An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

By Nan Jiang, M. Schneier. 2017

190 citations recorded by the source corpus.

Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller subphysics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each subphysics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a37fa8cff506ee353a924858808747a31d36e8c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Huan Fu
2. Dacheng Tao
3. S. Maybank
4. Lin Gao
5. Chunhui Yuan
6. Haitao Yang
7. Huan Liu
8. Rongfei Jia

In Statistical and Nonlinear Physics

1. Huan Liu
2. Lei Tang
3. Bryan Perozzi
4. Dacheng Tao
5. S. Maybank
6. Lin Gao
7. Binqiang Zhao
8. Huan Fu

In Statistics and Probability

1. Dacheng Tao
2. S. Maybank
3. Lin Gao
4. Binqiang Zhao
5. Huan Fu
6. Chunhui Yuan
7. Haitao Yang
8. Mingming Gong

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• Scalable learning of collective behavior based on sparse social dimensions (2009, background): “More complicated data structures such as kd-tree [1, 8] can be exploited to accelerate the process.”
• 3D-FUTURE: 3D Furniture Shape with TextURE (2020, methodology): “For theme color and real-world size, we first adopt k-Means Clustering (Kanungo et al., 2002) to discretize real values and then transform them into one-hot vectors.”