a fast integral equation method for elastic wave scattering free from a coefficient matrix

当波遇到波场中的障碍物时，在固体中传播的波会产生散射。研究固体中的散射波是重建物体信息的一项重要任务。通常，散射波的分析是通过积分方程组来进行的，这有时需要为数值计算而推导出庞大而稠密的系数矩阵。众所周知，积分方程组的系数矩阵庞大而密集，是数值计算的障碍。在此基础上，提出了一种快速求解积分方程组的方法，该方法不需要推导系数矩阵和数学理论，可以从观测到的散射波中重建出散射体。

Waves propagating in solids cause scattering in the case that waves encounter obstacles in a wave field. Investigation of scattered waves in solids is an important task to reconstruct the information of the objects. In general, analysis of the scattered waves are carried out by means of the class of integral equation, that sometimes requires the derivation of huge and dense coefficient matrix for numerical calculations. It is known that huge and dense coefficient matrices for the integral equations are the obstacles for the numerical calculations. The pesent study proposed a fast method for the integral equation free from the derivation of coefficient matrix and mathematical theory for reconstructing the scattering object from the observed scattered waves based on the proposed method.