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1. I need to be efficient
•
It is inherently beneficial to work in spherical
coordinates to lift the kernel singularity since:
dV=dS dr=r
2
dΩ dr = r
2
sinθ dθ dφ dr
•
Instead of evaluating ALL directions around a
scerma generating point, I can DISCRETIZE space
using a number M of solid angle elements, ΔΩ
M
,
defined by (θ
0
,φ
0
)
M
, and assume
scerma does not
vary with θ within ΔΩ (i.e. on dS for a given r)
−
=
−
=→
r
r b
B
dr d
r
rb
B
j i
dr
)
0
exp(
0
1sc,i
S
jρ
iρ
)
exp(
1sc,i
S
jρ
iρ
1scD
i
j
−
=
=→
r
sin2r
2r
)
exp(
i 1sc,
S
jρ
iρ
V
dVjh
i 1sc,
S
jρ
iρ
1sc
D
dr dd
rb
B
j i