Showing papers by "Eli Turkel published in 2021"
4 citations
TL;DR: In this article, a spatio-temporal neural network architecture is proposed to solve the one dimensional acoustic wave problem, which remains stable for larger time steps and produces better accuracy than the reference implicit method.
3 citations
2 citations
TL;DR: In this article, a method based on the Method of Difference Potentials (MDP) was proposed for numerical solution of multiple scattering problems in 3D space dimensions, where the propagation of waves was assumed time-harmonic and governed by the Helmholtz equation.
2 citations
DOI•
01 Aug 2021
TL;DR: In this article, an efficient high order accurate boundary algorithm for the numerical solution of unsteady exterior initial boundary problems for the three-dimensional wave equation is presented. The algorithm relies on the method of difference potentials combined with the Huygens' principle.
Abstract: We present an efficient high order accurate boundary algorithm for the numerical solution of unsteady exterior initial boundary problems for the three-dimensional wave equation. The algorithm relies on the method of difference potentials combined with the Huygens' principle.
Posted Content•
TL;DR: In this paper, the authors use the method of difference potential (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation, where the unknowns for the Calderon's equation are the Dirichlet and Neumann data.
Abstract: We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on its boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a straightforward direct solver. We provide numerical examples demonstrating that our method is insensitive to interior cross-points and mixed boundary conditions, as well as large jumps in the wavenumber for transmission problems, which are known to be problematic for many other Domain Decomposition Methods.