COMPUTATION OF EIGENVALUES FOR DOMAINS WITH COMPLICATED BOUNDARY SHAPE

Slávka Tkáčová

   The eigenvalue problem for the two-dimensional Laplace operator dened on domains with a complicated boundary shape arises in many practical situations, for example the cross vibration of membranes. The numerical technique presented in this paper uses the Rayleigh-Ritz method combined with conformal mapping in order to transform the region with complicated boundary shape to a standard region as a square or circle. This work deals only with the problems in which the domain under consideration is a conformal image of a rectangle. The convergence of the presented technique for the case when the retangle domain moves close to singular points of the used conformal mapping is also investigated.

Keywords: Ritz method, eigenvalues, matrix, conformal mapping

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