# Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

## Abstract

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Houston, TX (United States). Dept. of Mathematics

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1374334

- Report Number(s):
- LA-UR-17-22479

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 347; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Multi-material problems; Diffusion equations; Numerical methods for PDEs

### Citation Formats

```
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, and Shashkov, Mikhail.
```*Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces*. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.06.048.

```
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, & Shashkov, Mikhail.
```*Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces*. United States. doi:10.1016/j.jcp.2017.06.048.

```
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, and Shashkov, Mikhail. Sat .
"Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces". United States.
doi:10.1016/j.jcp.2017.06.048. https://www.osti.gov/servlets/purl/1374334.
```

```
@article{osti_1374334,
```

title = {Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces},

author = {Kikinzon, Evgeny and Kuznetsov, Yuri and Lipnikov, Konstatin and Shashkov, Mikhail},

abstractNote = {In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.},

doi = {10.1016/j.jcp.2017.06.048},

journal = {Journal of Computational Physics},

number = ,

volume = 347,

place = {United States},

year = {Sat Jul 08 00:00:00 EDT 2017},

month = {Sat Jul 08 00:00:00 EDT 2017}

}

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Cited by: 2 works

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