New Computational Geometry Methods Applied to Solve Complex Problems of Radiative Transfer

Francisco Salguero-Andújar and Joseph-Maria Cabeza-Lainez
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Francisco Salguero-Andújar: School of Engineering, University of Huelva, Campus de El Carmen, 21007 Huelva, Spain
Joseph-Maria Cabeza-Lainez: Higher Technical School of Architecture, University of Seville, 41012 Seville, Spain

Mathematics, 2020, vol. 8, issue 12, 1-25

Abstract: Diverse problems of radiative transfer remain as yet unsolved due to the difficulties of the calculations involved, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the equations that were previously derived into a graphical interface based on the projected solid-angle principle. Such a procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled in the basic examples by means of subroutines from the analytical software DianaX, developed at an earlier stage by the authors, though mainly oriented to closed cuboidal or curved volumes. With this innovative approach, the often cumbersome calculation procedure of lighting, thermal or even acoustic energy exchange can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

Keywords: mathematics applied to lighting and radiative transfer; configuration factors; computational geometry; parametric design; new solutions for equations of geometric optics; numerical computation of quadruple integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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