Concurrent Multiple-Time-Scale Simulations With Improved Numerical Dissipation for Structural Dynamics

Abstract

Work presented in this paper describes the formulation for implementation of a concurrent multiple-time-scale integration method with improved numerical dissipation capabilities. This approach generalizes the previous Multiple Grid and Multiple Time-Scale (MGMT) Method [1] implemented for the Newmark family of algorithms. The framework is largely based upon the fundamental principles of Lagrange multipliers used to enforce workless nonholonomic constraints and Domain Decomposition Methods (DDM) to obtain coupled equations of motion for distinct regions of a continuous domain. These methods when combined together systematically yield constraint forces that not only ensure conservation of energy but also enforce continuity of velocities across the interfaces. Multiple grid connections between (non-conforming) sub-domains are handled using Mortar elements whereas coupled multiple-time-scale equations are derived for the Generalized-α Method [2]. We show that MGMT Method can be easily extended to incorporate the Generalized-α family of time integration algorithms, hence allowing selective discretization in space and time along with controlled numerical dissipation for distinct grids. We also show that interface energy across connecting sub-domains is identically zero, further assuring global energy balance and continuity of velocities across connecting sub-domains.