New wavelet-like basis functions for the 2D mode analysis of coupled microstrips

Wavelets have been used as basis functions in the method of moments. These functions have certain advantages over classical (pulse) basis functions. They provide a sparse system matrix allowing fast matrix manipulation techniques, such as the calculation of the determinant or the solution of a system of linear equations. They also provide a multiresolution approach. This means that the system matrix of a coarser description of the problem is a subblock of the matrix belonging to the finer description. The present article deals with a new wavelet-like class of basis functions. The first part describes the construction of several sets of such basis functions. A basis is actually constructed for each value of the parameters length and order of the basis functions. The performance of the constructed basis is illustrated by its application to the 2D mode analysis of a coupled microstrip example. Classical and new basis are compared, the emphasis being on the sparseness of the resulting system matrix.