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Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems

Published online by Cambridge University Press:  28 May 2015

Paul T. Boggs ,
David M. Gay  and
Stephen G. Nash
Paul T. Boggs
Affiliation:
Sandia National Laboratories (retired), M.S. 9159, P.O. Box 969, Livermore, CA 94551, U.S.A.
David M. Gay
Affiliation:
AMPL Optimization, Inc., 900 Sierra Place SE, Albuquerque, NM 87108-3379 U.S.A.
Stephen G. Nash*
Affiliation:
George Mason University, M.S. 5C8, Fairfax, VA 22030 U.S.A.
*
*Email addresses: paulboggs@comcast.net (Paul T. Boggs), dmg@ampl.com (David M. Gay), snash@gmu.edu (Stephen G. Nash)

Abstract

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We consider using a discrete network model in combination with continuous nonlinear optimization models to solve the problem of optimizing channels in nanoporous materials. The problem and the hierarchical optimization algorithm are described in [2]. A key feature of the model is the fact that we use the edges of the finite element grid as the locations of the channels. The focus here is on the use of the discrete model within that algorithm. We develop several approximations to the relevant flow and a greedy algorithm for quickly generating a “good” tree connecting all of the nodes in the finite-element mesh to a designated root node. We also consider Metropolis-Hastings (MH) improvements to the greedy result. We consider both a regular triangulation and a Delaunay triangulation of the region, and present some numerical results.

Keywords

49M3765K0490C08Multigrid OptimizationMultilevel OptimizationNonlinear OptimizationComplex Hierarchical Optimization

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 2 , May 2015 , pp. 149 - 167
Copyright
Copyright © Global-Science Press 2015 

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