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The method
➢
if we define a spectral weighting factor: f(E) so that:
Our equations
become:
)5(
) (
) ,(
1
)( ,
)4(
4
'
)ˆ(
) (
)ˆ,(
1
1
) ( )(
,
)(
, ,
)3(
'
)' ( )
,(,
1 1'
'
)(
' ,,
)2(
0
) ,(
1'
)(
' , ,
)(
' ,,
)ˆ,( ,
)1(
)
(
1 4
,
,
)ˆ,(
,
)ˆ,(
ˆ
dEEfErt
gE
gE
rgt
dE d m
l
YEf
r
gE
gE
gE
g
E
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
rg scat
q
pr r
P
p
gpq
g scat q
rg gt
rg
−
=
−
−
=
=
→
−
−
=
−
=
−=
=
−
=
−
=
+
= +
=
=
E
dEEf
Ef
r
E
r
1 ) (
,
) (
)(
) ,(
➢
All that is left then is to discretize direction and space and solve iteratively!