Enhancing Efficiency in Multiscale Simulation: Comparing a Lagrange Multiplier Based Approach and a Weak Staggered Coupling With Optional SPML Interface for Wave Propagation

ABSTRACT

The representation of material failure due to wave propagation is essential for the numerical analysis of engineering structures under high dynamic loading. Explicit time integration schemes are well established for this kind of application. In order to realistically model the failure of certain material classes, it is necessary to resolve lower scale features accurately. Concurrent multiscale approaches are therefore well suited to this task. However, they are often complex and computationally demanding. The introduction of interfaces between disparately meshed domains may additionally lead to emerging reflections for waves that contain high frequencies, which the coarse domain cannot resolve. In this article, we compare accuracy, computational efficiency, versatility, and effort for two finite element implementations of concurrent two‐scale schemes. Both offer the possibility of adding a Selected Perfectly Matched Layer (SPML) to dampen incompatible frequencies. One approach is the widely used conventional Lagrange multiplier (LM) approach; the second is a weak staggered (WS) coupling, which was designed to maintain direct solution schemes' efficiency with explicit time integration and diagonal mass matrices. It turns out that, for typical discretizations, the WS coupling achieves an accuracy comparable to the LM coupling but requires fewer computational operations and, relevant for parallel computer architectures, significantly less communication efforts. Adaptive changes of interface topology, for example, due to explicitly resolved cracks crossing the interface, can easily be represented in the WS approach, making it a suitable candidate for the application in scenarios where gross damage is expected.