Nonlocal operators with local boundary conditions in higher dimensions

2019-02-01
Aksoylu, Burak
Celiker, Fatih
Kilicer, Orsan
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.
ADVANCES IN COMPUTATIONAL MATHEMATICS

Suggestions

Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients
ÖZBEKLER, ABDULLAH; Wong, J. S. W.; Zafer, Ağacık (Elsevier BV, 2011-07-01)
In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions.
A new boundary element formulation for wave load analysis
Yalcin, O. Fatih; Mengi, Yalcin (Springer Science and Business Media LLC, 2013-10-01)
A new boundary element (BEM) formulation is proposed for wave load analysis of submerged or floating bodies. The presented formulation, through establishing an impedance relation, permits the evaluation of the hydrodynamic coefficients (added mass and damping coefficients) and the coefficients of wave exciting forces systematically in terms of system matrices of BEM without solving any special problem, such as, unit velocity or unit excitation problem. It also eliminates the need for scattering analysis in ...
Strictly singular operators and isomorphisms of Cartesian products of power series spaces
Djakov, PB; Onal, S; Terzioglu, T; Yurdakul, Murat Hayrettin (1998-01-02)
V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E-0(p)(a) x E-infinity(q) (b) where 1 less than or equal to p, q < infinity, p not equal q, a = (a(n))(n=1)(infinity) and b = (b(n))(n=1)(infinity) are sequences of positive numbers and E-0(p)(a), E(infinity)q(b) are respectively l(p)-finite and l(q)-infinite type...
Global existence and boundedness for a class of second-order nonlinear differential equations
Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01)
In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM
Dosi, Anar (American Mathematical Society (AMS), 2011-02-01)
In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum *-algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative Albrecht-Vasilescu extension theorem, which in turn solves the quantum moment problem.
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.