African Journal of Mathematics and Computer Science Research
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Article Number - D53536766502


Vol.10(4), pp. 24-31 , October 2017
https://doi.org/10.5897/AJMCSR2017.0712
ISSN: 2006-9731


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Full Length Research Paper

Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars



Yajni Warnapala
  • Yajni Warnapala
  • Department of Mathematics, Roger Williams University, Bristol, Rhode Island 02809-2921, USA.
  • Google Scholar
Hien Ngo
  • Hien Ngo
  • Department of Mathematics, Roger Williams University, Bristol, Rhode Island 02809-2921, USA.
  • Google Scholar







 Received: 19 July 2017  Accepted: 21 September 2017  Published: 31 October 2017

Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0


The Galerkin method is used to numerically solve the exterior boundary value problem for the radiosity equation for the spherical quatrefoil. The radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces when their reflectivity and emissivity are given. On planet Mars the surface emissivity is closely related to its surface temperature. The radiosity of a surface is the rate at which the energy leaves that surface; it includes the energy emitted by a surface as well as the energy reflected from other surfaces.

Key words: Radiosity equation, Galerkin method, spherical quatrefoil.

Arqub OA (2017). Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm. Int. J. Numer. Methods for Heat Fluid Flow. doi:10.1108/HFF-07-2016-0278.

 

Arvo J (1995). The Role of the Functional Analysis in Global Illumination, Rendering Techniques '95, edited by PM Hanrahan and W Purgathofer, Springer-Verlag, NY. pp. 115-126.

 
 

Atkinson KE (1982). The numerical solution of the Laplace's equation in three dimensions. SIAM J. Numer. Anal. 19:263-274.

 
 

Atkinson KE, Chien D (2006). A Study of the Fast Solution of the Occluded Radiosity Equation. Electronic Trans. Numer. Anal. 23:219-250.

 
 

Beyer WH (1987). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press.

 
 

Colton D, Kress R (2013). Integral equation methods in scattering theory. Soc. Ind. Appl. Math. pp. 66-90.
Crossref

 
 

DeGroh KK, Banks BA, Dever JA, Jaworske DA, Miller SK, Sechkar EA, Panko SR (2008). NASA Glenn research center's materials international space station experiments (MISSE 1-7). In Proceedings of the International Symposium on "SM/MPAC&SEED" Experiment pp. 91-119.

 
 

El-Ajou A, Abu AO, Momani S, Baleanu D, Alsaedi A (2015). A novel expansion iterative method for solving linear partial differential equations of fractional order. Appl. Math. Comput. 257:119-133.

 
 

Ho C, Slobin S, Sue M, Njoku E (2012). Mars Background Noise Temperatures. IPN Progress Report. 42-149.

 
 

Holzman, DC (2010). What's in a color? The unique human health effects of blue light. Environ. Health Perspect. 118(1):A22-A27.

 
 

Lin TC (1982). The numerical solution of the Helmholtz equation using integral equations, Ph.D. thesis, University of Iowa, Iowa City, Iowa.

 
 

Markiewicz WJ, Sablotny RM, Keller HU (1999). Optical properties of the Martian aerosols as derived from Imager for Mars Pathfinder midday sky brightness data. J. Geophys. Res. Planets 104(E4):9009-9017.

 
 

Voigt A, Hanssen N, Weichmann C (2004). The radiosity equation for solving global heat transfer in industrial furnaces. Math. Comput. Model. 39(2-3):145-150.

 
 

Warnapala Y, Deng Q (1982). Numerical solutions of the radiosity's equation for low reflectivity and emissivity on planet Mars. Int. J. Math. Trends Technol. 34:9-14.

 
 

Wheelwright CD, Toole JR (1992). Spacecraft lighting systems. Industry Applications Society Annual Meeting, Conference Record of the IEEE. pp. 1840-1845.

 

 


APA Warnapala, Y., & Ngo, H. (2017). Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars. African Journal of Mathematics and Computer Science Research, 10(4), 24-31.
Chicago Yajni Warnapala and Hien Ngo. "Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars." African Journal of Mathematics and Computer Science Research 10, no. 4 (2017): 24-31.
MLA Yajni Warnapala and Hien Ngo. "Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars." African Journal of Mathematics and Computer Science Research 10.4 (2017): 24-31.
   
DOI https://doi.org/10.5897/AJMCSR2017.0712
URL http://academicjournals.org/journal/AJMCSR/article-abstract/D53536766502

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