A robust solver for elliptic PDEs in 3D complex geometries
•A fast accurate singular/near-singular quadrature scheme on complex 3D geometries is presented.•Robust geometry processing algorithms are detailed to support quadrature.•The proposed method is tested on non-trivial geometries and topologies and compared against a competing approach. We develop a bo...
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Published in | Journal of computational physics Vol. 442; p. 110511 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cambridge
Elsevier Inc
01.10.2021
Elsevier Science Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | •A fast accurate singular/near-singular quadrature scheme on complex 3D geometries is presented.•Robust geometry processing algorithms are detailed to support quadrature.•The proposed method is tested on non-trivial geometries and topologies and compared against a competing approach.
We develop a boundary integral equation solver for elliptic partial differential equations on complex 3D 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, hedgehog: a simple extrapolation of the solution along a line to the boundary. We present a series of geometry-processing algorithms required for hedgehog 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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ISSN: | 0021-9991 1090-2716 |
DOI: | 10.1016/j.jcp.2021.110511 |