Current distribution on a scatterer obtained by integral equations with semi-orthogonal and orthogonal wavelet basis sets

Originally the method of moments integral equation formulations for the electromagnetic field contained basis functions that offered simplicity, as in the case of subdomain pulses, or compatibility with the expected form of the solution, as with sinusoidal domain basis functions on a resonant wire scatterer. Now wavelet bases appear to offer an advantage over classical bases because the wavelet impedance matrix for a given scatterer is more sparse, yet it is of approximately the same order as that of a classical basis. This is because the impedance matrix elements obtained with a classical basis function contain components that convey only amplitude and phase information while each wavelet matrix element is constructed as a product of the amplitude, phase and the frequency information. Two types of wavelets are compared in order to show that the semi-orthogonal wavelet is best suited for integral equation solutions. The Battle-Lemarie orthogonal wavelet and the B-spline semi-orthogonal wavelet are each applied on the interval [0,1] in order to solve for the current distribution on a straight thin wire illuminated by a plane wave.