An adaptive implicit-explicit time-marching technique for elastodynamic analysis

Resumo

In this work, we discuss an implicit-explicit time-marching procedure with adaptive time integration parameters for the analysis of hyperbolic models. This methodology utilizes two locally evaluated time integration parameters, allowing for their different spatial and temporal distributions. The first parameter defines implicit/explicit subdomains within the model, ensuring stability and reducing errors related to period elongation.
The second parameter controls the dissipative properties of the methodology, effectively eliminating the influence of spurious high-frequency modes and reducing amplitude decay errors. Moreover, this implicit-explicit approach reduces computational effort by obtaining reduced systems of equations and serves as an efficient non-iterative single-step procedure. The key features of this novel methodology can be summarized as follows: it is simple, locally defined, guarantees stability, provides enhanced accuracy, enables advanced controllable algorithmic dissipation in higher modes, establishes a connection between temporal and spatial discretizations, operates as a single-solve framework based on reduced systems of equations, is self-starting, and fully automated. The paper concludes with the presentation and comparison of numerical results with those obtained using standard techniques, illustrating the remarkable effectiveness of the discussed approach.