Beyond the Courant-Friedrichs-Lewy condition: numerical methods for the wave problem using deep learning

DOI10.1016/j.jcp.2021.110493OpenAlexW3168635287MaRDI QIDQ2131007

Oded Ovadia, Adar Kahana, Shai Dekel, Eli Turkel

Publication date: 25 April 2022

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2021.110493

zbMATH Keywords

stabilitynumerical methodsspatio-temporalexplicit and implicit schemesphysically-informed

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical analysis (65-XX)

Related Items (4)

A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer ⋮ A convolutional dispersion relation preserving scheme for the acoustic wave equation ⋮ Multiscale extensions for enhancing coarse grid computations ⋮ Numerical wave propagation aided by deep learning

Uses Software

• mctoolbox
• Keras
• Adam

Cites Work

• Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Second-order large time step wave adding scheme for hyperbolic conservation laws
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Time-Dependent Problems and Difference Methods
• Finite Volume Methods for Hyperbolic Problems
• Partial Differential Equations
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
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