The ever-increasing demand for higher and higher fidelity simulations spurs the minimization of computational costs of each task comprising an analysis, while also ensuring its desired accuracy level. A good and established example is exploiting the inherently different spatial scales the involved physical phenomena act on [1]. However, coupled multiphysics problems often evolve over vastly different time scales as well, but approaches taking advantage of this fact are much less mature. The topic of this research is exploring heterogeneous time integration schemes within the context fluid-structure interaction, chemical-mechanical degradation, and other coupled problems.
Waveform relaxation is a fundamentally different method of computing approximate solutions to ODEs than the de facto standard schemes based on finite differences [2,3]. Its most appealing feature with respect to multiscale time integration is the ability to arbitrarily partition the system such that different time discretization can be applied to each partition. On the other hand, waveform relaxation involves iteratively solving the entire system on the full length of the time domain, possibly undermining any previous performance gain.
[1] E.Weinan, B.Engquist, X.Li, W.Ren, and E.Vanden-Eijnden. Heterogeneous multiscale methods: A review. Communications in Computational Physics}, 2(3):367–450, 2007.
[2] M.Pasetto, H.Waisman, and J.S. Chen. A waveform relaxation newmark method for structural dynamics problems. Computational Mechanics}, 63:1223–1242, 2019.
[3] J.White, F.Odeh, A.S. Vincentelli, and A.Ruehli. Waveform relaxation: Theory and practice. Transactions of the Society for Computer Simulation}, 2.
The project is part of the DFG programme GRK 2075 - Modelling the constitutional evolution of building materials and structures with respect to aging.