Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media

DOI10.1016/j.jcp.2022.111380OpenAlexW3176862315WikidataQ114950922 ScholiaQ114950922MaRDI QIDQ2157085

Shubin Fu, Eric T. Chung, Ka Chun Cheung, Tak Shing Au Yeung, Jianliang Qian

Publication date: 21 July 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.10523

zbMATH Keywords

Helmholtz equationray tracingdiscontinuous Galerkindeep learning

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65Nxx) General topics in optics and electromagnetic theory (78Axx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

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• A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation
• Discovery of point sources in the Helmholtz equation posed in unknown domains with obstacles
• Asymptotic solutions of oscillatory initial value problems
• A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media
• Numerical microlocal analysis of harmonic wavefields
• An edge multiscale interior penalty discontinuous Galerkin method for heterogeneous Helmholtz problems with large varying wavenumber
• Deep global model reduction learning in porous media flow simulation
• Reduced-order deep learning for flow dynamics. The interplay between deep learning and model reduction
• Deep multiscale model learning
• A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber
• Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
• Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
• A deep learning based nonlinear upscaling method for transport equations
• Numerical microlocal analysis of 2-D noisy harmonic plane and circular waves
• A Survey of Trefftz Methods for the Helmholtz Equation
• Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise
• Plane wave discontinuous Galerkin methods: Analysis of theh-version
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• Computational high frequency wave propagation
• Numerical Microlocal Analysis by Fast Gaussian Wave Packet Transforms and Application to High-Frequency Helmholtz Problems
• The high‐frequency asymptotic field of a point source in an inhomogeneous medium
• Discontinuous Galerkin Finite Element Method for the Wave Equation
• A generalized plane-wave numerical method for smooth nonconstant coefficients
• The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium
• A hybrid numerical asymptotic method for scattering problems