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

Pflaum C, Hartmann R (2016)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 54

Pages Range: 2707–2727

Journal Issue: 4

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

DOI: 10.1137/15M101508X

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

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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://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.

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