A collocation method based on localized radial basis functions with reproducibility for nonlocal diffusion models

DOI10.1007/s40314-021-01665-6zbMath1476.65343OpenAlexW3205738902MaRDI QIDQ2052316

Yu-Feng Nie, Jia-Shu Lu

Publication date: 25 November 2021

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-021-01665-6

zbMATH Keywords

collocation methodnonlocal diffusionreproducing kernel methodlocalized radial basis functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Linear integral equations (45A05)

Related Items (6)

Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints ⋮ A reduced-order fast reproducing kernel collocation method for nonlocal models with inhomogeneous volume constraints ⋮ On weak solutions for a nonlocal model with nonlocal damping term ⋮ Localized Chebyshev and MLS collocation methods for solving 2D steady state nonlocal diffusion and peridynamic equations ⋮ Adaptive residual Refinement in an RBF Finite difference scheme for 2D time-dependent problems ⋮ An Efficient Jacobi Spectral Collocation Method with Nonlocal Quadrature Rules for Multi-Dimensional Volume-Constrained Nonlocal Models

Cites Work

• Unnamed Item
• A radial basis function partition of unity collocation method for convection-diffusion equations arising in financial applications
• Radial basis collocation methods for elliptic boundary value problems
• Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
• Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations
• A fast discontinuous Galerkin method for a bond-based linear peridynamic model discretized on a locally refined composite mesh
• 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
• Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects
• Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
• Fast algorithm for computing nonlocal operators with finite interaction distance
• A preconditioned fast finite difference scheme for space-fractional diffusion equations in convex domains
• A conforming DG method for linear nonlocal models with integrable kernels
• Nonlocal convection-diffusion volume-constrained problems and jump processes
• Reproducing kernel enhanced local radial basis collocation method
• Radial Basis Functions
• A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Reproducing kernel particle methods
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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