Numerical Analysis of Asynchronous Time Scheme for Explicit-Implicit Problems

Articles in Press

Document Type : Research Paper

Authors
Radim Dvořák 1 , 2
Radek Kolman 1
1 Institute of Thermomechanics of the CAS, v. v. i., Dolejškova 1402/5, 182 00 Praha 8, Czech Republic
2 CTU in Prague Faculty of Transportation Sciences, Department of Mechanics and Materials, Na Florenci 25, 110 00 Praha 1, Czech Republic
10.22055/jacm.2026.49215.5812
Abstract
We present an asynchronous time integration framework for partitioned elastodynamic problems, where each subdomain advances with its own local time step. The strong formulation of partitioned elastodynamics is introduced, followed by a weak formulation that couples subdomains via localized Lagrange multipliers acting on accelerations and using linear shape functions, effectively resulting in a generalized mortar approach. After recapitulating the standard direct solution of the equations of motion and our asynchronous scheme for explicit integration, we investigate the dynamics of a small body attached to a larger structure. Three variants of subdomain integration are examined: explicit-explicit, implicit-implicit, and mixed explicit-implicit coupling. Their influence on solution accuracy, energy conservation, and drifting between subdomains is analyzed, with the results validated through comparisons with LS-DYNA simulations. The study highlights that accuracy is well preserved in the explicit-explicit case, while the other variants exhibit measurable drifting that is carefully quantified. Overall, we demonstrate that the proposed asynchronous integration scheme can provide substantial computational speedups in heterogeneous domains, highlighting its potential for efficient simulation of systems with localized fast dynamics.
Keywords
Direct time integration
Finite element method
Asynchronous scheme
Explicit-implicit
Wave propagation
Subjects

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Available Online from 18 May 2026