| Issue |
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
|
|
|---|---|---|
| Page(s) | 243 - 269 | |
| DOI | https://doi.org/10.1051/m2an/2022070 | |
| Published online | 03 February 2023 | |
Convergence results of a heterogeneous asynchronous newmark time integrators
EDF R&D ERMES, 7 boulevard Gaspard Monge, 91120 Palaiseau, France
* Corresponding author: eliass.zafati@edf.fr
Received:
7
December
2021
Accepted:
1
September
2022
This paper is concerned with the convergence analysis of the PH heterogeneous asynchronous time integrators algorithm, proposed by Prakash and Hjelmstad [Int. J. Numer. Methods Eng. 61 (2004) 2183–2204], and devoted to transient dynamic problems for structural analysis. According to PH method, the time discretization is performed using the well-known Newmark schemes, where the time step ratio, i.e., the ratio of the macro time step to the micro time step, of two subdomains separated by an interface is a positive integer. The analysis is restricted to linear problems with two subdomains for simplification. We show that L∞-uniform convergence of the approximated solutions is achieved taking into account damping terms and suitable regularities on load terms. We shall also give some error estimates of the method.
Mathematics Subject Classification: 74H15 / 74H25 / 65L20 / 65L05
Key words: Heterogeneous asynchronous time integrators / transient dynamic / stability and convergence analysis / Newmark time schemes / ordinary differential equations
© The authors. Published by EDP Sciences, SMAI 2023
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