Implicit Artificial Boundary Conditions

In this chapter, we discuss the implicit ABCs for the exterior problem of 2-D and 3-D Poisson equations, the Helmholtz equation, and the Navier system, and for the wave equation on unbounded domains. By using artificial boundaries, the original problems are reduced to boundary or initial boundary value problems on bounded computational domains. Implicit boundary conditions on the artificial boundaries are obtained, and then the finite element or finite difference method is applied to solve the reduced problems. Some error estimates are also given.