Numerical analysis of the radiosity equation using the collocation method
type: Item
instance of: scholarly article
title: Numerical analysis of the radiosity equation using the collocation method
zbMATH Open document ID: 0961.65118
author: David Da-Kwun Chien
author: Jaehoon Seol
author: Kendall E. Atkinson
publication date: 2000-11-30T00:00:00Z
full work available at URL: https://eudml.org/doc/120954
full work available at URL: pp94-120.html
review text: General stability and convergence results for the collocation solution of the radiosity equation when a surface \(S\) is occluded, are given. Particular attention is paid to the use of discontinuity meshing for both piecewise constant and piecewise linear approximants. The possibility of superconvergence of the approximating solutions is considered. Two different surfaces are used to illustrate the variety of behaviours which can occur in the radiosity solution. The numerical integration of the collocation integrals is examined. There are difficulties in such integrations when the integration element is close to an edge of surface. A near-analytic approximation procedure for such integrals is proposed. Experimental calculations are given.
reviewed by: Nikolay Yakovlevich Tikhonenko
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1533612
zbMATH Keywords: occluded radiosity equation
zbMATH Keywords: Lambertian diffuse reflector
zbMATH Keywords: triangulation
zbMATH Keywords: superconvergence
zbMATH Keywords: centroid method
zbMATH Keywords: singular behaviour
zbMATH Keywords: numerical examples
zbMATH Keywords: collocation methods
zbMATH Keywords: convergence
zbMATH Keywords: discontinuity meshing
zbMATH Keywords: stability
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 1533612