Numerical methods for the nonlocal wave equation of the peridynamics

DOI10.1016/j.apnum.2018.11.007zbMath1436.65195arXiv1808.00061OpenAlexW2962982010WikidataQ128882913 ScholiaQ128882913MaRDI QIDQ1989378

S. F. Pellegrino, Francesco Maddalena, A. Fanizzi, Giuseppe Maria Coclite, Luciano Lopez

Publication date: 21 April 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.00061

zbMATH Keywords

quadrature formulaspectral methodsperidynamic equationtrigonometric time discretization

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Integro-partial differential equations (45K05) Linear elasticity with initial stresses (74B10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical integration (65D30) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (14)

Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics ⋮ A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation ⋮ A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture ⋮ A space-time discretization of a nonlinear peridynamic model on a 2D lamina ⋮ A computationally efficient strategy for time-fractional diffusion-reaction equations ⋮ Dispersive effects in two- and three-dimensional peridynamics ⋮ A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models ⋮ Regularity and convergence results for nonlocal peridynamic equations with truncated tensor kernels ⋮ A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes ⋮ Regularity of solutions for nonlocal diffusion equations on periodic distributions ⋮ A fast convolution-based method for peridynamic transient diffusion in arbitrary domains ⋮ Well-posedness and regularity of Caputo-Hadamard fractional stochastic differential equations ⋮ Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics ⋮ A fast-convolution based space-time Chebyshev spectral method for peridynamic models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral properties and conservation laws in mimetic finite difference methods for PDEs
• Survey of existence results in nonlinear peridynamics in comparison with local elastodynamics
• Elastic media with microstructure. I: One-dimensional models. (Transl. from the Russian)
• The effect of long-range forces on the dynamics of a bar
• Preserving geometric properties of the exponential matrix by block Krylov subspace methods
• Rational approximation to trigonometric operators
• Computing the matrix cosine
• Free damage propagation with memory
• Mimetic finite difference methods for Hamiltonian wave equations in 2D
• A peridynamic model of fracture mechanics with bond-breaking
• Reformulation of elasticity theory for discontinuities and long-range forces
• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• On some generalizations of the implicit Euler method for discontinuous fractional differential equations
• Dynamic brittle fracture as a small horizon limit of peridynamics
• Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function
• Elasticity theory of materials with long range cohesive forces
• On nonlocal elasticity
• Peridynamic Theory and Its Applications
• Exponential integrators
• Nonlocal Continuum Field Theories
• On a class of nonlocal wave equations from applications
• An Efficient Solver for the Incompressible Navier–Stokes Equations in Rotation Form
• THE PERIDYNAMIC EQUATION AND ITS SPATIAL DISCRETISATION
• Convergence, adaptive refinement, and scaling in 1D peridynamics
• Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• Geometric numerical integration illustrated by the Störmer–Verlet method
• Analysis of Projection Methods for Rational Function Approximation to the Matrix Exponential
• Computation of Gauss-type quadrature formulas

This page was built for publication: Numerical methods for the nonlocal wave equation of the peridynamics