 
Summary: Electronic Transactions on Numerical Analysis.
Volume 11, pp. 94120, 2000.
Copyright © 2000, Kent State University.
ISSN 10689613.
ETNA
Kent State University
etna@mcs.kent.edu
NUMERICAL ANALYSIS OF THE RADIOSITY EQUATION USING THE
COLLOCATION METHOD
KENDALL ATKINSON, DAVID DAKWUN CHIEN, AND JAEHOON SEOL§
Abstract. The collocation method for solving the occluded radiosity equation is examined, theoretically and
empirically. Theoretical results are examined, including questions of superconvergence of the collocation solution.
The use of "discontinuity meshing" is examined for both piecewise constant and piecewise linear collocation. Also,
numerical integration of the collocation integrals is examined, and a nearanalytic evaluation method is given.
Key words. radiosity equation, integral equation, numerical integration, collocation methods, discontinuity
meshing.
AMS subject classifications. 65R20.
1. Introduction. 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. The
equation is
