Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers

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In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method.

• As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains.
• The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step.
• The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process.