Quasinonlocal coupling of nonlocal diffusions
This work provides a novel coupling method for nonlocal diffusion models, which is important for multiscale modeling in materials science and engineering.
The authors developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method. The coupling model is coercive and satisfies the maximum principle, and a numerical example shows that the coupled diffusion agrees with the fully nonlocal diffusion while the local diffusion does not.
We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with respect to the energy norms induced by the nonlocal diffusion kernels as well as the $L^2$ norm, and it satisfies the maximum principle. A finite difference approximation is used to discretize the coupled system, which inherits the property from the continuous formulation. Furthermore, we design a numerical example which shows the discrepancy between the fully nonlocal and fully local diffusions, whereas the result of the coupled diffusion agrees with that of the fully nonlocal diffusion.