Abstract
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically consistent coarse-grain models. However, its high computational cost is a known barrier for fast and accurate applications. Despite its good mathematical properties, there are very few works on the fast and efficient implementations of quasi-equilibrium approximations. In this paper, we give efficient implementations of quasi-equilibrium approximations for antipodally symmetric problems on unit circle and unit sphere using global polynomial and piecewise polynomial approximations. Comparing to the existing methods using linear or cubic interpolations, our approach achieves high accuracy (double precision) with much less storage cost. The methods proposed in this paper can be directly extended to handle other moment closure approximation problems.
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Data Availability Statement
All data and code generated or used during the study are available from the corresponding author by request.
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Acknowledgements
The authors would like to thank Prof. Chuanju Xu, Li-Lian Wang and Dr. Jie Xu for helpful discussions. This work is partially supported by NNSFC Grant 11771439, 91852116 and China Science Challenge Project No. TZ2018001.
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Jiang, S., Yu, H. Efficient Spectral Methods for Quasi-Equilibrium Closure Approximations of Symmetric Problems on Unit Circle and Sphere. J Sci Comput 89, 43 (2021). https://doi.org/10.1007/s10915-021-01646-1
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DOI: https://doi.org/10.1007/s10915-021-01646-1
Keywords
- Quasi-equilibrium approximation
- Moment closure
- Bingham distribution
- Spectral methods
- Piecewise polynomial approximation