519 / 1224
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)
)5(
) ( ) ,(
1
)( ,
)4(
) ˆ(
) (
1
)( ,
1
4
'
)ˆ(
) ( )ˆ,(
1
1
) ( )(
,
)(
, ,
)3(
'
)' ( )
,(,
1 1'
'
)(
' ,,
)2(
0
) ,(
1'
)(
' , ,
)(
' ,,
)ˆ,( , ,
)1(
) ˆ,(
)( ,
),
(
1 4
, ,
, ,
)( ,
,
)( ,
ˆ
dEEfErt
gE
gE
rgt
dEnwn
m
l
YEf
N
n
rng
gE
gE
dE d m
l
YEf
r
gE
gE
gE
gE
dEEf r
ml
r
gml
dEdE EfE Erls
gE
gE
gE
gE
rg gls
l
l
l m
m
l
Y
G
g
r
gml
rg gls
rng scat
q
n rg rng
pr r
P
p
ngpq
ng scat q rng gt
rng
−
=
=
−
=
−
−
=
=
→
−
−
= −
=
−=
=
−
=
=
−
=
+
=
+