A criterion of optimization of a modified green’s function in two dimensional elastic waves
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
In the work [*] an optimal choice of the multipoles coefficients is determined in a circular case of border. These complex factors involved in the modification of the Green’s function, who plays the role of the kernel of the modified integral operator’s in elasticity. In this note, it is intended to identify relatively simple expressions of this coefficients for the particular case of circular border. And then to find an estimate of the norm of the modified integral operator’s in elasticity. For this, we consider a domain D of circular border ?D ( ?D is a cercle for radius 0a 0 ), using the orthogonality proprieties between some vectors {F ?% m } ?,%=1:2 m=0:? who are involved in the definition of the modified Green’s function G1(p, q), and the expressions of optimal choice for the coefficients of multipoles for a general domain’s obtained in [*], and taking into account the fact that the scalar product of vectors {F ?% m } ?,%=1:2 m=0:? in this case, is a calculation of integral in circle of radius ’a’. We obtain a relatively simples expressions for optimal choice of the coefficients of multipoles, and thereafter, and by replacing the values of this coefficients in the expression of the modified integral operator’s K1, and using a developement of the modified Green’s function G1(p, q), given by [*]: G1(p, q) = 1 2 h GD(p, q) + GN (p, q) i Where GD and GN are the Green’s functions for the Dirichlet and Neumann problems respectively. We prof that the norm of the modified integral operator’s K1 is zero. The interest of this result (kK1k = 0) is that the more we rely on approximate method to solve the integral equation obtained from the use of the integral representations method for the bounded problem defined in [*], at the moment we have more integral equation to be solved, because the fact that (kK1k = 0) drive then directly to the solution of the bounded problem.
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Sahli, B. ve Bencheikh, L. (2009). A criterion of optimization of a modified green’s function in two dimensional elastic waves. Maltepe Üniversitesi. s. 120.
