Numerical analysis of the radiosity equation using the collocation method

Electronic Transactions on Numerical Analysis

Volumn 11, Issue , 2000, Pages 94-120

  Atkinson, Kendall ^a   Chien, David Da Kwun ^b   Seol, Jaehoon ^c  

^a University of Iowa   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF IOWA   (United States)

Author keywords

Collocation methods; Discontinuity meshing; Integral equation; Numerical integration; Radiosity equation

Indexed keywords

EID: 0002951290     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. K. ATKINSON, Piecewise polynomial collocation for integral equations on surfaces in three dimensions, J. Integral Equations, 9 (1985), suppl., pp. 25-48.
2. K. ATKINSON, An Introduction to Numerical Analysis, Second edition, John Wiley & Sons, Inc., New York, 1989.
3. K. ATKINSON, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.
4. K. ATKINSON, User's Guide to a Boundary Element Package for Solving Integral Equations on Piecewise Smooth Surfaces (Release #2), Reports on Computational Mathematics #103, Dept of Mathematics, University of Iowa, Iowa City, 1998. The programs and guide are available via the URL http://www.math.uiowa.edu/∼atkinson/bie.html.
5. K. ATKINSON, The planar radiosity equation and its numerical solution, IMA J. Numer. Anal., 20 (2000), pp. 303-332.
6. K. ATKINSON AND G. CHANDLER, The collocation method for solving the radiosity equation for unoccluded surfaces, J. Integral Equations Appl., 10 (1998), pp. 253-290.
7. K. ATKINSON AND D. CHIEN, A fast matrix-vector multiplication method for solving the radiosity equation, Adv. Comput. Math., 12 (2000), pp. 151-174.
8. K. Atkinson, I. Graham, and I. Sloan, Piecewise continuous collocation for integral equations, SIAM J. Numer. Anal., 20 (1983), pp. 172-186.
9. G. CHANDLER AND I. GRAHAM, Product integration-collocation methods for non-compact integral operator equations, Math. Comp., 50 (1988), pp. 125-138.
10. M. COHEN AND J. WALLACE, Radiosity and Realistic Image Synthesis, Academic Press Inc., New York, 1993.
11. M. COSTABEL AND E. STEPHAN, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, in Mathematical Models and Methods in Mechanics, Banach Center Publications, Warsaw, 15 (1985), pp. 175-251.
12. J. ELSCHNER, On spline approximation for a class of non-compact integral equations, Math. Nachr., 146 (1990), pp. 271-321.
13. S. GORTLER, P. SCHRODER, M. COHEN, AND P. HANRAHAN, Wavelet radiosity, Comput. Graph. Proc., Annual conference series, 1993, pp. 221-230.
14. F. JOHNSON, A general panel method for the analysis and design of arbitrary configurations in incompressible flow, NASA Tech. Rep. NASA-CR-3079, Nat. Tech. Inform. Service, Springfield, VA, 1980.
15. D. LISCHINSKI, F. TAMPIERI, AND D. GREENBERG, Discontinuity meshing for accurate radiosity, IEEE Comput. Graph. Appl., 12 (1992), pp. 25-39.
16. A. RATHSFELD, Edge asymptotics for the radiosity equation over polyhedral boundaries, Math. Methods Appl. Sci., 22 (1999), pp. 217-241.
17. HENNING SCHON, Effiziente Verfahren zur numerischen Lösung der Radiosity-Gleichung, PhD thesis, University of Karlsruhe, 1997.
18. C. SCHWAB, Variable order composite quadrature of singular and nearly singular integrals, Computing, 53 (1994), pp. 173-194.
19. C. SCHWAB AND W. WENDLAND, On numerical cubatures of singular surface integrals in boundary element methods, Numer. Math., 62 (1992), pp. 343-369.
20. J. SEOL, Solving the Occluded Radiosity Equation using Collocation Methods, PhD thesis, anticipated 2001, Univ. of Iowa, Iowa City.
21. F. SILLION AND C. PUECH, Radiosity and Global Illumination, Morgan Kaufmann Publishing Co., San Francisco, 1994.
22. A. STROUD, Approximate Calculation of Multiple Integrals, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1971.