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The method
if we define a spectral weighting factor: f(E) so that:
E
dEEf
Ef r
Er
1 ) (
,) ( )(
) ,(
)1(
)
(
1 4
,
,
)ˆ,(
,
)ˆ,(
ˆ
pr r
P
p
gpq
g scat q
rg gt
rg
Our equations
become:
1 1'
)2(
0
) ,(
1'
)( ' , ,
)(
' ,,
)ˆ,( ,
gE gE
l
l
l m
m
lY
G
g
r gml
rg gls
rg scat
q
1
1
)3(
'
)' ( )
,(,
'
)(
' ,,
gE
gE
dEdE EfE Erls
gE gE
rg gls
1
)4(
4
'
)ˆ(
) ( )ˆ,(
) ( )( ,
)( , ,
gE
dE d m
lYEf
r
gE
gE
dEEf rml
rgml
)5(
) ( ) ,(
)( ,
dEEfErt
gE
rgt
All that is left then is to discretize direction and space and solve iteratively!