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Volume 19, Issue 4
A Mesh-Less, Ray-Based Deep Neural Network Method for the Helmholtz Equation with High Frequency

Andy L Yang & Feng Gu

Int. J. Numer. Anal. Mod., 19 (2022), pp. 587-601.

Published online: 2022-06

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  • Abstract

This article introduces a mesh-less, ray-based deep neural network method to solve the Helmholtz equation with high frequency. This method does not use an adaptive mesh refinement method, nor does it design a numerical scheme using some specially designed basis function to calculate the numerical solution, but it has the advantages of easy implementation and no mesh. We have carried out various numerical examples to prove the accuracy and efficiency of the proposed numerical method.

  • Keywords

Deep learning, plane wave, deep Neural Network, loss, high frequency, Helmholtz equation.

  • AMS Subject Headings

65L15, 34L16

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-587, author = {Yang , Andy L and Gu , Feng}, title = {A Mesh-Less, Ray-Based Deep Neural Network Method for the Helmholtz Equation with High Frequency}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {4}, pages = {587--601}, abstract = {

This article introduces a mesh-less, ray-based deep neural network method to solve the Helmholtz equation with high frequency. This method does not use an adaptive mesh refinement method, nor does it design a numerical scheme using some specially designed basis function to calculate the numerical solution, but it has the advantages of easy implementation and no mesh. We have carried out various numerical examples to prove the accuracy and efficiency of the proposed numerical method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20660.html} }
TY - JOUR T1 - A Mesh-Less, Ray-Based Deep Neural Network Method for the Helmholtz Equation with High Frequency AU - Yang , Andy L AU - Gu , Feng JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 587 EP - 601 PY - 2022 DA - 2022/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20660.html KW - Deep learning, plane wave, deep Neural Network, loss, high frequency, Helmholtz equation. AB -

This article introduces a mesh-less, ray-based deep neural network method to solve the Helmholtz equation with high frequency. This method does not use an adaptive mesh refinement method, nor does it design a numerical scheme using some specially designed basis function to calculate the numerical solution, but it has the advantages of easy implementation and no mesh. We have carried out various numerical examples to prove the accuracy and efficiency of the proposed numerical method.

Yang , Andy L and Gu , Feng. (2022). A Mesh-Less, Ray-Based Deep Neural Network Method for the Helmholtz Equation with High Frequency. International Journal of Numerical Analysis and Modeling. 19 (4). 587-601. doi:
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