Periodic wavelet expansions for analysis of scattering from metallic cylinders

The application of wavelet-transform representations to the solution of integral equations and electromagnetic scattering problems has been a subject of much research. However, a difficulty is encountered when one is pursuing a complete and orthonormal set of basis functions that is made only of translation and dilation of a given smooth function. The difficulty lies in the inability to span a function of finite support by means of such a set, unless the domain of definition of some of the basis functions is allowed to extend beyond that finite support. The equivalent current in a problem of scattering from a finite-size perfectly conducting body is defined on the body surface which is inherently of finite size and the question of the number of wavelets and their proper location outside the scatterer surface naturally arises. This paper proposes a way to circumvent this difficulty in scattering problems involving two-dimensional cylinders by using periodic wavelet expansions. The periodic wavelets are implemented in a Galerkin-type method of moments solution to the magnetic field integral equation for the problem of scattering from a perfectly conducting cylinder. It is shown that by using this approach, and subsequently applying a threshold procedure, the resultant moment-method matrix, which is usually dense when standard bases are used, turns out sparsely populated, and hence a significant decrease in storage requirements and execution times is gained. Thus, the periodic wavelets can offer the very same advantages of the conventional systems in the more realistic case of finite volume scatterers.<>