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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman
On A Convex Set With Nondifferentiable Metric Projection, Shyan S. Akmal, Nguyen Mau Nam, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.
Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz
Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the …