# Simplified Radiosity Algorithm

Robinson, Darren, and Andrew Stone. "A simplified radiosity algorithm for general urban radiation exchange." Building services engineering research and technology 26.4 (2005): 271-284.

The radiant external environment may be described by two hemispheres, above and below the horizontal plane, which are discretized into a number of patches of known solid angle. Occlusions to these patches may be combined and represented as some patch fraction for which the radiant characteristics are defined by the dominant occlusion. By solving for radiant exchanges between each surface in a scene and its associated (un)occluded patches, we have a simplified radiosity algorithm (SRA). This paper describes the application of this SRA to solve for urban scale predictions of: (i) solar radiation; (ii) interior daylight; and (iii) longwave radiation. Comparisons of solar and daylight predictions with the ray-tracing program RADIANCE show that accurate results are achieved at a computational cost several orders of magnitude lower.

Practical application: This paper describes a new model for predicting external irradiance (shortwave and longwave) and internal illuminance in an accurate and very efficient way, in a single computational module. This module may be incorporated into existing software to improve the quality of predictions from single building thermal simulations as well as emerging software for urban scale predictions of integrated resource (energy, water, waste) flows, for which the model was developed.

Here is the installer for Windows : *Simplified Radiosity Algorithm*.

This algorithm has been developed for another project (*CitySim*), and can be used by SimStadt, e.g. in *IrradianceProcessor* when *SRA_Perez* is selected.

## SRA too slow or unstable?

If too many buildings are considered by SRA, the calculation might become very slow or unstable. More than 500 buildings might be already too much for some systems.

One possibility is to split the CityGML model in smaller tiles, which can be done automatically by selecting `SRA_Perez_with_tiling`

in *IrradianceProcessor*. The process has been detailed in *"Setting intelligent city tiling strategies for urban shading simulations"*.