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Volume 10, Issue 2
An Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation with PML

Z. Chen, D. Cheng, W. Feng & T. Wu

Int. J. Numer. Anal. Mod., 10 (2013), pp. 389-410.

Published online: 2013-10

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  • Abstract

In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersion, we propose global and refined choice strategies for choosing optimal parameters of the 9-point finite difference scheme. Numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion.

  • Keywords

Helmholtz equation, PML, 9-point finite difference scheme, numerical dispersion.

  • AMS Subject Headings

65N06, 65N22, 35L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-389, author = {Z. Chen, D. Cheng, W. Feng and T. Wu}, title = {An Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation with PML}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {2}, pages = {389--410}, abstract = {

In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersion, we propose global and refined choice strategies for choosing optimal parameters of the 9-point finite difference scheme. Numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/574.html} }
TY - JOUR T1 - An Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation with PML AU - Z. Chen, D. Cheng, W. Feng & T. Wu JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 389 EP - 410 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/574.html KW - Helmholtz equation, PML, 9-point finite difference scheme, numerical dispersion. AB -

In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersion, we propose global and refined choice strategies for choosing optimal parameters of the 9-point finite difference scheme. Numerical experiments are given to illustrate the improvement of the accuracy and the reduction of the numerical dispersion.

Z. Chen, D. Cheng, W. Feng and T. Wu. (2013). An Optimal 9-Point Finite Difference Scheme for the Helmholtz Equation with PML. International Journal of Numerical Analysis and Modeling. 10 (2). 389-410. doi:
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