  In this paper we design and analyze an explicit partitioned procedure for a
2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocal
Robin-type transmission condition. The nonlocal subproblem is modeled by the
nonlocal heat equation with a finite horizon parameter $\delta$ characterizing
the range of nonlocal interactions, and the local subproblem is described by
the classical heat equation. We consider a heterogeneous system where the local
and nonlocal subproblems present different physical properties, and employ no
overlapping region between the two subdomains. We first propose a new
generalization of classical local Neumann-type condition by converting the
local flux to a correction term in the nonlocal model, and show that the
proposed Neumann-type boundary formulation recovers the local case as
$O(\delta^2)$ in the $L^{\infty}$ norm. We then extend the nonlocal
Neumann-type boundary condition to a Robin-type boundary condition, and develop
a local-to-nonlocal coupling formulation with Robin-Dirichlet transmission
conditions. To stabilize the explicit coupling procedure and to achieve
asymptotic compatibility, the choice of the coefficient in the Robin condition
is obtained via amplification factor analysis for the discretized system with
coarse grids. Employing a high-order meshfree discretization method in the
nonlocal solver and a linear finite element method in the local solver, the
selection of optimal Robin coefficients are verified with numerical experiments
on heterogeneous and complicated domains. With the developed optimal coupling
strategy, we numerically demonstrate the coupling framework's asymptotic
convergence to the local limit with an $O(\delta)=O(h)$ rate, when there is a
fixed ratio between the horizon size $\delta$ and the spatial discretization
size $h$.
