基于时域体面积分方程的分块预条件方法

Block pre-conditioner based on time domain volume-surface integral equation

摘要:

时域体电场积分方程性态较好，但时域面积分方程性态较差，这就造成体面耦合的时域电场积分方程在迭代求解时经常遇到收敛较慢的问题，无法满足工程需要，并且一般预条件技术获得的加速效果也不甚理想。因此，时域体面积分方程迭代求解时间过长已成为体面积分方程在实际工程应用中的核心问题。针对时域体面电场积分方程矩阵性态差的问题，提出一种引入分块预条件方法(BMP)，可以加快矩阵迭代收敛的速度。将时域体面积分方程的矩阵分解成3块矩阵相乘的形式，而这3块矩阵都是稀疏的，并通过几个体面算例说明该预条件技术的效率。

Abstract:

The state of time domain electric field volume integral equation is good, while that of surface integral equation is poor, which results in slow convergence in the iterative solution of time domain electric field integral equation with volume-surface coupling, unable to meet the project requirements. Furthermore, the acceleration effect obtained by general preconditioning techniques is not very ideal. Therefore, a too long iteration time for time domain volume-surface integral equation has become the core issue in practical engineering applications. Aiming at the problem of poor behavior matrix, a new Block Matrix Pre-conditioner(BMP) method which can accelerate the convergence of matrix iteration is proposed. The time domain volume-surface integral equation matrix is decomposed into three pieces in the form of matrix multiplication, and the three matrices are all sparse. The efficiency of the preconditioning technique is illustrated by several volume-surface examples.