Utilization of wavelet concepts in finite elements for efficient solution of Maxwell´s equation

Summary form only given. The wavelet concept has been introduced in the applied mathematics literature as a new mathematical subject for performing localized "time-frequency" characterization. It is a versatile tool with "very rich mathematical content and great potential for applications". Because of this localized property both in the original and in the transform domain it is expected that its application particularly to solution of partial differential equations would be quite interesting. Utilization of a wavelet type basis has the advantage that the condition number of the system matrix does not increase rapidly with an increase in the number of unknowns unlike the original version of the finite element methods. In the paper the wavelet concepts have been developed and explained with application to 1D-differential equations. It is shown how this can be incorporated in a Galerkin\´s method (or equivalently, e.g. finite element method) for efficient solution of 2D problems. Numerical examples are presented for efficient solution of waveguide problems utilizing this approach.<>