A Sparse Grid Discretization of the Helmholtz Equation with Variable Coefficients in High Dimensions

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autor(en): Pflaum C, Hartmann R
Zeitschrift: SIAM Journal on Numerical Analysis
Verlag: Society for Industrial and Applied Mathematics Publications
Jahr der Veröffentlichung: 2016
Band: 54
Heftnummer: 4
Seitenbereich: 2707–2727
ISSN: 0036-1429
Sprache: Englisch


Abstract



The computational effort for solving elliptic differential equations can significantly be reduced by using sparse grids. We present a new Ritz--Galerkin discretization of the Helmholtz equation with variable coefficients on sparse grids. This discretization uses prewavelets and a semi-orthogonality property on sparse grids. A detailed convergence analysis is given for the arbitrary dimension d. The linear equation system of the discretization can efficiently be solved by a multigrid Q-cycle.



The computational effort for solving elliptic differential equations can significantly be reduced by using sparse grids. We present a new Ritz--Galerkin discretization of the Helmholtz equation with variable coefficients on sparse grids. This discretization uses prewavelets and a semi-orthogonality property on sparse grids. A detailed convergence analysis is given for the arbitrary dimension $d$. The linear equation system of the discretization can efficiently be solved by a multigrid Q-cycle.





Read More: http://epubs.siam.org/doi/abs/10.1137/15M101508X


The computational effort for solving elliptic differential equations can significantly be reduced by using sparse grids. We present a new Ritz--Galerkin discretization of the Helmholtz equation with variable coefficients on sparse grids. This discretization uses prewavelets and a semi-orthogonality property on sparse grids. A detailed convergence analysis is given for the arbitrary dimension $d$. The linear equation system of the discretization can efficiently be solved by a multigrid Q-cycle.





Read More: http://epubs.siam.org/doi/abs/10.1137/15M101508X


The computational effort for solving elliptic differential equations can significantly be reduced by using sparse grids. We present a new Ritz--Galerkin discretization of the Helmholtz equation with variable coefficients on sparse grids. This discretization uses prewavelets and a semi-orthogonality property on sparse grids. A detailed convergence analysis is given for the arbitrary dimension $d$. The linear equation system of the discretization can efficiently be solved by a multigrid Q-cycle.





Read More: http://epubs.siam.org/doi/abs/10.1137/15M101508X



FAU-Autoren / FAU-Herausgeber

Hartmann, Rainer
Professur für Informatik (Numerische Simulation mit Höchstleistungsrechnern)
Pflaum, Christoph Prof. Dr.
Professur für Informatik (Numerische Simulation mit Höchstleistungsrechnern)


Zitierweisen

APA:
Pflaum, C., & Hartmann, R. (2016). A Sparse Grid Discretization of the Helmholtz Equation with Variable Coefficients in High Dimensions. SIAM Journal on Numerical Analysis, 54(4), 2707–2727. https://dx.doi.org/10.1137/15M101508X

MLA:
Pflaum, Christoph, and Rainer Hartmann. "A Sparse Grid Discretization of the Helmholtz Equation with Variable Coefficients in High Dimensions." SIAM Journal on Numerical Analysis 54.4 (2016): 2707–2727.

BibTeX: 

Zuletzt aktualisiert 2018-28-11 um 06:02