A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
Abstract Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining
nonlocal and local modeling descriptions of a given system into a unified coupled …
nonlocal and local modeling descriptions of a given system into a unified coupled …
Overall equilibrium in the coupling of peridynamics and classical continuum mechanics
Coupling peridynamics based computational tools with those using classical continuum
mechanics can be very beneficial, because it can provide a means to generate a …
mechanics can be very beneficial, because it can provide a means to generate a …
[BOOK][B] Nonlocal Modeling, Analysis, and Computation: Nonlocal Modeling, Analysis, and Computation
Q Du - 2019 - SIAM
Nonlocal Modeling, Analysis, and Computation : Back Matter Page 1 Bibliography [1] L.
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …
A partitioned coupling framework for peridynamics and classical theory: analysis and simulations
We develop and analyze a concurrent framework for coupling peridynamics and the
corresponding classical elasticity theory, with applications to the numerical simulations of …
corresponding classical elasticity theory, with applications to the numerical simulations of …
An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlap** regions
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 …
to-nonlocal (LtN) coupling problem, based on a new nonlocal Robin-type transmission …
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling
Motivated by recent development on nonlocal mechanical models like peridynamics, we
consider nonlocal integral models with a spatially varying horizon that allows the finite range …
consider nonlocal integral models with a spatially varying horizon that allows the finite range …
Fractional potential: A new perspective on the fractional Laplacian problem on bounded domains
In this work, the fractional Laplacian operator is studied based on its spectral definition for a
bounded, one-dimensional domain. We first note that both the analytical and numerical …
bounded, one-dimensional domain. We first note that both the analytical and numerical …
An investigation of space distributed-order models for simulating anomalous transport in a binary medium
Recent studies highlight that diffusion processes in highly heterogeneous, fractal-like media
can exhibit anomalous transport phenomena, which motivates us to consider the use of …
can exhibit anomalous transport phenomena, which motivates us to consider the use of …
A domain decomposition scheme for couplings between local and nonlocal equations
We study a natural alternating method of Schwarz type (domain decomposition) for a certain
class of couplings between local and nonlocal operators. We show that our method fits into …
class of couplings between local and nonlocal operators. We show that our method fits into …
Coupling local and nonlocal evolution equations
We prove existence, uniqueness and several qualitative properties for evolution equations
that combine local and nonlocal diffusion operators acting in different subdomains and …
that combine local and nonlocal diffusion operators acting in different subdomains and …