English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we design and analyze an explicit partitioned procedure for a2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocalRobin-type transmission condition. The nonlocal subproblem is modeled by thenonlocal heat equation with a finite horizon parameter $\delta$ characterizingthe range of nonlocal interactions, and the local subproblem is described bythe classical heat equation. We consider a heterogeneous system where the localand nonlocal subproblems present different physical properties, and employ nooverlapping region between the two subdomains. We first propose a newgeneralization of classical local Neumann-type condition by converting thelocal flux to a correction term in the nonlocal model, and show that theproposed Neumann-type boundary formulation recovers the local case as$O(\delta^2)$ in the $L^{\infty}$ norm. We then extend the nonlocalNeumann-type boundary condition to a Robin-type boundary condition, and developa local-to-nonlocal coupling formulation with Robin-Dirichlet transmissionconditions. To stabilize the explicit coupling procedure and to achieveasymptotic compatibility, the choice of the coefficient in the Robin conditionis obtained via amplification factor analysis for the discretized system withcoarse grids. Employing a high-order meshfree discretization method in thenonlocal solver and a linear finite element method in the local solver, theselection of optimal Robin coefficients are verified with numerical experimentson heterogeneous and complicated domains. With the developed optimal couplingstrategy, we numerically demonstrate the coupling framework's asymptoticconvergence to the local limit with an $O(\delta)=O(h)$ rate, when there is afixed ratio between the horizon size $\delta$ and the spatial discretizationsize $h$.

An Asymptotically Compatible Formulation for Local-to-Nonlocal Coupling Problems without Overlapping Regions