The Representation of Derivative Operators in Yee´s Staggered Grid in Bases of Compactly Supported Daubechies Wavelets

During our work on adaptive algorithms for FDTD we derived an effective technique to calculate coefficients for a wavelet-based higher-order derivative approximation in Yee´s staggered grid. Other researchers have evaluated the coefficients numerically, either directly [1] or after a Fourier Transform [2]. We describe a technique based on the Two Scale Relation (TSR) of scaling functions that yields the exact values for the stencils. In the end of the paper, we present an application (anisotropic uniaxial PML formulated by Gedney) of the coefficients.