Multirate partially explicit scheme for multiscale flow problems

Abstract: In this talk, we will introduce a multirate partially explicit   splitting scheme for parabolic equation with heterogeneous diffusion   parameter. We first design multiscale subspaces to handle flow with different   speeds. Then a multirate time stepping is introduced for the partially   explicit splitting system. With a suitable construction of multiscale space,   we can achieve a stable temporal splitting scheme where the time step size is   independent of the contrast in the multiscale parameter. An adaptive local   temporal refinement algorithm is then proposed to achieve efficient   simulation with desired accuracy.

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