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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 ...