# A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

## Abstract

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK couplingmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22622251

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CORRELATIONS; COUPLING; DECOMPOSITION; DIFFUSION; ENFORCEMENT; ERRORS; FLUCTUATIONS; HYDROGEN; INTERFACES; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; RANDOMNESS; STOCHASTIC PROCESSES

### Citation Formats

```
Taverniers, Søren, and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu.
```*A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2016.10.052.

```
Taverniers, Søren, & Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu.
```*A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems*. United States. doi:10.1016/J.JCP.2016.10.052.

```
Taverniers, Søren, and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu. Wed .
"A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems". United States.
doi:10.1016/J.JCP.2016.10.052.
```

```
@article{osti_22622251,
```

title = {A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems},

author = {Taverniers, Søren and Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu},

abstractNote = {Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.},

doi = {10.1016/J.JCP.2016.10.052},

journal = {Journal of Computational Physics},

number = ,

volume = 330,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}