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 - <p style="text-align: justify;">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.</p>