A Study of Accelerated Adaptive Integral Method Based on Triangle Filling Strategy

基于三角形循环策略的自适应积分法加速研究

School of Electronic Information, Northwestern Polytechnical University, Xi'an 710072, China

Received: 14 September 2019

Abstract

In order to overcome the shortcomings of large time consuming in the near matrix filling and the slow convergence in iteration of adaptive integral method (AIM), the triangle filling strategy and the double-threshold criterion are combined to accelerate the near matrix filling speed in this paper. This method separates the near matrix filling procedure and the near correction during calculation. With the help of incomplete LU decomposition, the preconditioning matrix is constructed from the sparse near matrix before near correction, which could alleviate the ill-conditioned properties of the impedance matrix. Numerical simulation results show that, the triangle filling strategy with ILU preconditioning could improve the filling speed by 2 times and the iteration converges at most 20 times faster than traditional AIM without any accuracy reduction.

摘要

为解决传统自适应积分方法近场填充耗时长，迭代求解收敛慢的问题，利用三角形循环策略联合双重间距检测机制来加快近场矩阵的填充。这种方法将近场填充和矫正分离为2个不同的阶段，同时在2个阶段之间，利用不完全LU分解法对未矫正的近场稀疏矩阵进行预处理，改善阻抗矩阵的病态特性。仿真结果表明，在给定的精度下，采用三角形循环策略可以将填充效率提升至原来的2倍，并且经过不完全LU预处理，其迭代收敛速率最多可以提高20倍。