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Edge asymptotics for the radiosity equation over polyhedral boundaries
Author(s) -
Rathsfeld Andreas
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199902)22:3<217::aid-mma33>3.0.co;2-h
Subject(s) - mathematics , piecewise , integral equation , mathematical analysis , domain (mathematical analysis) , bounded function , boundary (topology) , operator (biology) , enhanced data rates for gsm evolution , term (time) , telecommunications , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene , computer science
In the present paper we consider the radiosity equation over the boundary of a polyhedral domain. Similarly to corresponding results on the double‐layer potential equation, the solution of the second kind integral equation with non‐compact integral operator is piecewise continuous. The partial derivatives, however, are not bounded. In the present paper we derive the first term in the asymptotic expansion of the solution in the vicinity of an edge. Note that, knowing this term, optimal mesh gradings can be designed for the numerical solution of this equation. Copyright © 1999 John Wiley & Sons, Ltd.