An alternative extended linear system for boundary value problems on locally perturbed geometries

TL;DR

This paper introduces a more efficient extended linear system and solver for boundary value problems on locally perturbed geometries, improving computational performance and handling specialized quadrature with ease.

Contribution

It develops a new extended linear system and a faster direct solver, enhancing efficiency and flexibility for boundary value problems on perturbed geometries.

Findings

The new solver outperforms previous methods in computational speed.

It effectively handles specialized quadrature for weakly singular kernels.

Numerical results confirm improved performance.

Abstract

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.