A compression technique for the boundary integral equation reduced from Helmholtz equation

Abstract

Applying the trigonometric wavelets and the multiscale Galerkin method, we investigate the numerical solution of the boundary integral equation reduced from the exterior Dirichlet problem of Helmholtz equation by the potential theory. Consequently, we obtain a matrix compression strategy, which leads us to a fast algorithm. Our truncated treatment is simple, the computational complexity and the condition number of the truncated coefficient matrix are bounded by a constant. Furthermore, the entries of the stiffness matrix can be evaluated from the Fourier coefficients of the kernel of the boundary integral equation. Examples given for demonstrating our numerical method shorten the runtime obviously.

Keywords:

• matrix compression
• trigonometric wavelets
• multiscale Galerkin method
• Helmholtz equation
• boundary integral equation

2000 AMS Subject Classifications:

• 65N38
• 65F30
• 42C40
• 65T50

Acknowledgements

This work was partially supported by the Hunan Provincial Natural Science Foundation of China (No. 11JJ6003), the Scientific Research Fund of Hunan Provincial Education Department (No. 10B040) and the Postdoctoral Science Foundation of Central South University.