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Computational analysis of thermal transfer in advanced buildings and their components stimulates the development of minimization algorithms for complicated functions, whose evaluation need numerical analysis of rather complicated initial and boundary value problems of differential or integral equations; consequently no effective evaluation of corresponding gradients is available. This occurs during optimization of design parameters of such buildings, as well as during identification of thermal conductivity, diffusivity, etc. of material samples from laboratory measurements. One reasonable approach is to implement a nonlinear downhill simplex method. The paper shows some results i) for the classical Nelder-Mead approach, ii) for its quasi-gradient modification and iii) for certain weighted variant of ii). [ABSTRACT FROM AUTHOR]

Evaluation of temperature development and related consumption of energy required for heating, air-conditioning, etc. in low-energy buildings requires the proper physical analysis, covering heat conduction, convection and radiation, including beam and diffusive components of solar radiation, on all building parts and interfaces. The system approach and the Fourier multiplicative decomposition together with the finite element technique offers the possibility of inexpensive and robust numerical and computational analysis of corresponding direct problems, as well as of the optimization ones with several design variables, using the Nelder-Mead simplex method. The practical example demonstrates the correlation between such numerical simulations and the time series of measurements of energy consumption on a small family house in Ostrov u Macochy (35 km northern from Brno). [ABSTRACT FROM AUTHOR]

The significance of reasonable prediction and control of energy consumption in building structures follows from the natural requirements of the development of new materials, structures and technologies, as well as from the formal ones from European directives. This paper presents the method based on the generalized multiplicative Fourier decomposition, applied to a model of a building as certain thermal system. The design of the computational algorithm highlights the important contribution of solar radiation, as well as the design and control of the heating equipments. One illustrative numerical example shows the results of the practical implementation of this algorithm in the MATLAB environment. [ABSTRACT FROM AUTHOR]

Modelling and simulation of thermal processes, based on the principles of classical thermodynamics, requires numerical analysis of partial differential equations of evolution of the parabolic type. This paper demonstrates how the generalized Fourier method can be applied to the development of robust and effective computational algorithms, with the direct application to the design and performance of buildings with controlled energy consumption. [ABSTRACT FROM AUTHOR]