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arXiv · 2002.04143

A robust solver for elliptic PDEs in 3D complex geometries

Matthew J. Morse·Abtin Rahimian·Denis Zorin
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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.

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Matthew J. Morse, Abtin Rahimian, Denis Zorin. 2020-02-11. A robust solver for elliptic PDEs in 3D complex geometries. https://doi.org/10.1016/j.jcp.2021.110511

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