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1. I need to be efficient, angular discretization
How can I relax the demand on SN without ray effects?
The LBTE is linear so assuming:
)ˆ ( )ˆ ( )ˆ (       r coll r
P unc
r   
For any direction, we can split our system of equations in two:
, ,
1
, ,

 g
p
gp g
P
)1( ) (
1 4
,
, ˆ pr r
p
gpq
uncg gt uncg
  
 

   


)2( , ,
ˆ     
P unc scat
q coll scat
q coll coll 

1
, ,


p
gp g g gt g
Equation (1) for the primary (uncolided) part of the fluence can be analytically solved!!!
I can ray-trace the solution for the spectrum of primary photons through the geometry and
arrive at very quick and accurate: initial guess and qscat,1,n 0 )( ,1   iter rn

Then I proceed to solve the system of equations (2) for the collided fluence to refine my
solution with the higher orders of scatter
This is known as the 1st scatter source method