Applications of Mathematics, Vol. 63, No. 3, pp. 305-331, 2018


Optimization approaches to some problems of building design

Jiří Vala, Petra Jarošová

Received March 31, 2018.   Published online June 18, 2018.

Abstract:  Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system of parabolic partial differential equations of evolution with at least two types of physically motivated nonlinearities, the usual gradient-based methods must be replaced by the downhill simplex Nelder-Mead approach or its quasi-gradient modifications. One example of the real low-energy house in Moravian Karst is demonstrated with references to other practical applications.
Keywords:  building design, heat transfer, inverse and optimization problems, Nelder-Mead algorithm
Classification MSC:  90C56, 49J20, 80A20


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Affiliations:   Jiří Vala, Petra Jarošová, Brno University of Technology, Faculty of Civil Engineering, Institute of Mathematics and Descriptive Geometry, Veveří 331/95, 602 00 Brno, Czech Republic, e-mail: vala.j@fce.vutbr.cz, jarope.jarope@seznam.cz


 
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