Efficient optimization-based quadrature for variational discretization of nonlocal problems
DOI10.1016/j.cma.2022.115104OpenAlexW4281389320MaRDI QIDQ2156793
Zhaoxiang Shen, Marta D'Elia, Marco Pasetto, Nathaniel Trask, Xiaochuan Tian, David Kamensky
Publication date: 20 July 2022
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.12391
numerical quadraturefinite element discretizationsperidynamicsgeneralized moving least squaresnonlocal models
Numerical optimization and variational techniques (65K10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical quadrature and cubature formulas (65D32) Peridynamics (74A70)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Identification of the diffusion parameter in nonlocal steady diffusion problems
- Analysis of a scalar nonlocal peridynamic model with a sign changing kernel
- Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approach
- Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization
- Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Reformulation of elasticity theory for discontinuities and long-range forces
- A reproducing kernel enhanced approach for peridynamic solutions
- An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics
- Data-driven learning of nonlocal physics from high-fidelity synthetic data
- Bilevel parameter learning for nonlocal image denoising models
- Towards a unified theory of fractional and nonlocal vector calculus
- nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
- Data-driven fractional subgrid-scale modeling for scalar turbulence: a nonlocal LES approach
- An energy-based coupling approach to nonlocal interface problems
- A machine-learning framework for peridynamic material models with physical constraints
- A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems
- Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes
- The Dirichlet problem for nonlocal operators
- A generalized moving least square reproducing kernel method
- On generalized moving least squares and diffuse derivatives
- Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
- A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems
- Nonlocal Linear Image Regularization and Supervised Segmentation
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints
- Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion
- A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems
- Image Denoising Methods. A New Nonlocal Principle
- Machine Learning of Space-Fractional Differential Equations
- fPINNs: Fractional Physics-Informed Neural Networks
- Two-point stress–strain-rate correlation structure and non-local eddy viscosity in turbulent flows
- Numerical methods for nonlocal and fractional models
- Stochastic models for fractional calculus
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
This page was built for publication: Efficient optimization-based quadrature for variational discretization of nonlocal problems
