Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation

BÍLEK, Petr, Max DUARTE, David NEČAS, Anne BOURDON and Zdeněk BONAVENTURA. Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation. In 69th Annual Gaseous Electronics Conference. 2016.

Basic information

• Original name: Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation
• Name in Czech: Řešení Poissonovy rovnice použitím kombinace rychlé multipólové metody a prostorově adaptivní metody multiresolution
• Name (in English): Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation
• Authors: BÍLEK, Petr, Max DUARTE, David NEČAS, Anne BOURDON and Zdeněk BONAVENTURA.
• Edition: 69th Annual Gaseous Electronics Conference, 2016.

Other information

• Type of outcome: Conference abstract
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Keywords (in Czech): Poissonova rovnice, metoda multiresolution, adaptovaný grid, rychlá multipólová metoda, multipólový rozvoj, potenciál, streamery
• Keywords in English: Poisson equation, multiresolution method, adaptive grid, fast multipole method, multipole expansion, potential, streamers

Abstract

This work focuses on the conjunction of the fast multipole method (FMM) with the space adaptive multiresolution (MR) technique for grid adaptation. Since both methods, MR and FMM provide a priori error estimates, both achieve O(N) computational complexity, and both operate on the same hierarchical space division, their conjunction represents a natural choice when designing a numerically efficient and robust strategy for time dependent problems. Special attention is given to the use of these methods in the simulation of streamer discharges in air. We have designed a FMM Poisson solver on multiresolution adapted grid in 2D. The accuracy and the computation complexity of the solver has been verified for a set of manufactured solutions. We confirmed that the developed solver attains desired accuracy and this accuracy is controlled only by the number of terms in the multipole expansion in combination with the multiresolution accuracy tolerance. The implementation has a linear computation complexity O(N).