### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Journal of Computational Physics |

Volume | 344 |

DOIs | |

State | Published - Sep 1 2017 |

### Fingerprint

### Keywords

- Fast multipole method
- Integral equations
- Poisson equation
- Quadrature by expansion

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Computer Science Applications

### Cite this

**An adaptive fast multipole accelerated Poisson solver for complex geometries.** / Askham, T.; Cerfon, Antoine.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 344, pp. 1-22. https://doi.org/10.1016/j.jcp.2017.04.063

}

TY - JOUR

T1 - An adaptive fast multipole accelerated Poisson solver for complex geometries

AU - Askham, T.

AU - Cerfon, Antoine

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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 C0 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.

AB - 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 C0 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.

KW - Fast multipole method

KW - Integral equations

KW - Poisson equation

KW - Quadrature by expansion

UR - http://www.scopus.com/inward/record.url?scp=85019067970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019067970&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2017.04.063

DO - 10.1016/j.jcp.2017.04.063

M3 - Article

VL - 344

SP - 1

EP - 22

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -