Multiresolution analysis using biorthogonal and interpolating wavelets

This paper discusses a multiresolution analysis for the discretisation of Maxwell equations based on second-generation wavelets (biorthogonal and interpolating). When this type of wavelet is used the physical representation and the scaling representation are essentially the same. The scaling coefficients and the sampling values coincide. Since the coefficients are directly obtained from the physical representation it is possible to implement nonlinear operators (products squares etc.) in an easy way. The implementation of the derivative is more complex and takes advantage of the reduction of the dimensionality given by multiresolution representation.