A fast algorithm with error bounds for Quadrature by Expansion

Matt Wala, Andreas Klöckner
2018 Journal of Computational Physics  
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
more » ... 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.
doi:10.1016/j.jcp.2018.05.006 fatcat:lsc546tswre33g3fwiiufbfqfm