关于广义边界元方程组迭代解的一个新预处理方法(英文)

A new preconditioniog algorithm for iterative solution of generalized boundary element systems

引入一个用于解偏微分方程广义边界无法代法的新预处理算法。文中首先考虑标准边界元法使用的稀疏预处理子。然后阐述广义边界元法及其推广。使用离散小波变换来加速基于分离的预处理子。广义边界元法能有效迭代的关键在于压缩轴基函数形成的矩阵，用有紧支撑集的轴基函数得到了预处理迭代的新结果。也给出一些数值试验结果。

A new preconditioning algorithm for iterative solution of the generalized boundary element systems for partial differential equations is introduced. Sparse preconditioners are first considered for standard boundary element methods and then developed for the generalized boundary element methods (extended dual reciprocity methods). The use of discrete wavelet transforms to accelerate splitting based preconditioners is described. Attempts to compress radial basis matrices are made and new results using compactly supported radial basis functions are obtained. Some numerical results are reported.