Nonlocal operators with local boundary conditions in higher dimensions

Aksoylu B., Celiker F., Kilicer O.

ADVANCES IN COMPUTATIONAL MATHEMATICS, cilt.45, sa.1, ss.453-492, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s10444-018-9624-6
  • Dergi Adı: ADVANCES IN COMPUTATIONAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.453-492
  • Anahtar Kelimeler: Nonlocal wave propagation, Nonlocal diffusion, Nonlocal operator, Local boundary condition, PERIDYNAMIC FORMULATION, DIFFUSION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.