Nonreflecting Artificial Boundary Conditions For The Time-dependent Problems

In this paper, we investigate the nonreflecting artificial boundary condi-tions(NRABCs) and their numerical methods for the time-dependent problems.Part I, a hyperbolic initial boundary value problem in unbounded domains in two dimensions is studied. Three kinds of equivalent exact and approximate artificial boundary conditions are obtained on circular boundary by a constructive method. After we introduce an artificial boundary, we get an initial-boundary value problem, which is equivalent to the original problem in a bounded domain. In addition we obtain three exact and approximate artificial boundary conditions. Finally, some numerical examples are presented. Numerical results show that our method is efficient.Part II, a parabolic initial boundary value problem in unbounded domains in three dimensions is studied. An exact artificial boundary condition is obtained on a spherical boundary by a constructive method. After we introduce an artificial boundary, we get an initial-boundary value problem, which is equivalent to the original problem in a bounded domain. Finally, a numerical example is presented to show the performance of the method.