Space-fractional diffusion with variable order and diffusivity: discretization and direct solution strategies
From MaRDI portal
Publication:2084920
DOI10.1007/s42967-021-00184-9OpenAlexW3198409656MaRDI QIDQ2084920
Omar M. Knio, Hasnaa Alzahrani, George M. Turkiyyah, David E. Keyes
Publication date: 13 October 2022
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2108.12772
singularity subtractionfractional diffusionvariable diffusivityvariable orderblock low rank matrixtile low rank (TLR) Cholesky
Numerical methods for integral equations (65R20) Fractional partial differential equations (35R11) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Related Items
Uses Software
Cites Work
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Fractional integration and differentiation of variable order: an overview
- Ten equivalent definitions of the fractional Laplace operator
- Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis.
- A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
- A fast method for variable-order space-fractional diffusion equations
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
- A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
- \(\mathcal H^2\)-matrix approximation of integral operators by interpolation
- Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
- Bilevel parameter learning for nonlocal image denoising models
- Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain
- What is the fractional Laplacian? A comparative review with new results
- Hierarchical matrix approximations for space-fractional diffusion equations
- \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
- Adaptive finite element method for fractional differential equations using hierarchical matrices
- A finite difference method for space fractional differential equations with variable diffusivity coefficient
- H2Opus: a distributed-memory multi-GPU software package for non-local operators
- Hierarchical Matrices: Algorithms and Analysis
- Fast algorithms for hierarchically semiseparable matrices
- Nonlocal Operators with Applications to Image Processing
- The Fractional Laplacian
- Why Finite Element Discretizations Can Be Factored by Triangular Hierarchical Matrices
- Nonlocal Modeling, Analysis, and Computation
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Hierarchical algorithms on hierarchical architectures
- A Simple Solver for the Fractional Laplacian in Multiple Dimensions
- Numerical solution of fractional elliptic stochastic PDEs with spatial white noise
- A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints
- Randomized GPU Algorithms for the Construction of Hierarchical Matrices from Matrix-Vector Operations
- fPINNs: Fractional Physics-Informed Neural Networks
- Fast Solvers for Two-Dimensional Fractional Diffusion Equations Using Rank Structured Matrices
- Hierarchical Matrix Operations on GPUs
- A Fast Finite Element Method for Space-Fractional Dispersion Equations on Bounded Domains in $\mathbb{R}^2$
- Numerical methods for nonlocal and fractional models
