Multirate Integration Schemes for Diffusive Problems with Interfacial Coupling
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We discuss problems coupled across an interface through boundary conditions for a diffusion operator, which can take various forms for different applications. The focus is coupling in the multirate setting of different time step sizes in each subdomain. Numerical coupling is based on a recently-developed technique that treats the subdomain integrators as piecewise polynomial in time using the mathematics of discontinuous-Galerkin-in-time methods. One product is multirate integration that can preserve stability and conservation properties with high-order accuracy. Various example methods will be illustrated, including multistep and multistage integrators.
