Approximate static condensation algorithm for solving multimaterial diffusion problems on meshes nonaligned with material interfaces
In this study, we describe a new algorithm for solving multimaterial 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 socalled multimaterial 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 multimaterial diffusion problems on such meshes and compare its performance with known homogenization methods.
 Authors:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Houston, TX (United States). Dept. of Mathematics
 Publication Date:
 Report Number(s):
 LAUR1722479
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 347; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 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) (NA10); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Multimaterial problems; Diffusion equations; Numerical methods for PDEs
 OSTI Identifier:
 1374334
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, and Shashkov, Mikhail. Approximate static condensation algorithm for solving multimaterial diffusion problems on meshes nonaligned with material interfaces. United States: N. p.,
Web. doi:10.1016/j.jcp.2017.06.048.
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, & Shashkov, Mikhail. Approximate static condensation algorithm for solving multimaterial diffusion problems on meshes nonaligned with material interfaces. United States. doi:10.1016/j.jcp.2017.06.048.
Kikinzon, Evgeny, Kuznetsov, Yuri, Lipnikov, Konstatin, and Shashkov, Mikhail. 2017.
"Approximate static condensation algorithm for solving multimaterial diffusion problems on meshes nonaligned 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 multimaterial diffusion problems on meshes nonaligned 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 multimaterial 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 socalled multimaterial 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 multimaterial 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 = {2017},
month = {7}
}