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

Oded Ovadia, Adar Kahana, Eli Turkel, Shai Dekel

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate a numerical method for approximating the solution of the one dimensional acoustic wave problem, when violating the numerical stability condition. We use deep learning to create an explicit non-linear scheme that remains stable for larger time steps and produces better accuracy than the reference implicit method. The proposed spatio-temporal neural-network architecture is additionally enhanced during training with a physically-informed term, adapting it to the physical problem it is approximating and thus more accurate.

Original languageEnglish
Article number110493
JournalJournal of Computational Physics
Volume442
DOIs
StatePublished - 1 Oct 2021

Keywords

  • Explicit and implicit schemes
  • Numerical methods
  • Physically-informed
  • Spatio-temporal
  • Stability

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