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Volume 13, Issue 4
An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems

Guanjie Wang & Qifeng Liao

DOI: 10.4208/nmtma.OA-2019-0101

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 1007-1026.

Published online: 2020-06

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  • Abstract

The implementation of an adaptive hybrid spectral method for Helmholtz equations with random parameters is addressed in this work. New error indicators for generalized polynomial chaos for stochastic approximations and spectral element methods for physical approximations are developed, and systematic adaptive strategies are proposed associated with these error indicators. Numerical results show that these error indicators provide effective estimates for the approximation errors, and the overall adaptive procedure results in efficient approximation method for the stochastic Helmholtz equations.

  • Keywords

Uncertainty quantification, generalized polynomial chaos, spectral elements, Helmholtz equations.

  • AMS Subject Headings

65C30, 65F08, 65N30, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-1007, author = {Wang , Guanjie and Liao , Qifeng}, title = {An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {1007--1026}, abstract = {

The implementation of an adaptive hybrid spectral method for Helmholtz equations with random parameters is addressed in this work. New error indicators for generalized polynomial chaos for stochastic approximations and spectral element methods for physical approximations are developed, and systematic adaptive strategies are proposed associated with these error indicators. Numerical results show that these error indicators provide effective estimates for the approximation errors, and the overall adaptive procedure results in efficient approximation method for the stochastic Helmholtz equations.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0101}, url = {http://global-sci.org/intro/article_detail/nmtma/16964.html} }
TY - JOUR T1 - An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems AU - Wang , Guanjie AU - Liao , Qifeng JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1007 EP - 1026 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0101 UR - https://global-sci.org/intro/article_detail/nmtma/16964.html KW - Uncertainty quantification, generalized polynomial chaos, spectral elements, Helmholtz equations. AB -

The implementation of an adaptive hybrid spectral method for Helmholtz equations with random parameters is addressed in this work. New error indicators for generalized polynomial chaos for stochastic approximations and spectral element methods for physical approximations are developed, and systematic adaptive strategies are proposed associated with these error indicators. Numerical results show that these error indicators provide effective estimates for the approximation errors, and the overall adaptive procedure results in efficient approximation method for the stochastic Helmholtz equations.

Wang , Guanjie and Liao , Qifeng. (2020). An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 1007-1026. doi:10.4208/nmtma.OA-2019-0101
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