Abstract
We propose the asynchronous multi-domain numerical time integration algorithms for initial boundary-value problems of parabolic type. Parabolic PDE’s are commonly solved by discretizing spatially using finite elements and then integrating over time using discrete solvers. For efficient parallel computing of large problems, we present the dual domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. As is well-known, the stability and accuracy requirements may necessitate different time steps for different domains, depending on material properties, element size, coupling scheme, etc. We propose a multi-time-step coupling method which enables us to use different methods and different time steps on different parts of a computational domain and provides a powerful approach to solving large scale problems very efficiently and accurately.
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