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Volume 8, Issue 3
A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case

S. Andouze, O. Goubet & P. Poullet

Int. J. Numer. Anal. Mod., 8 (2011), pp. 365-372.

Published online: 2011-08

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  • Abstract

In this paper we apply and discuss a multilevel method to solve a scattering problem. The multilevel method belongs to the class of incremental unknowns method as in [10]; in this work, the best performance was obtained with a coarsest grid having roughly two points per linear wavelength. We analyze this method for a simple model problem following H. Yserentant [17]. In this case, the main limitation to multilevel methods is closely linked to the indefiniteness of the Helmholtz problem.

  • Keywords

hierarchical basis, indefinite problem, Helmholtz equation, iterative methods.

  • AMS Subject Headings

35J05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-8-365, author = {S. Andouze, O. Goubet and P. Poullet}, title = {A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {365--372}, abstract = {

In this paper we apply and discuss a multilevel method to solve a scattering problem. The multilevel method belongs to the class of incremental unknowns method as in [10]; in this work, the best performance was obtained with a coarsest grid having roughly two points per linear wavelength. We analyze this method for a simple model problem following H. Yserentant [17]. In this case, the main limitation to multilevel methods is closely linked to the indefiniteness of the Helmholtz problem.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/690.html} }
TY - JOUR T1 - A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case AU - S. Andouze, O. Goubet & P. Poullet JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 365 EP - 372 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/690.html KW - hierarchical basis, indefinite problem, Helmholtz equation, iterative methods. AB -

In this paper we apply and discuss a multilevel method to solve a scattering problem. The multilevel method belongs to the class of incremental unknowns method as in [10]; in this work, the best performance was obtained with a coarsest grid having roughly two points per linear wavelength. We analyze this method for a simple model problem following H. Yserentant [17]. In this case, the main limitation to multilevel methods is closely linked to the indefiniteness of the Helmholtz problem.

S. Andouze, O. Goubet and P. Poullet. (2011). A Multilevel Method for Solving the Helmholtz Equation: The Analysis of the One-Dimensional Case. International Journal of Numerical Analysis and Modeling. 8 (3). 365-372. doi:
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