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Optimization of Finite Element Models with MathOptimizer and ModelMaker

János D. Pintér
Organization: Pintér Consulting Service Inc.
URL: http://www.pinterconsulting.com
Christopher J. Purcell
Organization: Defence R&D Canada

2003 Mathematica Developer Conference
Conference location


Quantitative decisions related to engineering, economic and scientific investigations are frequently made using optimization concepts and tools. The decision-maker or modeler typically wants to find the "absolutely best" decision, which corresponds to the minimum or maximum of a suitable objective function and satisfies certain feasibility constraints. The objective function expresses overall system performance, and the constraints originate from physical, technical, or economic considerations.

This paper describes two Mathematica packages: MathOptimizer, a general-purpose nonlinear (global and local) optimizer, and ModelMaker, a parametric finite-element modeller. As an example, we presented the optimized design of a tuning fork, where the design objective function involves a finite element calculation. This simple example illustrates a typical engineering optimization problem where the objective function may be a black box (containing an elaborate calculation that is costly to evaluate). A prototype optimizer for expensive objective functions was demonstrated; an improved implementation of this will be included in the next release of MathOptimizer (and perhaps also offered as a separate application package).

"Optimization of finite element models with MathOptimizer and ModelMaker" is available as the download devcon2003.nb.zip, below.

*Applied Mathematics > Optimization
*Wolfram Technology > Application Packages > Applications from Independent Developers > MathOptimizer

MathOptimizer, Black box, general purpose nonlinear (global and local) optimizer, finite element, Tuning fork, Janos Pinter
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devcon2003.nb (4.8 MB) - Mathematica Notebook