A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations
DOI10.1137/20M1350790zbMath1497.49044OpenAlexW4292949412WikidataQ114074183 ScholiaQ114074183MaRDI QIDQ5099871
Helmut Harbrecht, Stephan Dahlke, Thomas M. Surowiec
Publication date: 26 August 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m1350790
waveletsbound constraintsfractional LaplacianPDE-constrained optimizationnonlocal operatorssemismooth Newton
Newton-type methods (49M15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for wavelets (65T60) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Fractional partial differential equations (35R11) PDE constrained optimization (numerical aspects) (49M41)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- A PDE approach to fractional diffusion: a posteriori error analysis
- The \(\mathcal H^2\)-wavelet method
- On Riesz minimal energy problems
- Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- On the fast matrix multiplication in the boundary element method by panel clustering
- Multilevel preconditioning
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\)
- A fast direct solver for nonlocal operators in wavelet coordinates
- What is the fractional Laplacian? A comparative review with new results
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- Biorthogonal wavelet bases for the boundary element method
- Wavelets with patchwise cancellation properties
- A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
- Wavelet Methods for Fast Resolution of Elliptic Problems
- Primal-Dual Strategy for Constrained Optimal Control Problems
- The Primal-Dual Active Set Strategy as a Semismooth Newton Method
- Multiscale Bases for the Sparse Representation of Boundary Integral Operators on Complex Geometry
- An a posteriori error analysis for an optimal control problem involving the fractional Laplacian
- The Primal-Dual Active Set Method for Nonlinear Optimal Control Problems with Bilateral Constraints
- Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- Error Estimates for the Optimal Control of a Parabolic Fractional PDE
- Wavelet-based approximations of pointwise bound constraints in Lebesgue and Sobolev spaces
- A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
- An Extension Problem Related to the Fractional Laplacian
- Wavelet Galerkin Schemes for Boundary Integral Equations---Implementation and Quadrature
- Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates
- Finite element approximations of the nonhomogeneous fractional Dirichlet problem
- A fast algorithm for particle simulations
This page was built for publication: A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations