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Volume 13, Issue 5
Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers

L. Yuan, Q.-Y. Hu & H.-B. An

Int. J. Numer. Anal. Mod., 13 (2016), pp. 802-819.

Published online: 2016-09

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  • Abstract

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioners. The main goal of this paper is to implement in parallel these domain decomposition preconditioners for the system with large wave numbers. The numerical results indicate that the preconditioners are highly scalable and are effective for solving Helmholtz equation and Maxwell's equations with large wave numbers.

  • Keywords

Helmholtz equations, Maxwell's equations, large wave number, variational formulation, plane-wave basis, preconditioner, iteration counts.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-802, author = {L. Yuan, Q.-Y. Hu and H.-B. An}, title = {Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {5}, pages = {802--819}, abstract = {

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioners. The main goal of this paper is to implement in parallel these domain decomposition preconditioners for the system with large wave numbers. The numerical results indicate that the preconditioners are highly scalable and are effective for solving Helmholtz equation and Maxwell's equations with large wave numbers.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/466.html} }
TY - JOUR T1 - Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers AU - L. Yuan, Q.-Y. Hu & H.-B. An JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 802 EP - 819 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/466.html KW - Helmholtz equations, Maxwell's equations, large wave number, variational formulation, plane-wave basis, preconditioner, iteration counts. AB -

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioners. The main goal of this paper is to implement in parallel these domain decomposition preconditioners for the system with large wave numbers. The numerical results indicate that the preconditioners are highly scalable and are effective for solving Helmholtz equation and Maxwell's equations with large wave numbers.

L. Yuan, Q.-Y. Hu and H.-B. An. (2016). Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers. International Journal of Numerical Analysis and Modeling. 13 (5). 802-819. doi:
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