A higher order approximate static condensation method for multimaterial diffusion problems
Abstract
The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or momentoffluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P_{1} (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.
 Authors:

 Univ. of Houston, TX (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Houston, TX (United States); Sechenov Univ., Moscow (Russian Federation)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC21); USDOE
 OSTI Identifier:
 1530798
 Alternate Identifier(s):
 OSTI ID: 1529697
 Report Number(s):
 LAUR1920919
Journal ID: ISSN 00219991
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 395; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics
Citation Formats
Zhiliakov, Aleksandr, Svyatsky, Daniil, Olshanskii, Maxim, Kikinzon, Evgeny, and Shashkov, Mikhail Jurievich. A higher order approximate static condensation method for multimaterial diffusion problems. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.06.044.
Zhiliakov, Aleksandr, Svyatsky, Daniil, Olshanskii, Maxim, Kikinzon, Evgeny, & Shashkov, Mikhail Jurievich. A higher order approximate static condensation method for multimaterial diffusion problems. United States. doi:10.1016/j.jcp.2019.06.044.
Zhiliakov, Aleksandr, Svyatsky, Daniil, Olshanskii, Maxim, Kikinzon, Evgeny, and Shashkov, Mikhail Jurievich. Thu .
"A higher order approximate static condensation method for multimaterial diffusion problems". United States. doi:10.1016/j.jcp.2019.06.044. https://www.osti.gov/servlets/purl/1530798.
@article{osti_1530798,
title = {A higher order approximate static condensation method for multimaterial diffusion problems},
author = {Zhiliakov, Aleksandr and Svyatsky, Daniil and Olshanskii, Maxim and Kikinzon, Evgeny and Shashkov, Mikhail Jurievich},
abstractNote = {The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or momentoffluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.},
doi = {10.1016/j.jcp.2019.06.044},
journal = {Journal of Computational Physics},
number = C,
volume = 395,
place = {United States},
year = {2019},
month = {6}
}