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Work presented in this paper describes a general algorithm and its finiteelement implementation for performing concurrent multiple sub-domainsimulations in linear structural dynamics. Using this approach one can solveproblems in which the domain under analysis can be selectively discretizedspatially and temporally, hence allowing the user to obtain a desired level ofaccuracy in critical regions while improving computational efficiency globally.The mathematical background for this approach is largely based upon thefundamental principles of domain decomposition methods (DDM) and Lagrangemultipliers, used to obtain coupled equations of motion for distinct regions ofa continuous domain. These methods when combined together systematically yieldconstraint forces that not only ensure conservation of energy but also enforcecontinuity of velocities across sub-domain interfaces. Multiple grid (MG)connections between non-conforming sub-domains are modeled using mortarelements whereas coupled multiple time-scale (MT) equations are derived for theclassical Newmark integration algorithm (and its constituents). Fullydiscretized equations of motion for component sub-domains, augmented with aninterface condition are then solved using block elimination method and Croutfactorization.  A proof of stability is provided using Energy method and overall efficiency,accuracy and stability of multiple sub-domain coupling is evaluated using aseries of numerical examples. Primary observations are made for the evolutionand distribution of kinematic quantities and structural wave propagation acrossconnecting sub-domain. Numerical stability is verified by ensuring energybalance at global as well as component sub-domain level. Discussed exampleshighlight the greatest advantage of MGMT method; which is high simulationspeedups (at the cost of reasonably small errors).

Concurrent multi-domain simulations in linear structural dynamics using multiple grid multiple time-scale (MGMT) method