## Block preconditioning for fault/fracture mechanics saddle-point problems

## Abstract

The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. In conclusion, the proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.

- Authors:

- Univ. of Padova, Padua (Italy)
- Stanford Univ., CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1548375

- Report Number(s):
- LLNL-JRNL-746123

Journal ID: ISSN 0045-7825; 930434

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computer Methods in Applied Mechanics and Engineering

- Additional Journal Information:
- Journal Volume: 344; Journal Issue: C; Journal ID: ISSN 0045-7825

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Engineering - Mechanical and civil engineering, Geosciences, Mathematics and Computing; Fault mechanics; Lagrange multipliers; Preconditioners; Saddle point problems; Iterative methods

### Citation Formats

```
Franceschini, Andrea, Castelletto, Nicola, and Ferronato, Massimiliano. Block preconditioning for fault/fracture mechanics saddle-point problems. United States: N. p., 2018.
Web. doi:10.1016/j.cma.2018.09.039.
```

```
Franceschini, Andrea, Castelletto, Nicola, & Ferronato, Massimiliano. Block preconditioning for fault/fracture mechanics saddle-point problems. United States. doi:10.1016/j.cma.2018.09.039.
```

```
Franceschini, Andrea, Castelletto, Nicola, and Ferronato, Massimiliano. Thu .
"Block preconditioning for fault/fracture mechanics saddle-point problems". United States. doi:10.1016/j.cma.2018.09.039. https://www.osti.gov/servlets/purl/1548375.
```

```
@article{osti_1548375,
```

title = {Block preconditioning for fault/fracture mechanics saddle-point problems},

author = {Franceschini, Andrea and Castelletto, Nicola and Ferronato, Massimiliano},

abstractNote = {The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. In conclusion, the proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.},

doi = {10.1016/j.cma.2018.09.039},

journal = {Computer Methods in Applied Mechanics and Engineering},

number = C,

volume = 344,

place = {United States},

year = {2018},

month = {10}

}

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