CaltechAUTHORS
  A Caltech Library Service

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

Aarnes, Jørg and Hou, Thomas Y. (2002) Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios. Acta Mathematicae Applicatae Sinica, English Series, 18 (1). pp. 63-76. ISSN 0168-9673. doi:10.1007/s102550200004. https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446

Abstract

In this paper we study some nonoverlapping domain decomposition methods for solving a class of elliptic problems arising from composite materials and flows in porous media which contain many spatial scales. Our preconditioner differs from traditional domain decomposition preconditioners by using a coarse solver which is adaptive to small scale heterogeneous features. While the convergence rate of traditional domain decomposition algorithms using coarse solvers based on linear or polynomial interpolations may deteriorate in the presence of rapid small scale oscillations or high aspect ratios, our preconditioner is applicable to multiple-scale problems without restrictive assumptions and seems to have a convergence rate nearly independent of the aspect ratio within the substructures. A rigorous convergence analysis based on the Schwarz framework is carried out, and we demonstrate the efficiency and robustness of the proposed preconditioner through numerical experiments which include problems with multiple-scale coefficients, as well problems with continuous scales.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s102550200004DOIArticle
https://rdcu.be/b11NPPublisherFree ReadCube access
Additional Information:© 2002 Springer-Verlag. Manuscript received October 9, 2001. Supported by STATOIL under the VISTA program. Supported in part by a grant from National Science Foundation under the contract DMS-0073916, and by a grant from Army Research Office under the contract DAAD19-99-1-0141. We would like to express our sincere gratitude to Professor Jinchao Xu and Professor Jun Zou for their valuable comments and suggestions.
Funders:
Funding AgencyGrant Number
STATOILUNSPECIFIED
NSFDMS-0073916
Army Research Office (ARO)DAAD19-99-1-0141
Subject Keywords:Multiscale elliptic problems; Domain decomposition; Schwarz methods; Porous media
Issue or Number:1
Classification Code:2000 MR Subject Classification: 35R05; 65N55; 65F10; 76S05
DOI:10.1007/s102550200004
Record Number:CaltechAUTHORS:20200221-160350446
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446
Official Citation:Aarnes, J., Hou, T.Y. Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios. Acta Mathematicae Applicatae Sinica, English Series 18, 63–76 (2002). https://doi.org/10.1007/s102550200004
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101478
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Feb 2020 19:26
Last Modified:16 Nov 2021 18:02

Repository Staff Only: item control page