116
adjacent weak compartment we find
'l(awυ)2 , awW
.2 (∆x)2 4(∆x}2
a‰-l
faT - a-w
:NW
w
,2
2 (∆τ)2
'(aww)2
ɪ
aw
4(∆τ)2
aW Z
Nw — 1
LW
(∆rr)2 2(∆τ)2
‰-l
LW
= ‰,l√τ
Now we are ready to write the complete coupled strong-weak system. Letting
1 1 1
c =----jʊ- and cw = ———∑τ-
2Λαafr w 2Raa%-
and defining the coordinate vectors
eNw ∈ and eNr ∈ Rλ∖
we can write the coupling matrices as
Zw = e.‰,3(⅛r⅛) ∈ R^,∙×^,-<m+1>
7 Cw ,, („ erΓ ∖ c τpJVw(m+l)×Ns
ls — -^rXw,i\.eNiueNT) ∈ K ' '
and let Hs ∈ Rn≡×7v≈ be the Hines matrix for the strong part and Q be the quasi-active
matrix for the weak part. Then the coupled strong-weak “Hines” matrix is
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