Optimization approaches to some problems of building design

Applications of mathematics

iří Vala^1,2¹  Petra Jarošová^1,2² 

[1] Brno University of Technology, Faculty of Civil Engineering, Institute of Mathematics^1;Descriptive Geometry, Veveří 331/95, 602 00 Brno, Czech Republic^2

关键词: building design;    heat transfer;    inverse and optimization problems;    Nelder-Mead algorithm;   

DOI  :  10.21136/AM.2018.0094-18

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown