Download e-book for iPad: Acoustic and Electromagnetic Scattering Analysis Using by Adrian Doicu

Acoustics Sound

By Adrian Doicu

ISBN-10: 0122197402

ISBN-13: 9780122197406

The discrete assets technique is a good and robust instrument for fixing a wide classification of boundary-value difficulties in scattering concept. various numerical equipment for discrete assets now exist. during this ebook, the authors unify those formulations within the context of the so-called discrete resources procedure. Key positive aspects* complete presentation of the discrete assets process* unique concept - an extension of the traditional null-field procedure utilizing discrete assets* sensible examples that reveal the potency and adaptability of elaborated tools (scattering via debris with excessive point ratio, tough debris, nonaxisymmetric debris, a number of scattering)* record of discrete assets programmes to be had through the web

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Extra resources for Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources

Example text

74) 60 CHAPTER III SYSTEMS OF FUNCTIONS IN ACOUSTICS it seems to be possible to prove the completeness of the distributed quasiplane waves Qn{x) = Q(x,k„) using the same strategy as in the above theorem. Howeverj since the quasi-plane waves are difficult to compute, this system is attractive only from a theoretical point of view. 2 LINEAR INDEPENDENT SYSTEMS OF FUNCTIONS In this section we will prove the linear independence of the systems of discrete sources. We begin with the systems of localized spherical wave functions.

Assume S is a surface of class C^ enclosing Tg. , m € Z. Then the resulting systems are linearly independent in L^{S). 77) m=—nimax n = l for some constants amn, fn = —mmax? ,ninax' Then, the field ^'^max ''^max w= in=—nimax E E"'""^^" n=:l (^•'^^^ vanishes in D^. ™! 79) n=l for all m = —mmax? ''. 79) by rn '"'"^. e. 80) 62 CHAPTER III SYSTEMS OF FUNCTIONS IN ACOUSTICS we see that the conclusion readily follows. The proof of the rest of part (a) proceed analogously. , m € Z / f c ^ p ( A ) } we debut with mm ax max Y, n '•'max E "-"^mnCy) = 0, y € 5.

Proof: Repeating the arguments of the previous theorem we see that Uao y with a ~ ao G C^'°'{S)y solves the homogeneous interior Dirichlet problem. The assumption k ^ p{Di) implies Uao = 0 in A , and the proof can be completed as above. For the double-layer potential we can state the following results. 4: Consider Dt a bounded domain of class C^ with boundary S. 45) 29 2. SINGLE- AND DOUBLE-LAYER POTENTIALS Then a^O on S. 2 we obtain a--ao e C{S). Then, since /C maps C{S) into C^^'^iS) and C^'"(5) into C^'^'iS) we deduce that ao E C^'"(5).

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Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources by Adrian Doicu

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