Optimal operator preconditioning for pseudodifferential boundary problems
DOI10.1007/s00211-021-01193-9zbMath1477.65214arXiv1905.03846OpenAlexW2944146952MaRDI QIDQ2038413
Heiko Gimperlein, Jakub Stocek, Carolina Urzúa-Torres
Publication date: 6 July 2021
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.03846
Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary value problems for PDEs with pseudodifferential operators (35S15) Integral operators (45P05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary element methods for boundary value problems involving PDEs (65N38) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11) PDEs on manifolds (35R01)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Numerical methods for the computation of the confluent and Gauss hypergeometric functions
- An adaptive mesh-refining algorithm allowing for an \(H^1\) stable \(L^2\) projection onto Courant finite element spaces
- Spectral results for mixed problems and fractional elliptic operators
- Some observations on the Green function for the ball in the fractional Laplace framework
- A multilevel additive Schwarz method for a hypersingular integral equation on an open curve with graded meshes
- The construction of some efficient preconditioners in the boundary element method
- On a generalized \(L_2\) projection and some related stability estimates in Sobolev spaces
- Closed-form inverses of the weakly singular and hypersingular operators on disks
- Stability estimates for hybrid coupled domain decomposition methods
- Boundary element preconditioners for a hypersingular integral equation on an interval
- Space-time adaptive finite elements for nonlocal parabolic variational inequalities
- Uniform preconditioners of linear complexity for problems of negative order
- Uniform preconditioners for problems of positive order
- Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- The Dirichlet problem for nonlocal operators
- Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations
- On the \(H^1\)-stability of the \(L_2\)-projection onto finite element spaces
- Operator preconditioning
- Primer of Adaptive Finite Element Methods
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Explicit Variational Forms for the Inverses of Integral Logarithmic Operators Over an Interval
- Nonlocal Operators with Applications to Image Processing
- Distributions and Operators
- The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling
- Additive schwarz methods for the H-version boundary element method
- Red–green refinement of simplicial meshes in $d$ dimensions
- Integral representation of solutions to higher-order fractional Dirichlet problems on balls
- Advanced Boundary Element Methods
- Space-time fractional diffusion in cell movement models with delay
- Fractional Patlak--Keller--Segel Equations for Chemotactic Superdiffusion
- Financial Modelling with Jump Processes
- On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
- Mesh-Independent Operator Preconditioning for Boundary Elements on Open Curves
- Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
- Uniform preconditioners for problems of negative order
- Interacting Particles with Lévy Strategies: Limits of Transport Equations for Swarm Robotic Systems
This page was built for publication: Optimal operator preconditioning for pseudodifferential boundary problems
