Artificial Boundary Conditions For Two Exterior Problems With Concave Angles

In this paper, we investigate the artificial boundary conditions for the exterior hyperbolic problems and the parabolic problems with concave angles by a constructive method and their numerical methods.Part I, the artificial boundary condition for the exterior hyperbolic problems with concave angles and its numerical methods are studied. Three kinds of equivalent exact and approximate artificial boundary conditions arc obtained on circular boundary by a constructive method. An artificial boundaryΓ_R is first introduced, Three kinds of equivalent artificial boundary conditions arc obtained. Secondly, the original problem is reduced to a computation problem in a bounded domain, which is equivalent to the original problem, by means of artificial boundary conditions. The computation problem is solved numerically by the finite difference method and finite clement method. Finally, some numerical examples are presented. Numerical results show that artificial boundary conditions arc efficient.Part II, the artificial boundary condition for the exterior parabolic problems with concave angles and its numerical methods are studied. Firstly, An artificial boundaryΓ_R is introduced, Artificial boundary conditions onΓ_R arc obtained. Secondly, the original problem is reduced to a computation problem in a bounded domain, which is equivalent to the original problem, by means of artificial boundary conditions. Finally, some numerical examples arc presented to demonstrate the performance of the method in this paper.