| Title:
|
Optimization approaches to some problems of building design (English) |
| Author:
|
Vala, Jiří |
| Author:
|
Jarošová, Petra |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
305-331 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
building design |
| Keyword:
|
heat transfer |
| Keyword:
|
inverse and optimization problems |
| Keyword:
|
Nelder-Mead algorithm |
| MSC:
|
49J20 |
| MSC:
|
80A20 |
| MSC:
|
80M50 |
| MSC:
|
90C56 |
| idZBL:
|
Zbl 06945735 |
| idMR:
|
MR3833663 |
| DOI:
|
10.21136/AM.2018.0094-18 |
| . |
| Date available:
|
2018-07-16T08:50:54Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147313 |
| . |
| Reference:
|
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