Designing a Lighting System for a Structure

I wish to mathematically represent point light sources inside a structure, and figure out how much like is scattered throughout the structure.

Specifically, I have lighting values of a certain amount of lux, and I need to ensure that the structure has a minimum of (certain value) lux touching all surfaces (maybe excluding things like shadows under tables). I don't want to go overboard on power consumption, though.

How, mathematically, should I go about figuring out how to do this? I'm thinking of simplifying the structure to something like a rectangular prism, or even just a hollow sphere of equal surface area.

I'm very confused at this point and I don't really know where to start.
 

Danger

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Would it help to model the interior of the structure in a ray-tracing programme?
 
The only program I know about that is capable of giving actual lighting values on different surfaces is Radiance, and I don't have AutoCAD to interface it with.

At this point, I just want some real basic estimates that I can calculate by hand. I'm talking about big simplifications, because this is just a preliminary design for the lighting system. Extremely rough estimates that are only good for about an order of magnitude approximation.

I don't want to simply take the light intensity in lumens and divide by the interior surface area of the structure. I want to do something a little bit more detailed than that.

I would know the albedos of the different components of the interior walls/floor/ceiling.
 

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