# A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

## Abstract

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

- Authors:

- Idaho National Lab. (INL), Idaho Falls, ID (United States). Modeling and Simulation
- Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1375242

- Alternate Identifier(s):
- OSTI ID: 1413567

- Report Number(s):
- INL/JOU-16-39081

Journal ID: ISSN 0021-9991; PII: S0021999117302383

- Grant/Contract Number:
- AC07-05ID14517

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 340; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; isogeometric coarse mesh; Newton-Krylov-Schwarz; Nonlinear fluid-structure interaction; parallel software development; unstructured mesh

### Citation Formats

```
Kong, Fande, and Cai, Xiao-Chuan. A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.03.043.
```

```
Kong, Fande, & Cai, Xiao-Chuan. A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. United States. doi:10.1016/j.jcp.2017.03.043.
```

```
Kong, Fande, and Cai, Xiao-Chuan. Fri .
"A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D". United States. doi:10.1016/j.jcp.2017.03.043. https://www.osti.gov/servlets/purl/1375242.
```

```
@article{osti_1375242,
```

title = {A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D},

author = {Kong, Fande and Cai, Xiao-Chuan},

abstractNote = {Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.},

doi = {10.1016/j.jcp.2017.03.043},

journal = {Journal of Computational Physics},

number = C,

volume = 340,

place = {United States},

year = {2017},

month = {3}

}

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Works referencing / citing this record:

##
Simulation of unsteady blood flows in a patient‐specific compliant pulmonary artery with a highly parallel monolithically coupled fluid‐structure interaction algorithm

journal, May 2019

- Kong, Fande; Kheyfets, Vitaly; Finol, Ender
- International Journal for Numerical Methods in Biomedical Engineering, Vol. 35, Issue 7

##
Numerical aerodynamic simulation of transient flows around car based on parallel Newton–Krylov–Schwarz algorithm

journal, July 2019

- Yan, Zhengzheng; Chen, Rongliang; Zhao, Yubo
- Applicable Analysis