A novel mesh-less, Ray-Based Deep Neural Network with Perfec
School Name
Dutch Fork High School
Grade Level
11th Grade
Presentation Topic
Computer Science
Presentation Type
Mentored
Abstract
In this paper, we develop a novel meshless, ray-based deep neural network algorithm for solving the high-frequency Helmholtz scattering problem in the unbounded domain. While our recent work [44] designed a deep neural network method for solving the Helmholtz equation over finite bounded domains, this paper deals with the more general and difficult case of unbounded regions. The proposed method includes two steps. First, by using the perfectly matched layer method, the original mathematical model in the unbounded domain is transformed into a new form in a finite bounded domain with simple homogeneous Dirichlet boundary conditions. Second, a deep neural network algorithm is designed for the new system, where the rays in various random directions are used as the basis of the numerical solution. Various numerical examples have been carried out to demonstrate the accuracy and efficiency of the proposed numerical method. The proposed method has the advantage of easy implementation and meshless while maintaining high accuracy. To the best of the author's knowledge, this is the first deep neural network method to solve the Helmholtz equation in the unbounded domain.
Recommended Citation
Yang, Andy, "A novel mesh-less, Ray-Based Deep Neural Network with Perfec" (2023). South Carolina Junior Academy of Science. 28.
https://scholarexchange.furman.edu/scjas/2023/all/28
Start Date
3-25-2023 11:00 PM
Presentation Format
Written Only
Group Project
No
A novel mesh-less, Ray-Based Deep Neural Network with Perfec
In this paper, we develop a novel meshless, ray-based deep neural network algorithm for solving the high-frequency Helmholtz scattering problem in the unbounded domain. While our recent work [44] designed a deep neural network method for solving the Helmholtz equation over finite bounded domains, this paper deals with the more general and difficult case of unbounded regions. The proposed method includes two steps. First, by using the perfectly matched layer method, the original mathematical model in the unbounded domain is transformed into a new form in a finite bounded domain with simple homogeneous Dirichlet boundary conditions. Second, a deep neural network algorithm is designed for the new system, where the rays in various random directions are used as the basis of the numerical solution. Various numerical examples have been carried out to demonstrate the accuracy and efficiency of the proposed numerical method. The proposed method has the advantage of easy implementation and meshless while maintaining high accuracy. To the best of the author's knowledge, this is the first deep neural network method to solve the Helmholtz equation in the unbounded domain.
