Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling

DOI10.1137/18M1184576zbMath1447.45001WikidataQ127202621 ScholiaQ127202621MaRDI QIDQ5222101

Yunzhe Tao, Xiaochuan Tian, Qiang Du

Publication date: 31 March 2020

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

zbMATH Keywords

finite elementnonlocal diffusionnonlocal operatorperidynamic modellocal-nonlocal couplingheterogeneous localization

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Energy minimization in equilibrium problems in solid mechanics (74G65) Integral operators (47G10) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Linear integral equations (45A05)

Related Items (15)

Nonlocal trace spaces and extension results for nonlocal calculus ⋮ A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization ⋮ Numerical methods for nonlocal and fractional models ⋮ A comparative review of peridynamics and phase-field models for engineering fracture mechanics ⋮ Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions ⋮ Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization ⋮ An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions ⋮ Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings ⋮ Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon ⋮ An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions ⋮ Quasi-nonlocal Coupling of Nonlocal Diffusions ⋮ A partitioned coupling framework for peridynamics and classical theory: analysis and simulations ⋮ Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models ⋮ Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues ⋮ Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements

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