A Fast Algorithm with Error Bounds for Quadrature by Expansion
arXiv:1801.04070 · doi:10.1016/j.jcp.2018.05.006
Abstract
Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the singular integrals encountered in the evaluation of layer potentials. It exploits the smoothness of the layer potential by forming locally-valid expansion which are then evaluated to compute the near or on-surface value of the integral. Recent work towards coupling of a Fast Multipole Method (FMM) to QBX yielded a first step towards the rapid evaluation of such integrals (and the solution of related integral equations), albeit with only empirically understood error behavior. In this paper, we improve upon this approach with a modified algorithm for which we give a comprehensive analysis of error and cost in the case of the Laplace equation in two dimensions. For the same levels of (user-specified) accuracy, the new algorithm empirically has cost-per-accuracy comparable to prior approaches. We provide experimental results to demonstrate scalability and numerical accuracy.
Corrected version, see Appendix B for summary of corrections
References in corpus (3)
Cited by in corpus (9)
- A Fast Algorithm for Quadrature by Expansion in Three Dimensions
- Optimization of Fast Algorithms for Global Quadrature by Expansion Using Target-Specific Expansions
- Scalable Simulation of Realistic Volume Fraction Red Blood Cell Flows through Vascular Networks
- A robust solver for elliptic PDEs in 3D complex geometries
- Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries
- An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting Problem
- On the Approximation of Local Expansions of Laplace Potentials by the Fast Multipole Method
- High-order Finite Element--Integral Equation Coupling on Embedded Meshes
- Finite elements for Helmholtz equations with a nonlocal boundary condition