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

a 2016

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

BÍLEK, Petr, Max DUARTE, David NEČAS, Anne BOURDON, Zdeněk BONAVENTURA et. al.

Základní údaje

Originální název

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

Název česky

Řešení Poissonovy rovnice použitím kombinace rychlé multipólové metody a prostorově adaptivní metody multiresolution

Název anglicky

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

Autoři

BÍLEK, Petr, Max DUARTE, David NEČAS, Anne BOURDON a Zdeněk BONAVENTURA

Vydání

69th Annual Gaseous Electronics Conference, 2016

Další údaje

Typ výsledku

Konferenční abstrakt

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Klíčová slova česky

Poissonova rovnice, metoda multiresolution, adaptovaný grid, rychlá multipólová metoda, multipólový rozvoj, potenciál, streamery

Klíčová slova anglicky

Poisson equation, multiresolution method, adaptive grid, fast multipole method, multipole expansion, potential, streamers

Změněno: 28. 8. 2018 10:31, Mgr. Petr Bílek, Ph.D.

Anotace

V originále

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).

Citovat

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

@proceedings{1430236,
   author = {Bílek, Petr and Duarte, Max and Nečas, David and Bourdon, Anne and Bonaventura, Zdeněk},
   booktitle = {69th Annual Gaseous Electronics Conference},
   keywords = {Poisson equation, multiresolution method, adaptive grid, fast multipole method, multipole expansion, potential, streamers},
   title = {Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation},
   url = {http://adsabs.harvard.edu/abs/2016APS..GECMW6084B},
   year = {2016}
}

TY  - CONF
ID  - 1430236
AU  - Bílek, Petr - Duarte, Max - Nečas, David - Bourdon, Anne - Bonaventura, Zdeněk
PY  - 2016
TI  - Fast multipole and space adaptive multiresolution methods for the solution of the Poisson equation
KW  - Poisson equation, multiresolution method, adaptive grid, fast multipole method, multipole expansion, potential, streamers
UR  - http://adsabs.harvard.edu/abs/2016APS..GECMW6084B
N2  - 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).
ER  -

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

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