Now showing items 1-4 of 4
On a class of nonlocal wave equations from applications
(American Institute of Physics Inc., 2016-06)
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods ...
Comparison of Nonlocal Operators Utilizing Perturbation Analysis
(Springer Verlag, 2016)
We present a comparative study of integral operators used in nonlocal problems. The size of nonlocality is determined by the parameter ?. The authors recently discovered a way to incorporate local boundary conditions into ...
Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces
(Society for Industrial and Applied Mathematics Publications, 2014-03)
We study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional Sobolev spaces. These operators are used, for instance, in peridynamics formulation and nonlocal diffusion. In one ...
Robust preconditioners for the high-contrast Stokes equation
(Elsevier Science Bv, 2014-03)
We consider the Stokes equation with high-contrast viscosity coefficients. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by ...