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Blended force-based atomistic-continuum coupling method for the model adaptivity of a Frenkel-Kontorova model. (Chinese. English summary) Zbl 1449.65236

Summary: We use the blended force-based atomistic-continuum coupling (BQCF) method to solve a Frenkel-Kontorova model and consider its model adaptivity problem. We give a posteriori error estimator based on the residual. Then, by using such estimator, we construct the model adaptive algorithm, which adaptively determines the domain decomposition of an atomistic system, characterizes the partition of the atomistic domain and the continuous domain. The numerical experiments illustrate the validity of our estimator and algorithm.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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