Numerical Solution Of Wave Propagation Problems Based On Zero-moment Scaling Function

The study of wave scattering problem is the basis of the field of ultrasonic non-destructivetesting. As a simple and common wave, the propagation of SH wave satisfy the HelmholtzEquation and Wave Equation. In recent years, wavelet analysis has become a research hotspotin the area of numerical analysis, it is especially active in the numerical solution of boundaryintegral equation. Zero-moment scaling function has advantages in numerically solution ofHelmholtz Equation. The aim of this paper is to introduce zero-moment scaling function tothe numerical calculation of wave propagation problems, thus provides new ideas for solvingthe wave scattering problems.Firstly, according to the properties of wavelet multi-resolution analysis and double scalingrelations, specific values of the zero-moment scaling functions are calculated. Based onabove and the construction method of periodic wavelet scaling function and intervallicwavelet scaling function, the specific values of different scaling functions are calculated.Secondly, the boundary function of the boundary integral equation is expanded by thezero-moment scaling function as basis function, by using the properties of zero-momentscaling function, the method for solution of boundary integral equation based on the zero-moment is derived. Then, three examples about acoustic radiation and scattering problems aresolved by conventional boundary element method, higher order and lower order zero-momentscaling function method and periodic zero moment scaling function method respectively.Numerical results of the examples show that the method proposed in this paper is efficientand accurate, and also show the advantage which periodic wavelet method has, relative to thestandard wavelet and intervallic wavelet method in the solution of the boundary integralequation on the edge of interval.Finally, by use of the conventional finite element method, the two-dimensional Helmholtzequation and time domain Wave equation is solved.SH wave scattering problems is calculatedby solving some numerical examples.