A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions
DOI10.1002/num.22832arXiv2008.11780OpenAlexW3196639389WikidataQ115397288 ScholiaQ115397288MaRDI QIDQ6069467
Max D. Gunzburger, Marta D'Elia, Unnamed Author, Christian Vollmann, Pavel B. Bochev, Giacomo Capodaglio
Publication date: 16 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.11780
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)
Cites Work
- Unnamed Item
- 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
- Image recovery via nonlocal operators
- Variational theory and domain decomposition for nonlocal problems
- Domain decomposition methods for the numerical solution of partial differential equations
- A novel Lagrange-multiplier based method for consistent mesh tying
- Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
- Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization
- Multiscale dynamics of heterogeneous media in the peridynamic formulation
- An optimization based domain decomposition method for partial differential equations
- nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
- An energy-based coupling approach to nonlocal interface problems
- Peridynamics and material interfaces
- How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
- Nonlocal Linear Image Regularization and Supervised Segmentation
- A method of finite element tearing and interconnecting and its parallel solution algorithm
- Consistent mesh tying methods for topologically distinct discretized surfaces in non-linear solid mechanics
- Nonlocal Modeling, Analysis, and Computation
- 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
- Image Denoising Methods. A New Nonlocal Principle
- Machine Learning of Space-Fractional Differential Equations
- fPINNs: Fractional Physics-Informed Neural Networks
- A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
- An Optimization-Based Approach for Elliptic Problems with Interfaces
- MHD Turbulence: Nonlocal, Anisotropic, Nonuniversal?
- The Arlequin method as a flexible engineering design tool
- Numerical methods for nonlocal and fractional models
- Stochastic models for fractional calculus
- Solution of elliptic partial differential equations by an optimization-based domain decomposition method
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
