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Summary: COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
Commun. Numer. Meth. Engng 2009; 25:219236
Published online 3 April 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cnm.1116
A node-based agglomeration AMG solver for linear elasticity
in thin bodies
Prasad S. Sumant1,,, Andreas C. Cangellaris2 and Narayana R. Aluru1
1Department of Mechanical Science and Engineering, University of Illinois, 1206 W. Green St., Urbana,
IL 61801, U.S.A.
2Department of Electrical and Computer Engineering, University of Illinois, 1406 W. Green St., Urbana,
IL 61801, U.S.A.
SUMMARY
This paper describes the development of an efficient and accurate algebraic multigrid finite element solver
for analysis of linear elasticity problems in two-dimensional thin body elasticity. Such problems are
commonly encountered during the analysis of thin film devices in micro-electro-mechanical systems. An
algebraic multigrid based on element interpolation is adopted and streamlined for the development of
the proposed solver. A new node-based agglomeration scheme is proposed for computationally efficient,
aggressive and yet effective generation of coarse grids. It is demonstrated that the use of appropriate finite
element discretization along with the proposed algebraic multigrid process preserves the rigid body modes
that are essential for good convergence of the multigrid solution. Several case studies are taken up to
validate the approach. The proposed node-based agglomeration scheme is shown to lead to development of
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