Geodesic
Optimization approaches to some problems of building design
Applications of Mathematics, Tome 63 (2018) no. 3, pp. 305-331 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2018.0094-18
Classification : 49J20, 80A20, 80M50, 90C56
Keywords: building design; heat transfer; inverse and optimization problems; Nelder-Mead algorithm 
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     title = {Optimization approaches to some problems of building design},
     journal = {Applications of Mathematics},
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Vala, Jiří; Jarošová, Petra. Optimization approaches to some problems of building design. Applications of Mathematics, Tome 63 (2018) no. 3, pp. 305-331. doi: 10.21136/AM.2018.0094-18

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