Some Optimally Convergent Algorithms for Decoupling the Computation of Biot's Model

Cai, Mingchao1; Gu, Huipeng2; Li, Jingzhi3,4,5; Mu, Mo6

2023-11-01

10.1007/s10915-023-02365-5

JOURNAL OF SCIENTIFIC COMPUTING   Impact Factor & Quartile

0885-7474

1573-7691

We study numerical algorithms for solving Biot's model. Based on a three-field reformulation, we present some algorithms that are inspired by the work of Chaabane et al. (Comput Math Appl 75(7):2328-2337) and Lee (Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity arXiv:1901.06078, 2019) for decoupling the computation of Biot's model. A new theoretical framework is developed to analyze the algorithms. Considering a uniform temporal discretization, these algorithms solve the coupled model on the first time level. On the remaining time levels, one algorithm solves a reaction-diffusion subproblem first and then solves a generalized Stokes subproblem. Another algorithm reverses the order of solving the two subproblems. Our algorithms manage to decouple the numerical computation of the coupled system while retaining the convergence properties of the original coupled algorithm. Theoretical analysis is conducted to show that these algorithms are unconditionally stable and optimally convergent. Numerical experiments are also carried out to validate the theoretical analysis and demonstrate the advantages of the proposed algorithms.

Biot's model Decoupled algorithms Finite element method Unconditionally stable

SCI

English

Others

The work of M. Cai is partially supported by the NIH BUILD Grant through UL1GM118973, NIH-RCMI Grant through U54MD013376, XSEDE HPC allocation resource TG-MCH200022, the Army Research Office award W911NF2310004, and the National Science Foundation awards ([UL1GM118973] ; NIH BUILD Grant[U54MD013376] ; NIH-RCMI[TG-MCH200022] ; XSEDE HPC allocation resource[W911NF2310004] ; Army Research Office["1700328","1831950"] ; National Science Foundation[11971221] ; NSF of China[2021ZDZX1001] ; Guangdong NSF Major Fund["RCJC20200714114556020","JCYJ20200109115422828","JCYJ20190809150413261"] ; SUSTech International Center for Mathematics[HKUST16301218]

Mathematics

Mathematics, Applied

WOS:001079422500002

SPRINGER/PLENUM PUBLISHERS

MATHEMATICS

Web of Science

1.Morgan State Univ, Dept Math, 1700 E Cold Spring Lane, Baltimore, MD 21251 USA
2.Southern Univ Sci & Technol, Dept Math, 1088 Xueyuan Rd, Shenzhen 518055, Guangdong, Peoples R China
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
4.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Guangdong, Peoples R China
5.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China
6.Hong Kong Univ Sci & Technol, Dept Math, Clear Water Bay, Hong Kong, Peoples R China

Cai, Mingchao,Gu, Huipeng,Li, Jingzhi,et al. Some Optimally Convergent Algorithms for Decoupling the Computation of Biot's Model[J]. JOURNAL OF SCIENTIFIC COMPUTING,2023,97(2).

Cai, Mingchao,Gu, Huipeng,Li, Jingzhi,&Mu, Mo.(2023).Some Optimally Convergent Algorithms for Decoupling the Computation of Biot's Model.JOURNAL OF SCIENTIFIC COMPUTING,97(2).

Cai, Mingchao,et al."Some Optimally Convergent Algorithms for Decoupling the Computation of Biot's Model".JOURNAL OF SCIENTIFIC COMPUTING 97.2(2023).