Tropical daylighting : predicting sky types and interior illuminance in north-east Brazil.

Daylight is present in tropical regions in a considerable intensity throughout the year. The sky characteristics are changeable and sunlight cannot be disregarded. Daylighting techniques are still wanted to answer particular tropical features. The main aim of this thesis is to present a daylighting analysis tool for the tropics developed out of existing procedures. It is structured in three parts. The first part provides a broad view of climatic aspects related to daylighting studies in a typical tropical city - Maceiö, Brazil. A brief climatic description of the city and a study relating climate and building are followed by a literature review of climatic fundamentals. A study is made of meteorological station measurements in relation to the city and a field investigation is described. These lead to a simplified method for sky type selection. It shows that a reasonable assumption about daylight climate can be made from very simple data and that new structure of CIE standard general sky could be applied everywhere. The second part investigates methods that could be appropriated for calculating daylighting in humid climates and concludes with a methodology based on an adaptation of existing techniques. The Monte Carlo and ray tracing techniques are reviewed, as well as the daylight coefficients concept. These are incorporated in prototype software, TropLux, written in MATLAB code. The development of the method in this thesis can be seen as an extension of the daylight factor concept to the CIE Standard General Sky and reflected sunlight. The software validation is done and results show that the level of prediction is comparable with those produced by Radiance and overall the results appear to be robust. Analysis indicates that it is not essential to have climate-specific calculation technique. Universal lighting software is viable, providing the local climate and architectural characteristics are taken into account. The last part applies TropLux to ground-reflected light. It is found that the influence of reflected sunlight on interior illuminance can be very large. Among shading devices analysed, overhang has shown the best performance. There is a key zone of ground outside window that provides the majority of the reflected light. A direct design implication can be the reduction of window size

Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 243-251).Modern engineering problems often require accurate, reliable, and efficient evaluation of quantities of interest, evaluation of which demands the solution of a partial differential equation. We present in this thesis a technique for the prediction of outputs of interest of parabolic partial differential equations. The essential ingredients are: (i) rapidly convergent reduced-basis approximations - Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest: the error estimates serve a priori to construct our samples and a posteriori to confirm fidelity; and (iii) offline-online computional procedures - in the offline stage the reduced- basis approximation is generated; in the online stage, given a new parameter value, we calculate the reduced-basis output and associated error bound. The operation count for the online stage depends only on N (typically small) and the parametric complexity of the problem; the method is thus ideally suited for repeated, rapid, reliable evaluation of input-output relationships in the many-query or real-time contexts. We first consider parabolic problems with affine parameter dependence and subsequently extend these results to nonaffine and certain classes of nonlinear parabolic problems.(cont.) To this end, we introduce a collateral reduced-basis expansion for the nonaffine and nonlinear terms and employ an inexpensive interpolation procedure to calculate the coefficients for the function approximation - the approach permits an efficient offline-online computational decomposition even in the presence of nonaffine and highly nonlinear terms. Under certain restrictions on the function approximation, we also introduce rigorous a posteriori error estimators for nonaffine and nonlinear problems. Finally, we apply our methods to the solution of inverse and optimal control problems. While the efficient evaluation of the input-output relationship is essential for the real-time solution of these problems, the a posteriori error bounds let us pursue a robust parameter estimation procedure which takes into account the uncertainty due to measurement and reduced-basis modeling errors explicitly (and rigorously). We consider several examples: the nondestructive evaluation of delamination in fiber-reinforced concrete, the dispersion of pollutants in a rectangular domain, the self-ignition of a coal stockpile, and the control of welding quality. Numerical results illustrate the applicability of our methods in the many-query contexts of optimization, characterization, and control.by Martin A. Grepl.Ph.D