On metrics for computation of strength of coupling in multiphysics simulation

Abstract

<p>Many multiphysics applications arise in the world of mathematical modeling and simulation. Much of the time in scientific computation these multiphysics applications are solved by decoupling the physics, giving no heed to how this affects the numerical results. However, a fully coupled approach is often not computationally cost effective. Consequently, having a metric for determining the strength of coupling could give insight into whether a simulation should be decoupled in the computation. If the fully coupled approach is not available, then a metric that measures the strength of coupling dynamically in time could help determine when smaller time steps are required to better incorporate coupling into the split solution. In this paper, we report on an Institute for Mathematics and Its Applications student project where we explored metrics for dynamically measuring the strength of coupling between two physical components in a model multiphysics simulation. Four metrics were considered: two based on measured components of the Jacobian matrix, one on error estimates, and the last on timescales of the system components. The metrics are all developed based on the previous work found in the literature and tested on a diffusion–reaction problem.<br></p>