ANHA(Applied and numerical harmonic analysis)was born as powerful tool of nonlinear analysis and then is applying widely to particular analysis, digital processing, diagnosis system of fault, image processing, financial time series processing. ANHA was born at the latter of 1980's and then after that it has been applied widely with the fashion in technology. The important problem is basis study of construction of wavelet basis.
By Y. Meyer, S. Mallat, I. Daubechies, D. Donoho, J. Benedetto, the MRA principle composing wavelet as a tool for nonlinear analysis and especial wavelet function were born. The all the class of wavelet is the set of functions satisfying admission condition of wavelet. Their achievement is limited to composition of some class of wavelet function and only principle method. In some case, only special wavelet function was get. Such as Meyer's wavelet, Daubechies's wavelet and so on.
The wavelet function specify technical function by it's mathematical behavior. We propose the method that compose the wavelet function with bandlimitted, normality, interpolation property, symmetry and orthogonal and we get the wavelet formula of the class.
And we proposed the united method of composing wavelet filter and then we get material wavelet filter. Therefore we can design optimal filter depends on technical subject.
We applied the result of wavelet basis function to the solver of Schrodinger equation, KDV equation and Maxwell equation.
And we get the excellent result with the precision of nano-order.
These results can be used in material design, exploration of the new electronic product and analysis of electronic information such as signal processing with high precision.
We will advance in ANHA and electronic information technology.
Specially, we studied on the adaptive wavelet collocation time domain method by composing our new interpolating wavelet for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources.
