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Domain decomposition preconditioners of Neumann–Neumann type for hp-approximations on boundary layer meshes in three dimensions

Toselli, Andrea and Vasseur, Xavier (2004) Domain decomposition preconditioners of Neumann–Neumann type for hp-approximations on boundary layer meshes in three dimensions. IMA Journal of Numerical Analysis, 24 (1). pp. 123-156. ISSN 0272-4979. doi:10.1093/imanum/24.1.123.

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We develop and analyse Neumann–Neumann methods for hp finite-element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. These are meshes that are highly anisotropic where the aspect ratio typically grows exponentially with the polynomial degree. The condition number of our preconditioners is shown to be independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients. In addition, it only grows polylogarithmically with the polynomial degree, as in the case of p approximations on shape-regular meshes. This work generalizes our previous one on two-dimensional problems in Toselli & Vasseur (2003a, submitted to Numerische Mathematik, 2003c to appear in Comput. Methods Appl. Mech. Engng.) and the estimates derived here can be employed to prove condition number bounds for certain types of FETI methods.

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Additional Information:© 2003 Institute of Mathematics and its Applications. Received on 8 January 2003; revised on 15 April 2003. The authors are grateful to Christoph Schwab and Olof Widlund for enlightening discussions of their work. This work was partially supported by the Swiss National Science Foundation under Project 20-63397.00.
Funding AgencyGrant Number
Swiss National Science Foundation20-63397.00
Subject Keywords:domain decomposition; preconditioning; hp finite elements; spectral elements; anisotropic meshes
Issue or Number:1
Record Number:CaltechAUTHORS:20111019-113934085
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27309
Deposited On:19 Oct 2011 20:10
Last Modified:09 Nov 2021 16:47

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