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|Title:||APPLYING THE EXPONENTIAL CHEBYSHEV INEQUALITY TO THE NONDETERMINISTIC COMPUTATION OF FORM FACTORS|
|Authors:||Baranoski, Gladimir V.G.|
Rokne, Jon G.
|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.|
|Appears in Collections:||Rokne, Jon |
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