequency serves as the preconditioner for the preconditioned conjugate gradient method to obtain subsequent frequencies. For the problem examined in this report, in which the matrix comes from the finite-element analysis of a cube, the iterative method is more than an order of magnitude faster than Gaussian elimination.