Asynchronous time integrator applicable to explicit and implicit problems with explicitly integrated isolated interfaces
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An asynchronous direct time integration scheme for domain-decomposed finite element models is presented. The algorithm is described in a linear-elastic stress wave propagation case. Individual subdomains of the FE model are integrated with different time steps without any requirement for their relation such as integer ratio etc. Different time integration methods can be applied for different subdomains (method of central differences, newmark methods, etc.). Explicit-explicit problem is demonstrated and an implicit-explicit case is discussed. For domain decomposition, localized Lagrange multipliers are used and the subdomains are connected by the condition of the continuity of the acceleration field at the interface. This method allows for keeping exclusively Lagrange multipliers for each domain separately. In addition, the a posteriori technique is applied to satisfy the continuity of the displacement and velocity fields at the interface for the cost of small dissipation of the energy. The functionality of the asynchronous integrator is verified by solving selected problems and comparing them with analytical solutions.
