Convergence Acceleration for Iterative Finite-Element Methods
Publication: Journal of Engineering Mechanics
Volume 121, Issue 1
Abstract
Sequence-to-sequence transformations are examined as a means to accelerate the convergence of iterative finite-element methods; in particular, the Shanks transform, the scalar epsilon algorithm (SEA), and the vector epsilon algorithm (VEA) are applied to dynamic relaxation (DR) solutions. One of the features of these algorithms is that they operate directly on the solution iterates and, therefore, do not require modification of the finite-element code itself. The accelerators are applied to a linear spring system and a cantilever elastica. Nonlinear sequence-to-sequence transformations are found to accelerate convergence by a factor of more than 10 and, thus, to largely overcome a major drawback of iterative finite-element methods, namely their slow rate of convergence. The VEA transformation is especially stable, is invariant with respect to coordinate transformations, and is compatible with typical kinematic constraints. Therefore, it is well suited to the acceleration of finite-element solution iterates.
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Published In
Journal of Engineering Mechanics
Volume 121 • Issue 1 • January 1995
Pages: 1 - 6
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
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