Applied Math Colloquium
Absorbing Boundary Conditions for Atomic and Electronic-level Models
The molecular dynamics model and time-dependent Schrodinger equation have been widely used to model material structures and optical properties. Direct simulations based on these models, however, inevitably involve an enormous amount of degrees of freedom. This talk will present a formulation of absorbing boundary conditions (ABC) so that the computation can be confined to much smaller subdomains to significantly reduce the computational cost. In particular, we will represent the boundary conditions as a Dirichlet-to-Neumann map by using lattice Green's functions. Our emphasis will be placed on the flexibility to deal with domains of general geometry and ensuring the stability of the boundary conditions.