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In this paper we present a Fourier feature based deep domain decompositionmethod (F-D3M) for partial differential equations (PDEs). Currently, deepneural network based methods are actively developed for solving PDEs, but theirefficiency can degenerate for problems with high frequency modes. In this newF-D3M strategy, overlapping domain decomposition is conducted for the spatialdomain, such that high frequency modes can be reduced to relatively lowfrequency ones. In each local subdomain, multi Fourier feature networks(MFFNets) are constructed, where efficient boundary and interface treatmentsare applied for the corresponding loss functions. We present a generalmathematical framework of F-D3M, validate its accuracy and demonstrate itsefficiency with numerical experiments.

A deep domain decomposition method based on Fourier features