An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics

Type: Article

Publication Date: 2018-09-05

Citations: 80

DOI: https://doi.org/10.1016/j.cma.2018.08.016

Locations

  • Computer Methods in Applied Mechanics and Engineering - View
  • arXiv (Cornell University) - View - PDF
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) - View - PDF

Similar Works

Action Title Year Authors
+ PDF Chat Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation 2020 Yu Leng
Xiaochuan Tian
Nathaniel Trask
John T. Foster
+ Computational Methods Based on Peridynamics and Nonlocal Operators 2023 Timon Rabczuk
Huilong Ren
Xiaoying Zhuang
+ Efficient Numerical Methods for Non-local Operators 2010 Steffen BĂśrm
+ Numerical Quadrature in the Presence of a Singularity 1967 Walter Gautschi
+ Numerical quadrature 2010 Michael R. King
Nipa A. Mody
+ Nonlinear quadrature rules in the presence of a singularity 1978 H. Werner
L. Wuytack
+ Numerical Quadrature 2004 Kenneth A. Eriksson
Donald Estep
Claes Johnson
+ A brief review of numerical methods for collision operators 2003 StĂŠphane Cordier
Simona Mancini
+ Numerical methods for nonlocal problems 2018 Adem Kaya
+ Geometric and Low-regularity Integrators for the Matching and Preservation of Structure in the computation of dispersive Equations 2022
+ Unbounded divergence of simple quadrature formulas 1991 Ioan Muntean
+ Low-Regularity Integrator for the Quadratic NLS Equation 2022 翠 厁
+ Truncated Gauss-Laguerre quadrature rules 2000 G. Mastroianni
Giovanni Monegato
+ Low Regularity Integrators for the Conservative Allen–Cahn Equation with a Nonlocal Constraint 2024 Cao-Kha Doan
Thi‐Thao‐Phuong Hoang
Lili Ju
+ Numerical quadrature methods of analytic functions 1978 Dorel Homentcovschi
+ Numerical integration rules near gaussian quadrature 1973 Charles A. Micchelli
T. J. Rivlin
+ A Numerical Quadrature for the Schwarz-Chimera Method 2007 J.-B. Apoung Kamga
Olivier Pironneau
+ Numerical quadrature problems in the GOCE spacewise approach 2003 F. Migliaccio
M. Reguzzoni
Fernando Sansò
+ Integrable difference equations and numerical analysis algorithms 1996 V. Papageorgiou
B. Grammaticos
A. Ramani
+ Numerics for nonlocal potentials and highly-oscillatory PDEs 2016

Works That Cite This (47)

Action Title Year Authors
+ PDF Chat Multi-time-step coupling of peridynamics and classical continuum mechanics for dynamic brittle fracture 2024 Jiandong Zhong
Fei Han
Zongliang Du
Xu Guo
+ Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon 2021 Xiaoxuan Yu
Yan Xu
Qiang Du
+ PDF Chat A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials 2022 Somdatta Goswami
Minglang Yin
Yue Yu
George Em Karniadakis
+ PDF Chat Simulating Grain Shape Effects and Damage in Granular Media Using PeriDEM 2023 Debdeep Bhattacharya
Robert Lipton
+ Asymptotically compatible meshfree discretization of state-based peridynamics for linearly elastic composite materials 2019 Nathaniel Trask
Benjamin Huntington
David John Littlewood
+ PDF Chat A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials 2022 Yi‐Ming Fan
Huaiqian You
Xiaochuan Tian
Yang Xiu
Xingjie Li
Naveen Prakash
Yue Yu
+ Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws 2020 Huaiqian You
Yue Yu
Stewart Silling
Marta D’Elia
+ PDF Chat On the treatment of boundary conditions for bond-based peridynamic models 2020 Serge Prudhomme
P. Diehl
+ PDF Chat An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems 2021 Huaiqian You
Xin LĂź
Nathaniel Trask
Yue Yu
+ PDF Chat On the Prescription of Boundary Conditions for Nonlocal Poisson’s and Peridynamics Models 2022 Marta D’Elia
Yue Yu