Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints
From MaRDI portal
Publication:2123925
DOI10.1016/j.jcp.2020.109865OpenAlexW3090593404MaRDI QIDQ2123925
Gennadij Heidel, Boris N. Khoromskij, Volker H. Schulz, Venera Khoromskaia
Publication date: 14 April 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.01971
optimal control problemstensor numerical methodsfractional multidimensional Laplacianlow Kronecker rank preconditionerreduced higher order SVDTucker and canonical tensor decompositions
Related Items (4)
Tensorized low-rank circulant preconditioners for multilevel Toeplitz linear systems from high-dimensional fractional Riesz equations ⋮ Structure and approximation properties of Laplacian-like matrices ⋮ Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems ⋮ \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Tensor numerical methods in scientific computing
- Fourier spectral methods for fractional-in-space reaction-diffusion equations
- Ten equivalent definitions of the fractional Laplace operator
- Optimal control of a class of fractional heat diffusion systems
- Fast tensor product solvers for optimization problems with fractional differential equations as constraints
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- Numerically solving an equation for fractional powers of elliptic operators
- Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- A fast algorithm for solving the space-time fractional diffusion equation
- Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
- \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
- Low rank Tucker-type tensor approximation to classical potentials
- Tensor Numerical Methods in Quantum Chemistry
- Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity
- Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions
- Krylov Subspace Methods for Linear Systems with Tensor Product Structure
- Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
- Algorithms for PDE-constrained optimization
- Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
- Computational Optimization of Systems Governed by Partial Differential Equations
- Tensor Spaces and Numerical Tensor Calculus
- A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
- Optimization with PDE Constraints
- Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
- Multigrid Methods for PDE Optimization
- Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
- A Multilinear Singular Value Decomposition
- Optimal solvers for linear systems with fractional powers of sparse SPD matrices
- Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
- Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions
- Data-sparse approximation to the operator-valued functions of elliptic operator
- Solution of Linear Systems and Matrix Inversion in the TT-Format
- Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains
- Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains
- An Extension Problem Related to the Fractional Laplacian
- Functions of Matrices
- Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D
- Fractional Calculus with Applications in Mechanics
This page was built for publication: Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints
