کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4643028 1341365 2007 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Eigenfrequencies of fractal drums
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Eigenfrequencies of fractal drums
چکیده انگلیسی

A method for the computation of eigenfrequencies and eigenmodes of fractal drums is presented. The approach involves first conformally mapping the unit disk to a polygon approximating the fractal and then solving a weighted eigenvalue problem on the unit disk by a spectral collocation method. The numerical computation of the complicated conformal mapping was made feasible by the use of the fast multipole method as described in [L. Banjai, L.N. Trefethen, A multipole method for Schwarz–Christoffel mapping of polygons with thousands of sides, SIAM J. Sci. Comput. 25(3) (2003) 1042–1065]. The linear system arising from the spectral discretization is large and dense. To circumvent this problem we devise a fast method for the inversion of such a system. Consequently, the eigenvalue problem is solved iteratively. We obtain eight digits for the first eigenvalue of the Koch snowflake and at least five digits for eigenvalues up to the 20th. Numerical results for two more fractals are shown.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 198, Issue 1, 1 January 2007, Pages 1–18
نویسندگان
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