| This dissertation contains studies on numerical techniques for solving boundary value problems in infinite domains by introducing artificial boundary conditions (ABC). The problem domain is assumed to be composed of a large regular domain, which can be handled analytically, and a small irregular region, which must be treated by numerically. One example is the atomistic strain model problem with a film deposited on a semi-infinite substrate which occurs during the total elastic energy minimization of a solid composed of two materials.; The method suggested here can be described as follows: First an artificial boundary is introduced, thus deviding a whole domain into a small computational domain and a semi-infinite domain. This boundary is chosen to be a line in 2D and a plane in 3D. Next, on this artificial boundary we find a relation between unknown variables and their derivatives. For example, for the linear elasticity problem, the relations between the displacements and the normal stress tensor are obtained. Results are consistent with the energy minimization problem. Lastly, we use this ABC as a boundary condition on the artificial boundary, and solve the problem in the small computational domain.; We will show that this ABC preseves important properties such as symmetry and the total energy of the system. The method is applied to the continuum elasticity problems; the discrete elasticity problems and atomistic strain model problems. Numerical examples are given for each case. |
