Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Estep, D., Ginting, V., Ropp, D., Shadid, J.N., Tavener, S.: An a posteriori-a priori analysis of multiscale operator splitting. SIAM J. Numer. Anal. 46, 1116–1146 (2008). 10.1137/07068237X. http://portal.acm.org/citation.cfm?id=1362718.1362720
Hooper, R., Hopkins, M., Pawlowski, R., Carnes, B., Moffat, H.: Final report on LDRD project: Coupling strategies for multi-physics applications. Tech. Rep. SAND2007-7146, Sandia National Laboratory (2007)
Keyes, D.E., McInnes, L.C., Woodward, C., Gropp, W., Myra, E., Pernice, M., Bell, J., Brown, J., Clo, A., Connors, J., Constantinescu, E., Estep, D., Evans, K., Farhat, C., Hakim, A., Hammond, G., Hansen, G., Hill, J., Isaac, T., Jiao, X., Jordan, K., Kaushik, D., Kaxiras, E., Koniges, A., Lee, K., Lott, A., Lu, Q., Magerlein, J., Maxwell, R., McCourt, M., Mehl, M., Pawlowski, R., Randles, A.P., Reynolds, D., Rivire, B., Rde, U., Scheibe, T., Shadid, J., Sheehan, B., Shephard, M., Siegel, A., Smith, B., Tang, X., Wilson, C., Wohlmuth, B.: Multiphysics simulations: Challenges and opportunities. Int. J. High Perform. C. 27(1), 4–83 (2013). 10.1177/1094342012468181
Knoll, D., Chacon, L., Margolin, L., Mousseau, V.: On balanced approximations for time integration of multiple time scale systems. J. Comput. Phys. 185, 583–611 (2003)
Romero, L.: On the accuracy of operator-splitting methods for problems with multiple time scales. Tech. Rep. SAND2002-1448, Sandia National Laboratory (2002)
Ropp, D., Shadid, J., Ober, C.: Studies of the accuracy of time integration methods for reaction-diffusion equations. J. Comput. Phys. 194, 544–574 (2004)
Ropp, D.L., Shadid, J.N.: Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems. J. Comput. Phys. 228, 3508–3516 (2009). 10.1016/j.jcp.2009.02.001. http://portal.acm.org/citation.cfm?id=1518324.1518454
Acknowledgments
The authors wish to thank Yekaterina Epshteyn for her guidance during the writing of this paper. This work was partially performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media New York
About this chapter
Cite this chapter
Wilson, A., Du, W., Li, G., Moosavi, A., Woodward, C.S. (2016). On Metrics for Computation of Strength of Coupling in Multiphysics Simulations. In: Brenner, S. (eds) Topics in Numerical Partial Differential Equations and Scientific Computing. The IMA Volumes in Mathematics and its Applications, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6399-7_6
Download citation
DOI: https://doi.org/10.1007/978-1-4939-6399-7_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-6398-0
Online ISBN: 978-1-4939-6399-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)