Coifman wavelets in electromagnetic wave scattering by a groove in a conducting plane

Scattering ofelectromagnetic waves from a groove in an infinite conducting plane is studied using the Coifman wavelets (Coiflets) under the integral equation formulation. The induced current is expressed in terms ofthe known Kirchhoff solution plus a localized correction current in the vicinity ofthe groove. The Galerkin procedure is implemented, employing the Coiflets as expansion and testing functions to find the correction current numerically. Owing to the vanishing moments, the Coiflets lead to a one-point quadrature formula in O(h⁵), which reduces the computational effort in filling the impedance matrix entries. The resulting matrix is sparse, which is desirable for iterative algorithms. Numerical results show that the new method is 2 to 5 times faster than the pulse based method of moments.