A Novel Deep Neural Network Algorithm for the Helmholtz Scattering Problem In the Unbounded Domain

Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Cites Work

Absorbing PML boundary layers for wave-like equations
The numerical solution of linear ordinary differential equations by feedforward neural networks
A perfectly matched layer for the absorption of electromagnetic waves
High-order local artificial boundary conditions for problems in unbounded domains
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
Reflectionless sponge layers for the numerical solution of Maxwell's equations in cylindrical and spherical coordinates
DGM: a deep learning algorithm for solving partial differential equations
A mesh-free method for interface problems using the deep learning approach
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
MgNet: a unified framework of multigrid and convolutional neural network
Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
Relu Deep Neural Networks and Linear Finite Elements
A Finite Element Method for Solving Helmholtz Type Equations in Waveguides and Other Unbounded Domains
Calculation of eigenvalues of the Helmholtz equation by an integral equation
Absorbing Boundary Conditions for the Numerical Simulation of Waves
The Perfectly Matched Layer in Curvilinear Coordinates
Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
Complex space approach to perfectly matched layers: a review and some new developments
Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders
Reflectionless Sponge Layers as Absorbing Boundary Conditions for the Numerical Solution of Maxwell Equations in Rectangular, Cylindrical, and Spherical Coordinates
Solving high-dimensional partial differential equations using deep learning
A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
Error bounds for approximations with deep ReLU neural networks in Ws,p norms
DeepXDE: A Deep Learning Library for Solving Differential Equations
Spectral Approximation of the Helmholtz Equation with High Wave Numbers
An Adaptive Perfectly Matched Layer Technique for Time-harmonic Scattering Problems
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item