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Effective Implementation of Wavelet Galerkin Method

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Effective Implementation of Wavelet Galerkin Method

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    S - Specificky vyzkum na vysokych skolach

Others

  • Publication year

    2012

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

    978-0-7354-1111-1

  • ISSN

  • e-ISSN

  • Number of pages

    6

  • Pages from-to

    107-112

  • Publisher name

    AMER INST PHYSICS

  • Place of publication

    MELVILLE, NY 11747-4501 USA

  • Event location

    Sozopol, BULGARIA

  • Event date

    Dec 6, 2012

  • Type of event by nationality

    EUR - Evropská akce

  • UT code for WoS article

    312260000014