Parallel Implementation of Wavelet Galerkin Method in Higher
Dimensions

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Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions

Přehled o publikaci

D 2013

Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions

FINĚK, Václav and Martina ŠIMŮNKOVÁ

Basic information

Original name

Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions

Authors

FINĚK, Václav (203 Czech Republic, guarantor, belonging to the institution) and Martina ŠIMŮNKOVÁ (203 Czech Republic)

Edition

MELVILLE, NY 11747-4501 USA, APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'13), AIP Conference Proceedings, Vol. 1570, p. 235-240, 6 pp. 2013

Publisher

American Institute of Physics

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

General mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/46747885:24510/13:#0001139

Organization

Faculty of Science, Humanities and Education – Technical University of Liberec – Repository

ISSN

UT WoS

000346051300026

Keywords in English

Wavelets; numerical methods; differential equations

Changed: 1/4/2015 08:21, Václav Finěk

Abstract

V originále

Due to storage requirements and computational complexity, the approximate solution of PDEs computed by standard numerical methods is usually limited to problems with up to three or four dimensions. In our contribution, we use recently proposed wavelets based on quadratic splines to solve the Poisson equation with Dirichlet boundary conditions in higher dimensions. We describe here our algorithm of matrix-vector multiplication which takes account of the special structure of wavelet stiffness matrices and enables scalable parallelization. At the end, we show its performance for problems up to six dimensions.

Cite

FINĚK, Václav and Martina ŠIMŮNKOVÁ. Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions. Online. In Venkov, G; Pasheva, V. APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'13), AIP Conference Proceedings, Vol. 1570. MELVILLE, NY 11747-4501 USA: American Institute of Physics, 2013, p. 235-240. ISSN 0094-243X.

@inproceedings{18222,
   author = {Finěk, Václav and Šimůnková, Martina},
   address = {MELVILLE, NY 11747-4501 USA},
   booktitle = {APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'13), AIP Conference Proceedings, Vol. 1570},
   editor = {Venkov, G; Pasheva, V},
   keywords = {Wavelets; numerical methods; differential equations},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {MELVILLE, NY 11747-4501 USA},
   pages = {235-240},
   publisher = {American Institute of Physics},
   title = {Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions},
   url = {http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4854761},
   year = {2013}
}

TY  - CONF
ID  - 18222
AU  - Finěk, Václav - Šimůnková, Martina
PY  - 2013
TI  - Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions
PB  - American Institute of Physics
CY  - MELVILLE, NY 11747-4501 USA
KW  - Wavelets
KW  - numerical methods
KW  - differential equations
UR  - http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4854761
L2  - http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4854761
N2  - Due to storage requirements and computational complexity, the approximate solution of PDEs computed by standard numerical methods is usually limited to problems with up to three or four dimensions. In our contribution, we use recently proposed wavelets based on quadratic splines to solve the Poisson equation with Dirichlet boundary conditions in higher dimensions. We describe here our algorithm of matrix-vector multiplication which takes account of the special structure of wavelet stiffness matrices and enables scalable parallelization. At the end, we show its performance for problems up to six dimensions.
ER  -

FINĚK, Václav and Martina ŠIMŮNKOVÁ. Parallel Implementation of Wavelet Galerkin Method in Higher Dimensions. Online. In Venkov, G; Pasheva, V. \textit{APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'13), AIP Conference Proceedings, Vol. 1570}. MELVILLE, NY 11747-4501 USA: American Institute of Physics, 2013, p.~235-240. ISSN~0094-243X.