Solution of plane Dirichlet problem using compactly supported 2D wavelet scaling functions

• Autorzy: Katunin A.
• Języki publikacji: EN

Abstrakty

EN

The paper presents the solution of the homogeneous plane Dirichlet problem using the wavelet-Galerkin method with various 2D compactly supported wavelet scaling functions. An analysis of approximation accuracy was performed with respect to the orders of investigated wavelet scaling functions and the level of approximation. The most effective scaling functions for solving the Dirichlet problem were indicated and discussed.

Słowa kluczowe

EN

Dirichlet problem; wavelet-Galerkin method

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2012
• Tom: Vol. 11, nr 1
• Strony: 31--40
• Opis fizyczny: Bibliogr. 19 poz., rys., tab.

Twórcy

autor

Katunin A.

• Department of Fundamentals of Machinery Design, Silesian University of Technology, Poland,

Bibliografia

• [1] Chui C.K., Wavelets: A Mathematical Tool for Signal Analysis, SIAM Monographs on Mathematical Modeling and Computation, Society for Industrial and Applied Mathematics, Pennsylvania 1997.
• [2] Nikolaou M., You Y., Use of Wavelets for Numerical Solution of Differential Equations, [in:] Wavelet Applications in Chemical Engineering, eds. B. Joseph, R. Motard, Kluwer 1994, 209-274.
• [3] Lakestani M., Razzaghi M., Dehghan M., Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets, Math. Probl. Eng. 2005, 1, 113-121.
• [4] Neelov A.I., Goedecker S., An efficient numerical quadrature for the calculation of potential energy of wavefunctions expressed in the Daubechies wavelet basis, J. Comput. Phys. 2006, 217, 312-339.
• [5] Liu Ya, Liu Yi, Cen Zh, Multi-scale Daubechies wavelet-based method for 2-D elastic problems, Finite Elem. Anal. Des. 2011, 47, 334-341.
• [6] Akbari H., Kerayechian A., Coiflet-Galerkin method for solving second order BVPs with variable coefficients in three dimensions, Numer. Algor., in press, doi: 10.1007/s11075-012-9558-x.
• [7] Nowak Ł.D., Pasławska-Południak M., Twardowska K., On the convergence of the wavelet- Galerkin method for nonlinear filtering, Int. J. Math. Comput. Sci. 2010, 20, 93-108.
• [8] Lakestani M., Dehghan M., The solution of second-order nonlinear differential equation with Neumann boundary conditions using semi-orthogonal B-spline wavelets, Int. J. Comput. Math. 2006, 83, 685-694.
• [9] Glowinski R., Rieder A., Wells R.O., Zhou X., A wavelet multigrid preconditioner for Dirichlet boundary-value problems in general domains, Math. Mod. Numer. Anal. 1996, 30, 711-729.
• [10] Shiyou Y., Guangzheng N., Jingen Q., Ronglin L., Wavelet-Galerkin method for computations of electromagnetic fields, IEEE Trans. Magn. 1998, 34, 2493-2496.
• [11] Hashish H., Behiry S.H., Elsaid A., Solving the 2-D heat equations using wavelet-Galerkin method with variable time step, App. Math. Comput. 2009, 213, 209-215.
• [12] Yanan L., Liang S., Yinghua L., Zhangzhi C., Multi-scale B-spline method for 2-D elastic problems, App. Math. Mod. 2011, 35, 3685-3697.
• [13] Xiong L., Li H., Zhang L., Two dimensional tensor product B-spline wavelet scaling functions for the solution of two-dimensional unsteady diffusion equations, J. Ocean Univ. Chin. 2008, 7, 258-262.
• [14] Mallat S., A theory of multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 1989, 11, 674-693.
• [15] Daubechies I., Ten Lectures on Wavelets, SIAM, Philadelphia 1992.
• [16] Chui C.K., Introduction to Wavelets, Academic Press Professional, San Diego 1994.
• [17] Latto A., Resnikoff H.L., Tenenbaum E., The evaluation of connection coefficients of compactly supported wavelets, Proceedings of the French-USA Workshop on Wavelets and Turbulence, ed. Y. Maday, New York 1992.
• [18] Glowinski R., Pan T.W., Wells R.O., Zhou X., Wavelet and finite element solutions for the Neumann problem using fictitious domains, J. Comput. Phys. 1996, 126, 40-51.
• [19] Katunin A., Damage identification in composite plates using two-dimensional B-spline wavelets, Mech. Syst. Signal Pr. 2011, 25, 3153-3167.