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math.NA2022
Finding the Shape of Lacunae of the Wave Equation Using Artificial Neural Networks
Alina Chertock, Christopher Leonard, Semyon Tsynkov
We apply a fully connected neural network to determine the shape of the lacunae in the solutions of the wave equation. Lacunae are the regions of quietness behind the trailing fron…
math.NA2021
Non-iterative domain decomposition for the Helmholtz equation using the method of difference potentials
Evan North, Semyon Tsynkov, Eli Turkel
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 ea…