Volume 8, Issue 2
Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems

Paul T. Boggs, David M. Gay & Stephen G. Nash

Numer. Math. Theor. Meth. Appl.,8 (2015), pp. 149-167

Published online: 2015-08

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  • Abstract

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.

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@Article{NMTMA-8-149, author = {Paul T. Boggs, David M. Gay and Stephen G. Nash}, title = {Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {2}, pages = {149--167}, abstract = {

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.}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w13si}, url = {http://global-sci.org/intro/article_detail/nmtma/12405.html} }

TY - JOUR T1 - Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems AU - Paul T. Boggs, David M. Gay & Stephen G. Nash JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 149 EP - 167 PY - 2015 DA - 2015/08 SN - 8 DO - http://dor.org/10.4208/nmtma.2015.w13si UR - https://global-sci.org/intro/article_detail/nmtma/12405.html KW - AB -

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.

Paul T. Boggs, David M. Gay & Stephen G. Nash. (1970). Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems. Numerical Mathematics: Theory, Methods and Applications. 8 (2). 149-167. doi:10.4208/nmtma.2015.w13si
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