A robust solver for elliptic PDEs in 3D complex geometries
Abstract
We develop a boundary integral equation solver for elliptic partial differential equations on complex 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, : a simple extrapolation of the solution along a line to the boundary. We present a series of geometry-processing algorithms required for 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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