Hybrid asynchronous isogeometric Perfectly Matched Layer for transient elastodynamics

Abstract

This paper presents an isogeometric formulation (IGA) of the Perfectly Matched Layer (PML) for two-dimensional time-domain elastodynamics in unbounded media. The displacement-based unsplit-field PML formulation is first discretized in space using B-spline basis functions of increasing polynomial order p, from 2 to 10, able to deal with the strong solution gradients in the thickness of the PML thanks to the high order continuity provided by the B-spline basis functions. In order to keep the high accuracy of IGA, implicit time integration is chosen in the PML subdomains, whereas the physical domain is integrated with an explicit time integration scheme. The domain decomposition is based on a dual formulation and Heterogeneous Asynchronous Time Integrator (HATI) approach. The coupling between non-conforming IGA-patches for the PML subdomains and the physical domain is carried out using a standard mortar method. It enables us to select for the IGA-PML subdomains both the appropriate space discretization and the appropriate time discretization with an implicit time integrator and a larger time step size. The hybrid multi-time step IGA-PML performance in terms of computation time, is assessed for two-dimensional elastodynamic problems in single and multi-layer media depending on the chosen discretization parameters in space and time.