A robust solver for elliptic PDEs in 3D complex geometries
Numerical Analysis
2021-07-07 v4 Numerical Analysis
Abstract
We develop a boundary integral equation solver for elliptic partial differential equations on complex \threed geometries. Our method is efficient, high-order accurate and robustly handles complex geometries. A key component is our singular and near-singular layer potential evaluation scheme, \qbkix: a simple extrapolation of the solution along a line to the boundary. We present a series of geometry-processing algorithms required for \qbkix to run efficiently with accuracy guarantees on arbitrary geometries and an adaptive upsampling scheme based on a iteration-free heuristic for quadrature error. We validate the accuracy and performance with a series of numerical tests and compare our approach to a competing local evaluation method.
Cite
@article{arxiv.2002.04143,
title = {A robust solver for elliptic PDEs in 3D complex geometries},
author = {Matthew J. Morse and Abtin Rahimian and Denis Zorin},
journal= {arXiv preprint arXiv:2002.04143},
year = {2021}
}