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ON THE USE OF FFT ALGORITHM FOR THE CIRCUMFERENTIAL CO‐ORDINATE IN BOUNDARY ELEMENT FORMULATION OF AXISYMMETRIC PROBLEMS
Author(s) -
OZKAN GONCA,
MENGI YALCIN
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970715)40:13<2385::aid-nme169>3.0.co;2-f
Subject(s) - fast fourier transform , boundary element method , gaussian quadrature , mathematics , fourier transform , mathematical analysis , discrete time fourier transform , quadrature (astronomy) , discrete fourier transform (general) , fourier series , boundary (topology) , split radix fft algorithm , fractional fourier transform , boundary value problem , geometry , algorithm , fourier analysis , finite element method , physics , nyström method , optics , thermodynamics
A new numerical method is proposed for the boundary element analysis of axisymmetric bodies. The method is based on complex Fourier series expansion of boundary quantities in circumferential direction, which reduces the boundary element equation to an integral equation in ( r – z ) plane involving the Fourier coefficients of boundary quantities, where r and z are the co‐ordinates of the ( r , θ, z ) cylindrical co‐ordinate system. The kernels appearing in these integral equations can be computed effectively by discrete Fourier transform formulas together with the fast Fourier transform (FFT) algorithm, and the integral equations in ( r – z ) plane can be solved by Gaussian quadrature, which establishes the Fourier coefficients associated with boundary quantities. The Fourier transform solution can then be inverted into ( r , θ, z ) space by using again discrete Fourier transform formulas together with FFT algorithm. In the study, first we present the formulation of the proposed method which is outlined above. Then, the method is assessed by using three sample problems. A good agreement is observed in the comparisons of the predictions of the method with those available in the literature. It is further found that the proposed method provides considerable saving in computer time compared to existing methods of literature. © 1997 by John Wiley & Sons, Ltd.