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Title: A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/18M120645X· OSTI ID:1548353
 [1];  [2]; ORCiD logo [1]
  1. Univ. of Padova (Italy)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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In this work, we introduce a relaxed physical factorization (RPF) preconditioner for the efficient iterative solution of the linearized algebraic system arising from the mixed finite element discretization of coupled poromechanics equations. The preconditioner is obtained by using a proper factorization of the $$3\times3$$ block matrix and setting a relaxation parameter $$\alpha$$. The preconditioner is inspired by the relaxed dimensional factorization introduced by Benzi et al. [J. Comput. Phys., 230 (2011), pp. 6185--6202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129--145]. A stable algorithm is advanced to compute the optimal value of $$\alpha$$, along with a lower bound to control the possible ill-conditioning of the $$\alpha$$ dependent inner blocks. Lastly, numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.

Research Organization:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1548353
Report Number(s):
LLNL-JRNL-756041; 943354
Journal Information:
SIAM Journal on Scientific Computing, Vol. 41, Issue 4; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Figures / Tables (19)

Algorithm 3.1(p. 12)figure Algorithm 3.1
Fig. 1(p. 12)figure Fig. 1
Algorithm 3.2(p. 13)figure Algorithm 3.2
Algorithm 3.3(p. 13)figure Algorithm 3.3
Fig. 2(p. 14)figure Fig. 2
Table 1(p. 14)table Table 1
Fig. 3(p. 15)figure Fig. 3
Table 3(p. 16)table Table 3
Table 4(p. 16)table Table 4
Table 5(p. 16)table Table 5
Fig. 4(p. 17)figure Fig. 4
Fig. 5(p. 17)figure Fig. 5
Fig. 6(p. 17)figure Fig. 6
Fig. 7(p. 18)figure Fig. 7
Table 6(p. 18)table Table 6
Fig. 8(p. 19)figure Fig. 8
Fig. 9(p. 19)figure Fig. 9
Table 7(p. 20)table Table 7
Table 8(p. 20)table Table 8

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Related Subjects

97 MATHEMATICS AND COMPUTING
preconditioning
Krylov subspace methods
mixed finite elements
poromechanics