# A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

## Abstract

Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.

- Authors:

- Fujian Normal University, School of Mathematics and Computer Science & FJKLMAA (China)

- Publication Date:

- OSTI Identifier:
- 22769376

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; EIGENVALUES; MATRICES; NAVIER-STOKES EQUATIONS; POLYNOMIALS

### Citation Formats

```
Ke, Yi-Fen, and Ma, Chang-Feng.
```*A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0357-1.

```
Ke, Yi-Fen, & Ma, Chang-Feng.
```*A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations*. United States. doi:10.1007/S40314-016-0357-1.

```
Ke, Yi-Fen, and Ma, Chang-Feng. Thu .
"A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations". United States. doi:10.1007/S40314-016-0357-1.
```

```
@article{osti_22769376,
```

title = {A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations},

author = {Ke, Yi-Fen and Ma, Chang-Feng},

abstractNote = {Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.},

doi = {10.1007/S40314-016-0357-1},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}

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