An adaptive fast multipole accelerated Poisson solver for complex geometries

JOURNAL OF COMPUTATIONAL PHYSICS

卷:344

Article

Askham, T.¹  Cerfon, A. J.² 

[1] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

关键词: Poisson equation;    Fast multipole method;    Quadrature by expansion;    Integral equations;   

DOI  :  10.1016/j.jcp.2017.04.063

来源: Elsevier

【 摘 要 】

We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C-0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient black box fast solver. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free