Absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations

The solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques, which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition (ABC) is applied. In order to minimize the size of the domain to be meshed and, consequently, the number of unknowns, if may be advisable to implement ABC´s devised for outer boundaries of arbitrary shapes. Such ABC´s are obtained for the 3D scalar and vector wave equations; they incorporate most of existing boundary conditions. When used in conjunction with a finite element technique, the numerical results derived by using a simplified form of these ABC´s compare favourably to those obtained by using a rigorous hybrid finite element-integral equation formulation. These boundary conditions have been obtained in the frequency-domain framework; they may, however, be used in time-domain calculations