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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)
)1(
) ˆ,(
)( ,
),
(
1 4
, ,
, ,
)( ,
,
)( ,
ˆ
l
G
n rg rng
pr r
P
p
ngpq
ng scat q rng gt
rng
1 1'
)2(
0
) ,(
1'
)( ' , ,
)(
' ,,
)ˆ,( , ,
gE gE
l
l m
m
lY
g
r gml
rg gls
rng scat
q
)4(
) ˆ(
) ()(
1
'
)ˆ(
) ( )ˆ (
1
1
) ( )(
)(
)3(
'
)' ( )
,(,
'
)(
' ,,
dE
mYEf
N gE
dE d mYEf
gE
gE
dEEf
dEdE EfE Erls
gE gE
rg gls
)5(
) ( ) (
1
)(
1
,
4
,
,
, ,
dEEfEr
gE
r
nwn l
n
rng
gE
l
r
gE
gE
rml
rgml
,
,
t
gE
gt