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

In order to minimize the size of the domain to be meshed and, consequently, the number of unknowns, it may be advisable to implement ABCs (absorbing boundary conditions) devised for outer boundaries of arbitrary shapes. Such ABCs are obtained for the 3-D scalar and vector wave equations. Most already published boundary conditions for the 2-D and 3-D problems are found to be particular cases of the ones presented here. The numerical implementation of these ABCs is particularly simple and, when used in conjunction with a finite element technique, they lead to symmetric matrices. The numerical results derived by using these ABCs compare favorably to those obtained by using a rigorous hybrid finite element - integral equation formulation.<>