On multi-time-step monolithic coupling algorithms for elastodynamics

TL;DR

This paper introduces a novel multi-time-step monolithic coupling method for elastodynamics that allows different time steps and schemes across subdomains, ensuring stability and energy conservation.

Contribution

The paper develops a new coupling approach using dual Schur form and Newmark schemes, enabling flexible multi-time-step simulations with stability and energy preservation analysis.

Findings

Method is stable under certain conditions.

Can handle multiple subdomains with different time steps.

Demonstrated accuracy through numerical examples.

Abstract

We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and enforce the continuity of velocities at system time levels. The resulting equations will be in the form of differential-algebraic equations. To crystallize the ideas we shall employ Newmark family of time-stepping schemes. The proposed method can handle multiple subdomains, and allows different time-steps as well as different time stepping schemes from the Newmark family in different subdomains. We shall use the energy method to assess the numerical stability, and quantify the influence of perturbations under the proposed coupling method. We also discuss the conditions under which the proposed method will be energy preserving, and the conditions under which the method will be energy conserving. Several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method. We shall also compare the proposed multi-time-step coupling method with some other similar methods available in the literature.