Energy Boundary Element Method for Computing High Frequency ...
Energy Boundary Element Method for Computing High Frequency ...
Energy Boundary Element Method for Computing High Frequency ...
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Technical Background<br />
Governing Integral Equations:<br />
e~<br />
Y<br />
2<br />
⎛ ρ k ρ<br />
∫ ( )<br />
⎟ ⎞<br />
= σ P<br />
⎜ + dS<br />
S 2 4 2 2<br />
⎝ 64π<br />
r 32π<br />
r ⎠<br />
2<br />
~ k ρc<br />
I Y<br />
= ∫ σ<br />
S<br />
( P)<br />
ErdS<br />
2 2<br />
32π<br />
r<br />
Numerical Implementation:<br />
n<br />
e ~ ⎡<br />
⎤<br />
Y<br />
= ∑ σ<br />
j<br />
⎢⎣<br />
∫ G(<br />
, Y ) dS<br />
S j<br />
⎥⎦<br />
j=<br />
1<br />
ξ IY<br />
= ∑ σ<br />
j∫<br />
~<br />
n<br />
j = 1<br />
⎡<br />
⎢⎣<br />
S<br />
j<br />
H(<br />
ξ,<br />
Y)<br />
dS<br />
⎤<br />
⎥⎦<br />
ρ<br />
G ( ξ Y)<br />
+<br />
2 4<br />
64π<br />
r<br />
, 2<br />
k<br />
2<br />
( ξ,<br />
Y) 32π<br />
r ( ξ,<br />
Y)<br />
2<br />
ρ<br />
= H ( ξ Y )<br />
2<br />
k ρc<br />
2<br />
32π<br />
r<br />
, =<br />
2<br />
E<br />
r<br />
( ξ,<br />
Y) [ K ]{} σ = { P}<br />
JSV 278 (2004) pp. 413 - 436