Exact and approximate artificial boundary conditions for the hyperbolic problems in unbounded domains

In this paper, the numerical solutions of the problems of wave equation in two dimensions in unbounded domains are considered. For a given problem, we introduce an artificial boundary B to make the computational domain finite. Three kinds of equivalent exact and approximate artificial boundary conditions are obtained on circular artificial boundary B by a constructive method. On the artificial boundary B, we propose an exact or approximate boundary condition to reduce the given problem an initial-boundary value problem of wave equation in the finite computational domain, which is equivalent to the original problem. Then the finite difference method and finite element method are used to solve the reduced problem in the finite computational domain. Some numerical examples are presented to show the feasibility and effectiveness of the method given in this paper.