A fast trigonometric wavelets method for the biharmonic equation

Abstract

In this article, the trigonometric wavelets are used as trial functions to discretize the natural boundary integral equation reduced from the biharmonic equation in an exterior circular. Consequently, we obtain a fast numerical method for the natural boundary integral equation which has an unique solution in the quotient space. We decompose the stiffness matrix in our numerical method into four symmetrical and circulant submatrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Examples are given for demonstrating that our method has good accuracy even though the exact solution is almost singular.

Keywords:

• natural boundary integral equation
• trigonometric wavelets
• matrix decomposition
• FFT
• biharmonic equation

AMS Subject Classifications::

• 65N38
• 65F30
• 42C40
• 65T50

Acknowledgements

This work was partially supported by the Natural Science Foundation of Hunan Province (No. 07JJ3006), the Scientific Research Fund of Hunan Provincial Education Department (Nos. 07C335 and 07A025), and the Construct Program of the Key Discipline in Hunan Province.