Advanced Physics for Brachytherapy 2018
The method
Let us make the final step: We ask our equations to hold for a number of directions M determined by a quadrature set S N of order N (Discrete Ordinates Method-DOM) (M is linked to N in a different way for different quadrature sets)
P
( ngpq ng scat q rng gt − + , , , ,
ˆ
rng
, )( ,
= +
)( ,
), pr r
)( ,
=
) ˆ,( n rg rng
)1(
p
=
1 4
l
G
=
m
q
rng scat
)( rg gls −
r gml
)( Y
)ˆ,( , , =
) ,(
)2(
' ,,
' , ,
l
l
1' l m g =
0
−=
' gE rg gls − = − )( gE
gE −
1 1'
' )' ( ) dEdE EfE Erls
,(,
→
)3(
' ,,
gE
gE −
gE −
gE −
1
1
1
N =
m
r gml
dEEf r
r
' )ˆ( ) ( )ˆ,( l YEf
n gE dE d m =
)( , rng
l YEf
dEnwn
)(
=
) ( )( =
) (
) ˆ(
)4(
ml
, ,
,
1
4
gE
gE
gE −
1
rgt
) ( ) ,( dEEfErt
)( , =
)5(
gE
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