POTENTIAL PROBLEMS 53
In order for this expression to be zero in the limit we need to have,
(q
+ üu)r=>0 asr=>oo (2.106)
Notice that we assume the term in u will go to zero as u
-►
0 when
r
-►
oo.
The above condition (2.106) is the Sommerfeld radiation con-
dition
5
in three dimensions and can be written as,
r(—- + üu l=>0 asr=>oo (2.107)
For two dimensions the condition is
y7/-^
+
ÜH
j=>0 (2.108)
These conditions are satisfied by the fundamental solution.
REFERENCES
1.
Brebbia, C. A. and Butterfield, R., The Formal Equivalence of the Direct and
Indirect Boundary Element Methods', Appl. Math. Modelling,
2,
No. 2, June (1978)
2.
Stroud, A. H. and Secrest, D., Gaussian Quadrature Formulae, Prentice Hall, New
York, (1966)
3.
Martin, H. C. 'Finite Element Analysis of Fluid Flows', Proc.
Conf.
on Matrix
Methods in Structural Mechanics, AFFDL TR 68-150, Patterson Air Force Base,
Ohio,
USA (1969)
4.
Lau, P. and Brebbia, C. A., The Cell Collocation Method', Int. J. Mech. Sei., 20,
83-95 (1978)
5. Sommerfeld, A., Partial Differential Equations in Physics New York, Academic
Press,
pp. 256-344 (1949)
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