Concurrent Multi-Domain Simulations in Structural Dynamics Using Multiple Grid and Multiple Time-Scale (MGMT) Method

Abstract

This paper describes a generic algorithm for concurrently solving multiple sub-domains that are selectively discretized in space and time. The mathematical background for this approach is largely based upon the fundamental principles of domain decomposition methods (DDM) and Lagrange multipliers. A proof of stability is provided using energy method and overall efficiency, accuracy and stability of multiple sub-domain coupling is evaluated using a series of numerical examples. Numerical stability is verified by ensuring energy balance at global as well as component sub-domain level. Discussed examples highlight the greatest advantage of MGMT method; which is high simulation speedups (at the cost of reasonably small errors).