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Volume 9, Issue 3
Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs

Guanjie Wang & Qifeng Liao

DOI: 10.4208/eajam.140119.160219

East Asian J. Appl. Math., 9 (2019), pp. 601-621.

Published online: 2019-06

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  • Abstract

The implementation of spectral stochastic Galerkin finite element approximation methods for Helmholtz equations with random inputs is considered. The corresponding linear systems have matrices represented as Kronecker products. The sparsity of such matrices is analysed and a mean-based preconditioner is constructed. Numerical examples show the efficiency of the mean-based preconditioners for stochastic Helmholtz problems, which are not too close to a resonant frequency.

  • Keywords

Helmholtz equations, PDEs with random data, generalised polynomial chaos, stochastic finite elements, iterative solvers.

  • AMS Subject Headings

65C30, 65F08, 65N30, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-601, author = {Guanjie Wang and Qifeng Liao}, title = {Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {601--621}, abstract = {

The implementation of spectral stochastic Galerkin finite element approximation methods for Helmholtz equations with random inputs is considered. The corresponding linear systems have matrices represented as Kronecker products. The sparsity of such matrices is analysed and a mean-based preconditioner is constructed. Numerical examples show the efficiency of the mean-based preconditioners for stochastic Helmholtz problems, which are not too close to a resonant frequency.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.140119.160219}, url = {http://global-sci.org/intro/article_detail/eajam/13169.html} }
TY - JOUR T1 - Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs AU - Guanjie Wang & Qifeng Liao JO - East Asian Journal on Applied Mathematics VL - 3 SP - 601 EP - 621 PY - 2019 DA - 2019/06 SN - 9 DO - http://doi.org/10.4208/eajam.140119.160219 UR - https://global-sci.org/intro/article_detail/eajam/13169.html KW - Helmholtz equations, PDEs with random data, generalised polynomial chaos, stochastic finite elements, iterative solvers. AB -

The implementation of spectral stochastic Galerkin finite element approximation methods for Helmholtz equations with random inputs is considered. The corresponding linear systems have matrices represented as Kronecker products. The sparsity of such matrices is analysed and a mean-based preconditioner is constructed. Numerical examples show the efficiency of the mean-based preconditioners for stochastic Helmholtz problems, which are not too close to a resonant frequency.

Guanjie Wang and Qifeng Liao. (2019). Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs. East Asian Journal on Applied Mathematics. 9 (3). 601-621. doi:10.4208/eajam.140119.160219
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