Multigrid treatment of “Thin” domains
SIAM Journal on Scientific and Statistical Computing
An improved incomplete Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Automating the CAD/CAE dimensional reduction process
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
An Algebraic Multigrid Method for Linear Elasticity
SIAM Journal on Scientific Computing
Algebraic Multigrid Based on Computational Molecules, 2: Linear Elasticity Problems
SIAM Journal on Scientific Computing
A 27-node hybrid brick and a 21-node hybrid wedge element for structural analysis
Finite Elements in Analysis and Design
Algebraic reduction of beams for CAD-integrated analysis
Computer-Aided Design
CAD-integrated analysis of 3-D beams: a surface-integration approach
Engineering with Computers
A dual-representation strategy for the virtual assembly of thin deformable objects
Virtual Reality - Special Issue on Manufacturing and Construction
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For very large systems of equations arising from 3D finite element formulation, pre-conditioned iterative solvers are preferred over direct solvers due to their reduced memory requirements. However, in the finite-element analysis of thin structures such as beam and plate structures, iterative solvers perform poorly due to the presence of poor quality elements. In particular, their efficiency drops significantly with increase in the aspect ratio of such structures. In this paper, we propose a dual-representation based multi-grid framework for efficient iterative analysis of thin structures. The proposed iterative solvers are relatively insensitive to the quality of the elements since they exploit classical beam and plate theories to spectrally complement 3D finite element analysis. This leads to significant computational gains, as supported by the numerical experiments.