Extension of the hybrid Monte-Carlo method to view factor systems

In this article, the hybrid Monte-Carlo method is extended to calculate view factor systems. The extension includes the application of view factor algebra and standard deviation weighting. The application of view factor algebra is straight forward but more efficient than when used with ray tracing. Standard deviation weighting is a novel algorithm that makes it possible to determine an optimal distribution of function evaluations of the view factor integral kernel when applied to view factor systems. The hybrid Monte-Carlo method has been extended to 2-Dimensional domains but is not as efficient as the Monte-Carlo method with ray tracing, the standard approach. In the evaluation of the hybrid quasi-Monte-Carlo method two low-discrepancy sequencies are considered, Halton sequencies and Sobol sequencies. One interesting conclusion of the investigation is that when standard deviation weighting is particularly effective Halton sequencies consistently outperform Sobol sequencies in reducing the RMS error. In previous applications to view factor evaluation the choice of low-discrepancy sequence has not been a significant issue.