External coupling software based on macro- and micro-time scales for explicit/implicit multi-time-step co-computations in structural dynamics

Hybrid Asynchronous Perfectly Matched Layer for seismic wave propagation in unbounded domains

“…However, discrepancies can be observed for the largest time step ratio, indicating numerical errors coming from the following two points: first, the increase of the time step size Δt 2 in PML leading to increased spurious reflections at the interface between the soil and the PML, and second, the classical drawback of the GC coupling algorithm which is known to be dissipative at the interface as soon as different time steps are considered. This energy dissipative feature has been demonstrated on the basis of the socalled energy method in [2] and has been highlighted in numerical examples (Brun et al [33,30,34]). …”

A computational framework for fast‐time hybrid simulation based on partitioned time integration and state‐space modeling

“…In order to facilitate the assembly of nonlinear NSs simulated with well‐known differential models, for example, Ismail et al or Mostaghel hysteretic springs, the HS framework presented in this section relies on a newly conceived parallel partitioned algorithm tailored to state‐space systems. More precisely, the monolithic generalized‐ α (MG‐ α ) time stepping scheme proposed by Brüls and Arnold is used as basic solver for the partitioned generalized‐ α (PG‐ α ) method, which adopts the coupling scheme of the modified PH method conceived by Brun and co‐workers . Both algorithms solve the system of equations of motion recasted in state‐space form that, for a generic nonlinear mechanical system, reads where …”

“…Before introducing Step 12, we shortly derive the Steklov–Poincaré operator, which is used to calculated link solutions based on free solutions already computed on both PS and NS. In order to do this, the PG‐ α method adopts the coupling strategy of the modified PH method, which imposes kinematic compatibility at the end of the coarse time step ∆t N . In detail, link solutions are expressed as linear functions of interface Lagrange multipliers, which are obtained by linearizing decoupled subsystems equations at zero states.…”

“…More precisely, the monolithic generalized-α (MG-α) time stepping scheme proposed by Brüls and Arnold 17 is used as basic solver for the partitioned generalized-α (PG-α) method, which adopts the coupling scheme of the modified PH method conceived by Brun and co-workers. 18 Both algorithms solve the system of equations of motion recasted in state-space form that, for a generic nonlinear mechanical system, reads…”

Multiple length/time-scale simulation of localized damage in composite structures using a Mesh Superposition Technique

“…Recently, Brun et al [48] analysed a flat composite stiffened panel subjected to localised loads. In Brun et al's work [48], damage was not modelled and the time-scale transition was not combined with an effective coupling between different length scales.…”