A fast direct solver for boundary value problems on locally perturbed geometries

JOURNAL OF COMPUTATIONAL PHYSICS

卷:356

Article

Zhang, Yabin¹  Gillman, Adrianna¹ 

[1] Rice Univ, Dept Computat & Appl Math, 6100 Main St,MS 134, Houston, TX 77005 USA

关键词: Fast direct solver;    Integral equations;    Locally perturbed geometries;   

DOI  :  10.1016/j.jcp.2017.12.013

来源: Elsevier

【 摘 要 】

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free