This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique for which the authors have constructed a fast direct solver. The key features of the work presented in this paper are that the fast direct solver is more efficient for the new extended linear system and that problems involving specialized quadrature for weakly singular kernels can be easily handled. Numerical results illustrate the improved performance of the fast direct solver for the new extended system when compared to the fast direct solver for the original extended system.

该手稿为基于积分方程的技术提出了一种新的扩展线性系统，用于解决局部扰动几何上的边值问题。新的扩展线性系统类似于先前提出的技术，作者为此构建了快速直接求解器。本文提出的工作的关键特征是，快速直接求解器对于新的扩展线性系统更有效，并且可以轻松处理涉及弱奇异内核的专用正交问题。数值结果表明，与原始扩展系统的快速直接求解器相比，新扩展系统的快速直接求解器的性能有所提高。