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

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

Year:    2022

Author:    Andy L Yang, Feng Gu

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2022-IJNAM-20660

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 587–601

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

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

Author Details

Andy L Yang

Feng Gu