Nonlocal operators with local boundary conditions in higher dimensions

Date

2019-02-01

Author

Aksoylu, Burak
Celiker, Fatih
Kilicer, Orsan

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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.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/67242

Journal

ADVANCES IN COMPUTATIONAL MATHEMATICS

DOI

https://doi.org/10.1007/s10444-018-9624-6

Collections

Department of Mathematics, Article

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Citation Formats

B. Aksoylu, F. Celiker, and O. Kilicer, “Nonlocal operators with local boundary conditions in higher dimensions,” ADVANCES IN COMPUTATIONAL MATHEMATICS, pp. 453–492, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67242.