A robust solver for elliptic PDEs in 3D complex geometries

Matthew J. Morse, Abtin Rahimian, Denis Zorin

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number110511
JournalJournal of Computational Physics
Publication statusPublished - 1 Oct 2021
Externally publishedYes


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