A fast matrix--vector multiplication method for solving the radiosity equation
type: Item
instance of: scholarly article
title: A fast matrix--vector multiplication method for solving the radiosity equation
zbMATH Open document ID: 0944.65144
DOI: 10.1023/A:1018961001209
author: David Da-Kwun Chien
author: Kendall E. Atkinson
published in: Advances in Computational Mathematics
publication date: 2000-03-21T00:00:00Z
review text: This paper is devoted to the numerical solution of the radiosity equation in the unoccluded case, which takes the form \[ u(P) - {\rho (P) \over \pi} \int_S u(Q) {\cos \Theta_P \cos \Theta_Q \over |P-Q|^2} dS_Q = E(P),\quad P \in S , \tag{1} \] with \(u(P)\) the radiosity, \(E(P)\) the emissivity and \(\rho (P)\) the reflectivity at \(P \in S\). Furthermore, \(\Theta_p\) is the angle between the inner normal to \(S\) at \(P\) and \(Q-P\), and the surface \(S\) need not to be connected and is usually only piecewise smooth. The authors discuss stability and convergence of the centroid collocation method applied to (1). They present a fast iteration method for the solution of the corresponding linear system using fewer than \(O(n^2)\) operations. A detailed numerical example shows a large speedup compared to direct solvers for the radiosity equation. The restriction to unoccluded surfaces will be removed in a later paper.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1419502
zbMATH Keywords: radiosity equation
zbMATH Keywords: integral equation
zbMATH Keywords: numerical example
zbMATH Keywords: collocation methods
zbMATH Keywords: fast matrix-vector multiplication
zbMATH Keywords: stability
zbMATH Keywords: convergence
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: a:1018961001209
OpenAlex ID: W2126155032
description: scientific article; zbMATH DE number 1419502