Reflection error analysis for wave propagation problems solved by a heterogeneous asynchronous time integrator. (9th May 2018)

• Record Type: Journal Article
• Authors: Zafati, Eliass; Al Hout, Julie
• Is Part Of: International journal for numerical methods in engineering. Volume 115:Number 6(2018)
• Page Start: 651
• Page End: 694
• Publication Date: 2018-05-09
• Subjects: dispersion relations -- hybrid multi–time‐step methods -- numerical reflection coefficient -- wave propagation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5820
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: Within the framework of dynamic calculations, the hybrid multi–time‐step method proposed by Gravouil and Combescure (GC method) has proven to be an efficient algorithm that enables the use of arbitrary time steps and Newmark time schemes in each subdomain. Nonetheless, when dealing with wave propagation problems, the amount of reflections at the interfaces between subdomains strongly depends on the choice of the time integrators and the time steps used for the simulation study. In this paper, we deal with both one‐ and two‐dimensional wave propagation problems (only the anti‐plane shear wave problem is considered for the two‐dimensional case) with the aim of deriving an analytical estimation of the numerical reflection coefficient at the interface between two linear elastic subdomains having their own time integrators and time scales. The model is approximated using the lowest‐order finite elements, whereas the propagation process is described using harmonic waves. The study is carried out on the explicit/implicit and explicit/explicit integrations using arbitrary time‐step ratios. The numerical reflection coefficient is then analyzed with emphasis on the effect of the time‐step ratio and the direction of incidence.