Title: Novel nonlocal operators in arbitrary dimension enforcing local boundary conditions

Date: 10/27/2017

Time: 4:10 PM - 5:00 PM

Place: C100 Wells Hall

Speaker: Prof. Fatih Celiker, Department of Mathematics, Wayne State University

Abstract: We present novel nonlocal governing operators in 2D/3D for
wave propagation and diffusion that enforce local boundary conditions
(BC). The main ingredients are periodic, antiperiodic, and mixed
extensions of kernel functions together with even and odd parts of
bivariate functions. We present all possible 36 different types of BC
in 2D which include pure and mixed combinations of Neumann, Dirichlet,
periodic, and antiperiodic BC. Our construction is systematic and
easy to follow. We provide numerical experiments that validate our
theoretical findings. We also compare the solutions of the classical
wave and heat equations to their nonlocal counterparts.