二维均匀介质中积分方程的快速精确算法

A fast and accurate algorithm for integral equations in a 2D homogeneous medium

采用稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法精确计算二维均匀介质中的积分方程.采用一种新的插值函数作为基函数和试探函数对积分方程进行弱化离散,离散后的积分方程采用稳定型双共轭梯度迭代方法进行求解,从而得到异常体内电场的分布.计算时采用快速Fourier变换技术将积分方程内Green函数与电场的乘积表示成褶积形式以加快计算速度.数值计算举例说明了算法的精确性和有效性.

The integral equations in a 2D homogeneous medium are accurately calculated by the stabilized biconjugate-gradient fast Fourier transform（BCGS-FFT）algorithm.The new interpolating function is chosen as basis and testing functions to get the weak-form discretization of the integral equations.The discrete form of the integral equations is solved via the stabilized biconjugate-gradient iteration method,and the distribution of the electric field within the abnormal objects can be obtained.The product between the Green＇s function and the electric field within the integral equations can be expressed in the form of convolution,which can be accelerated by fast Fourier transform.Numerical examples have shown the accuracy and efficiency of the algorithm.