Finite element implementation of Bayliss-Turkel boundary operators in the three-dimensional vector wave equation

摘要

The finite element solution of the vector Helmholtz equation is more difficult than that of the scalar one. Absorbing boundary conditions (ABCs) that were developed earlier for the vector wave equation were complex [l]-[3]. In fact, the numericalimplementations of second-order ABCs were the only that were reported in the literature because ABCs of order three or higher were immensely difficult to implement in a finite element numerical code. Secondorder operators were found to yield satisfactorysolutions only when the outer boundary was positioned one or more wavelengths away from the scattererP thus increasing the computational cost substantially. Absorptive material, on the other hand, such as the perfectly matched layer (PML), promisesperfect matching in the analytic domain only, and the performance when incorporated into a discrete system might not be very satisfactory. The development Of PML for three-dimensional spherical coordinates has recently been reportedin [4],[6].