A reduced conjugate gradient basis method for fractional diffusion
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Publication:6623676
DOI10.1137/23m1575913MaRDI QIDQ6623676
Yuwen Li, Cheng Zuo, Ludmil T. Zikatanov
Publication date: 24 October 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
preconditioningconjugate gradient methodreduced basis methodrational approximationfractional PDEorthogonal greedy algorithm
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Preconditioners for iterative methods (65F08)
Cites Work
- Nonlocal diffusion and applications
- Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
- The superconvergent cluster recovery method
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- Rational approximation to \(x^\alpha\)
- Iterative solution of large sparse systems of equations. Transl. from the German
- A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
- Best uniform rational approximation of \(x^ \alpha\) on \([0,1\).]
- Some remarks on greedy algorithms
- Simplicial grid refinement: On Freudenthal's algorithm and the optimal number of congruence classes
- Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
- An algorithm for best rational approximation based on barycentric rational interpolation
- A reduced basis method for fractional diffusion operators. II
- Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation
- A unified view of some numerical methods for fractional diffusion
- Superconvergent recovery of Raviart-Thomas mixed finite elements on triangular grids
- Residual-driven online generalized multiscale finite element methods
- Approximation and learning by greedy algorithms
- Rational approximation to \(|x|\)
- Sur la détermination des polynomes d'approximation de degré donné.
- A reduced basis method for fractional diffusion operators. I
- On rational Krylov and reduced basis methods for fractional diffusion
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
- Preconditioning discretizations of systems of partial differential equations
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations
- UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS
- Greedy approximation
- Iterative Methods by Space Decomposition and Subspace Correction
- Some Nonoverlapping Domain Decomposition Methods
- Unstructured Additive Schwarz--Conjugate Gradient Method for Elliptic Problems with Highly Discontinuous Coefficients
- The method of alternating projections and the method of subspace corrections in Hilbert space
- Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
- Optimal solvers for linear systems with fractional powers of sparse SPD matrices
- Algebraic multigrid methods
- Global Superconvergence of the Lowest-Order Mixed Finite Element on Mildly Structured Meshes
- 6 Localized model reduction for parameterized problems
- Optimal Convergence Rates for the Orthogonal Greedy Algorithm
- Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form
- A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
- Numerical approximation of fractional powers of elliptic operators
- A New Finite Element Gradient Recovery Method: Superconvergence Property
- Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients
- Reduced Basis Methods for Partial Differential Equations
- The AAA Algorithm for Rational Approximation
- Methods of conjugate gradients for solving linear systems
- Numerical methods for nonlocal and fractional models
- Adaptive greedy approximations
- Rational approximation preconditioners for multiphysics problems
- Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks
- Entropy-based convergence rates of greedy algorithms
- Nodal auxiliary space preconditioning for the surface de Rham complex
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