By Adrian Doicu

ISBN-10: 0122197402

ISBN-13: 9780122197406

The discrete resources process is an effective and strong instrument for fixing a wide classification of boundary-value difficulties in scattering concept. numerous numerical tools for discrete resources now exist. during this publication, the authors unify those formulations within the context of the so-called discrete resources technique. Key gains* accomplished presentation of the discrete resources technique* unique thought - an extension of the normal null-field procedure utilizing discrete assets* functional examples that reveal the potency and suppleness of elaborated tools (scattering via debris with excessive element ratio, tough debris, nonaxisymmetric debris, a number of scattering)* record of discrete resources programmes to be had through the net

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Example text

N. ,m = - n , . . , n / f c ^ p ( A ) } is complete in L'^{S) it follows that a ~ 0 on 5 and the theorem is proved. We mention that we can consider a system of functions satisfying the radiation condition at infinity and having similar properties to the system of homogeneous plane waves. 73) n=Om=—n and the integration is over C^ ii z > 0 and over C_ if ^ < 0. ' plane from 0 to 7r/2 — joo, and n/2 4- joo to TT, respectively. Unlike the plane waves P ( x , k) the quasi-plane waves Q(x, k) obey Sommerfeld's radiation condition.

Consider Di a bounded domain of class C^ with boundary S and unit normal vector n directed into the exterior of Di. 87) s where hg = h — UQ. 88) 4. 86) and as dg{x,y,k) ^^(x) = / U. du^ . dS(y), x e D . 87). We note that the existence of solutions to the general null-field equations is guaranteed by the existence of solutions to the Dirichlet and Neumann boundary-value problems. When the boundary values are the restriction of the analytic function UQ to S we see that hg = dug/dn € C°'"(5) solves the null-field equation for the Dirichlet problem, while for the Neumann problem the solution is hs =^ Ug £ C^'^{S).

Let us define the scalar functions fn by setting /n(y) = (£x5)(xn,y), n = l,2,.... 10). Thus, the following result is valid. 3: Let S be a closed surface of class C^. Then the system { / n } ^ i is complete in L'^{S) . Two parameters are essential for complete system construction: the support H of discrete sources and the vanishing conditions for the singlelayer potential in Di. Both parameters determine the type of discrete sources. In general we can use as support a point, a curve, a surface, etc.

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Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources by Adrian Doicu

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