Nonlocal operators with local boundary conditions in higher dimensions


Aksoylu B., Celiker F., Kilicer O.

ADVANCES IN COMPUTATIONAL MATHEMATICS, vol.45, no.1, pp.453-492, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1007/s10444-018-9624-6
  • Journal Name: ADVANCES IN COMPUTATIONAL MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.453-492
  • Keywords: Nonlocal wave propagation, Nonlocal diffusion, Nonlocal operator, Local boundary condition, PERIDYNAMIC FORMULATION, DIFFUSION
  • Middle East Technical University Affiliated: Yes

Abstract

We present novel nonlocal governing operators in 2D/3D for wave propagation and diffusion. The operators are inspired by peridynamics. They agree with the original peridynamics operator in the bulk of the domain and simultaneously enforce local boundary conditions (BC). The main ingredients are periodic, antiperiodic, and mixed extensions of separable kernel functions together with even and odd parts of bivariate functions on rectangular/box domains. The operators are bounded and self-adjoint. 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 verify our theoretical findings. We also compare the solutions of the classical wave and heat equations to their nonlocal counterparts.