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physics.comp-ph2024★ 9 cited
From Mesh to Neural Nets: A Multi-Method Evaluation of Physics-Informed Neural Networks and Galerkin Finite Element Method for Solving Nonlinear Convection-Reaction-Diffusion Equations
Fardous Hasan, Hazrat Ali, Hasan Asyari Arief
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynam…
physics.comp-ph2020★ 13 cited
Iterative solution of the Lippmann-Schwinger equation in strongly scattering acoustic media by randomized construction of preconditioners
Kjersti Solberg Eikrem, Geir Nævdal, Morten Jakobsen
In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equa…