This paper proposes an adaptive space-time algorithm based on domain decomposition for the large-scale simulation of a recently developed thermodynamically consistent reservoir problem. In the approach, the bound constraints are represented by means of a minimum-type complementarity function to enforce the positivity of the reservoir model, and a space-time mixed finite element method is applied for the parallel-in-time monolithic discretization. In particular, we propose a time-adaptive strategy using the improved backward differencing formula of second order, to take full advantage of the high degree of space-time parallelism. Moreover, the complicated dynamics with higher nonlinearity of space-time discretization require some innovative nonlinear and linear solution strategies. Therefore, we present a class of modified semismooth Newton algorithms to enhance the convergence rate of nonlinear iterations. Multilevel space-time restricted additive Schwarz algorithms, whose sub domains cover both space and time variables, are also studied for domain decomposition-based preconditioning. Numerical experiments demonstrate the robustness and parallel scalability of the proposed adaptive space-time algorithm on a supercomputer with tens of thousands of processor cores.

Publication:

SIAM Journal on Scientific Computing Volume 46, Issue 3, Jun 2024

https://doi.org/10.1137/23M1578139

Author:

TIANPEI CHENG

School of Mathematics, Hunan University, Changsha, Hunan 410082, People's Republic of China

Email: chengtianpei@hnu.edu.cn

HAIJIAN YANG

School of Mathematics, Hunan University, Changsha, Hunan 410082,People's Republic of China

Email: haijianyang@hnu.edu.cn

JIZU HUANG

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

Email: huangjz@lsec.cc.ac.cn