A Fast Algorithm for Quadrature by Expansion in Three Dimensions
arXiv:1805.06106 · doi:10.1016/j.jcp.2019.03.024
Abstract
This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a modified version of the Fast Multipole Method (FMM). Our scheme extends a recently developed formulation of the FMM for QBX in two dimensions, which, in that setting, achieves mathematically rigorous error and running time bounds. In addition to generalization to three dimensions, we highlight some algorithmic and mathematical opportunities for improved performance and stability. Lastly, we give numerical evidence supporting the accuracy, performance, and scalability of the algorithm through a series of experiments involving the Laplace and Helmholtz equations.
References in corpus (5)
- A fast integral equation method for solid particles in viscous flow using quadrature by expansion
- Adaptive quadrature by expansion for layer potential evaluation in two dimensions
- A local target specific quadrature by expansion method for evaluation of layer potentials in 3D
- Estimation of quadrature errors in layer potential evaluation using quadrature by expansion
- A Fast Algorithm with Error Bounds for Quadrature by Expansion
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- Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
- Quadrature by Two Expansions: Evaluating Laplace Layer Potentials using Complex Polynomial and Plane Wave Expansions
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