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Volume 11, Issue 3
A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations

Q. Hu & L. Yuan

Int. J. Numer. Anal. Mod., 11 (2014), pp. 587-607.

Published online: 2014-11

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  • Abstract

In this paper we are concerned with numerical methods for solving Helmholtz equations. We propose a new variant of the Variational Theory of Complex Rays (VTCR) method introduced in [15, 16]. The approximate solution generated by the new variant has higher accuracy than that generated by the original VTCR method. Moreover, the accuracy of the resulting approximate solution can be further increased by adding two suitable positive relaxation parameters into the new variational formula. Besides, a simple domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Numerical results confirm the efficiency of the new method.

  • Keywords

Helmholtz equations, wave basis functions, variational formulation, error estimate, preconditioner, iteration counts.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-587, author = {Q. Hu and L. Yuan}, title = {A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {587--607}, abstract = {

In this paper we are concerned with numerical methods for solving Helmholtz equations. We propose a new variant of the Variational Theory of Complex Rays (VTCR) method introduced in [15, 16]. The approximate solution generated by the new variant has higher accuracy than that generated by the original VTCR method. Moreover, the accuracy of the resulting approximate solution can be further increased by adding two suitable positive relaxation parameters into the new variational formula. Besides, a simple domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Numerical results confirm the efficiency of the new method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/543.html} }
TY - JOUR T1 - A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations AU - Q. Hu & L. Yuan JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 587 EP - 607 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/543.html KW - Helmholtz equations, wave basis functions, variational formulation, error estimate, preconditioner, iteration counts. AB -

In this paper we are concerned with numerical methods for solving Helmholtz equations. We propose a new variant of the Variational Theory of Complex Rays (VTCR) method introduced in [15, 16]. The approximate solution generated by the new variant has higher accuracy than that generated by the original VTCR method. Moreover, the accuracy of the resulting approximate solution can be further increased by adding two suitable positive relaxation parameters into the new variational formula. Besides, a simple domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Numerical results confirm the efficiency of the new method.

Q. Hu and L. Yuan. (2014). A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations. International Journal of Numerical Analysis and Modeling. 11 (3). 587-607. doi:
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