Effective Implementation of Wavelet Galerkin Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F12%3A%230000823" target="_blank" >RIV/46747885:24510/12:#0000823 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.aip.org/resource/2/apcpcs/1497/1/107_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1497/1/107_1?isAuthorized=no</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.4766773" target="_blank" >10.1063/1.4766773</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Effective Implementation of Wavelet Galerkin Method

Popis výsledku v původním jazyce

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Delta u = f on hypercube with homogeneous Dirichlet boundary conditions. In ourimplementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

Název v anglickém jazyce

Effective Implementation of Wavelet Galerkin Method

Popis výsledku anglicky

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Delta u = f on hypercube with homogeneous Dirichlet boundary conditions. In ourimplementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12)

ISBN

978-0-7354-1111-1

ISSN

—

e-ISSN

—

Počet stran výsledku

6

Strana od-do

107-112

Název nakladatele

AMER INST PHYSICS

Místo vydání

MELVILLE, NY 11747-4501 USA

Místo konání akce

Sozopol, BULGARIA

Datum konání akce

6. 12. 2012

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

312260000014