Applications of one-shot methods in PDEs constrained shape optimization

Svetozara I. Petrova

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 3, 581-597

Abstract: The paper deals with applications of numerical methods for optimal shape design of composite materials structures and devices. We consider two different physical models described by specific partial differential equations (PDEs) for real-life problems. The first application relates microstructural biomorphic ceramic materials for which the homogenization approach is invoked to formulate the macroscopic problem. The obtained homogenized equation in the macroscale domain is involved as an equality constraint in the optimization task. The second application is connected to active microfluidic biochips based on piezoelectrically actuated surface acoustic waves (SAWs). Our purpose is to find the best material-and-shape combination in order to achieve the optimal performance of the materials structures and, respectively, an improved design of the novel nanotechnological devices. In general, the PDEs constrained optimization routine gives rise to a large-scale nonlinear programming problem. For the numerical solution of this problem we use one-shot methods with proper optimization algorithms and inexact Newton solvers. Computational results for both applications are presented and discussed.

Keywords: One-shot method; Shape optimization; Primal-dual interior-point approach; Path-following predictor–corrector strategy; Newton solver (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:3:p:581-597

DOI: 10.1016/j.matcom.2009.09.010

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