Detroit, MI 48202
Speaker: Burak Aksoylu, Wayne State University
Title: Novel nonlocal operators in arbitrary dimension enforcing local boundary conditions
We present novel governing operators in arbitrary dimension for nonlocal diffusion. The operators are inspired by the theory of peridynamics (PD). They agree with the original PD operator in the bulk of the domain and simultaneously enforce local boundary conditions. We present pure and mixed combinations of Neumann, Dirichlet, periodic, and anti periodic boundary conditions. Our construction is systematic and easy to follow. We provide numerical experiments that validate our theoretical findings.
We recently proved that the nonlocal diffusion operator is a function of the classical operator. This observation opened a gateway to incorporate local boundary conditions to nonlocal problems on bounded domains. The main tool we use to define the novel governing operators is functional calculus, in which we replace the classical governing operator by a suitable function of it. We present how to apply functional calculus to general nonlocal problems in a methodical way.