APPLYING THE EXPONENTIAL CHEBYSHEV INEQUALITY TO THE NONDETERMINISTIC COMPUTATION OF FORM FACTORS
Date
1999-03-01
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Abstract
The computation of the fraction of radiation power that leaves a surface and
arrives at another, which is specified by the form factor linking both
surfaces, is central to radiative transfer simulations. Although there are
several approaches that can be used to compute form factors, the application
of nondeterministic methods is becoming increasingly important due to the
simplicity of their procedures and their wide range of applications. These
methods compute form factors implicitly through the application of standard
Monte Carlo techniques and ray casting algorithms. Their accuracy and
computational costs are, however, highly dependent on the ray density used in
the computations. In this paper a mathematical bound, based on probability
theory, is proposed to determine the number of rays needed to obtain
asymptotically convergent estimates for form factors in a computationally
efficient stochastic process. Specifically, the exponential Chebyshev
inequality is introduced to the radiative transfer field in order to determine
the ray density required to compute form factors with a high reliability/cost
ratio. Numerical experiments are provided which illustrate the validity and
usefulness of the proposed bound.
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Computer Science