A fast discontinuous Galerkin method for a bond-based linear peridynamic model discretized on a locally refined composite mesh
DOI10.1007/s10915-018-0645-6zbMath1397.65279OpenAlexW2785324926MaRDI QIDQ1669982
Aijie Cheng, Hong Wang, Huan Liu
Publication date: 4 September 2018
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-018-0645-6
discontinuous Galerkin finite element methodperidynamic modelfast solution methodlocally refined composite mesh
Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Toeplitz, Cauchy, and related matrices (15B05) Preconditioners for iterative methods (65F08)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A fast and faithful collocation method with efficient matrix assembly for a two-dimensional nonlocal diffusion model
- Continuous and discontinuous finite element methods for a peridynamics model of mechanics
- A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
- A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh
- Crack nucleation in a peridynamic solid
- Numerical methods for the solution of partial differential equations of fractional order.
- Numerical solution of the space fractional Fokker-Planck equation.
- Higher order finite difference method for the reaction and anomalous-diffusion equation
- A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media
- A fast collocation method for a variable-coefficient nonlocal diffusion model
- Finite difference approximations for fractional advection-dispersion flow equations
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Reformulation of elasticity theory for discontinuities and long-range forces
- Convergence studies in meshfree peridynamic simulations
- A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions
- A fast collocation method for a static bond-based linear peridynamic model
- On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models
- A preconditioned fast Hermite finite element method for space-fractional diffusion equations
- Peridynamic states and constitutive modeling
- Kinetics of phase transformations in the peridynamic formulation of continuum mechanics
- A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension
- A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models
- Hierarchical Matrices: Algorithms and Analysis
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- THE PERIDYNAMIC EQUATION AND ITS SPATIAL DISCRETISATION
- Convergence, adaptive refinement, and scaling in 1D peridynamics
- An Optimal Circulant Preconditioner for Toeplitz Systems
- Conjugate Gradient Methods for Toeplitz Systems
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
- A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
