弱奇性积分方程的最优阶多尺度Petrov-Galerkin快速算法

摘要

The compressed multiscale Petrov-Galerkin algorithm for solving the second kind weakly singular integral equations is considered. We give the range of the truncation parameters and prove that the corresponding compression algorithm can achieve the optimal convergent order while preserving the stability, computational complexity and the uniformly boundedness of the condition number of the coefficient matrix. The numerical results verify the validity of the theoretical analysis.%考虑求解第二类Fredholm弱奇性积分方程的多尺度Petrov-Galerkin压缩格式,给出压缩策略中截断参数的选取范围,证明了相应的压缩格式在保持稳定性、计算复杂度和系数矩阵条件数一致有界的基础上,收敛阶达到最优.并以数值算例验证了理论结果的正确性和有效性.