Preconditioners and Tensor Product Solvers for Optimal Control Problems from Chemotaxis
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Publication:5243525
DOI10.1137/18M1198041zbMath1427.35301arXiv1806.08539OpenAlexW2970744785WikidataQ126791839 ScholiaQ126791839MaRDI QIDQ5243525
John W. Pearson, Sergey V. Dolgov
Publication date: 18 November 2019
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.08539
Factorization of matrices (15A23) Control/observation systems governed by partial differential equations (93C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Iterative numerical methods for linear systems (65F10) Multilinear algebra, tensor calculus (15A69) Cell movement (chemotaxis, etc.) (92C17) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08) PDEs in connection with control and optimization (35Q93)
Related Items (3)
Fast preconditioned iterative methods for fractional Sturm–Liouville equations ⋮ Parallel cross interpolation for high-precision calculation of high-dimensional integrals ⋮ Fast algorithms for high-dimensional variable-order space-time fractional diffusion equations
Cites Work
- Unnamed Item
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- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- Computation of extreme eigenvalues in higher dimensions using block tensor train format
- An aggregation-based algebraic multigrid method
- Fast tensor product solvers for optimization problems with fractional differential equations as constraints
- Efficient, accurate and flexible finite element solvers for chemotaxis problems
- A mesh-independence result for semismooth Newton methods.
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis
- Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II
- Model for chemotaxis
- Chebyshev semi-iteration in preconditioning for problems including the mass matrix
- Model and analysis of chemotactic bacterial patterns in a liquid medium
- Rectangular maximum-volume submatrices and their applications
- Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization
- A positivity-preserving finite element method for chemotaxis problems in 3D
- Quasioptimality of maximum-volume cross interpolation of tensors
- A new scheme for the tensor representation
- Second order optimality conditions and their role in PDE control
- Fast solvers for optimal control problems from pattern formation
- Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data
- Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
- Fast iterative solvers for convection-diffusion control problems
- Semi-smooth Newton methods for state-constrained optimal control problems
- A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations
- A Note on Preconditioning Nonsymmetric Matrices
- A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
- Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity
- A literature survey of low-rank tensor approximation techniques
- Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes
- The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
- An Algebraic Multigrid Method with Guaranteed Convergence Rate
- Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations
- The density-matrix renormalization group
- Optimal Solvers for PDE-Constrained Optimization
- Semi-smooth Newton method for an optimal control problem with control and mixed control-state constraints
- Nonstandard Norms and Robust Estimates for Saddle Point Problems
- Tensor Spaces and Numerical Tensor Calculus
- Aggregation-Based Algebraic Multigrid for Convection-Diffusion Equations
- Numerical solution of saddle point problems
- Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Realistic Eigenvalue Bounds for the Galerkin Mass Matrix
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Semismooth Newton Methods for Operator Equations in Function Spaces
- The Primal-Dual Active Set Strategy as a Semismooth Newton Method
- A Note on Preconditioning for Indefinite Linear Systems
- Tensor approximations of matrices generated by asymptotically smooth functions
- Efficient iterative solvers for elliptic finite element problems on nonmatching grids
- Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
- Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems
- Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
- Identification of Chemotaxis Models with Volume-Filling
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
- Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications
- Fractional step methods applied to a chemotaxis model
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