Smooth local cosine based Galerkin method for scattering problems

The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.