Numerical solution of diffraction problems by a least-squares finite element method

Consider the diffraction of a time-harmonic wave incident upon a periodic (grating) structure. Under certain assumptions, the diffraction problem may be modelled by a Helmholtz equation with transparent boundary conditions, in this paper, the diffraction problem is formulated as a first-order system of linear equations and solved by a least-squares finite element method. The method follows the general minus one norm approach of Bramble, Lazarov, and Pasciak. Our computational experiments indicate that the method is accurate with the optimal convergence property, and it is capable of dealing with complicated grating structures. Copyright (C) 2000 John Wiley & Sons, Ltd.