Random Sampling and Efficient Algorithms for Multiscale PDEs
From MaRDI portal
Publication:5132000
DOI10.1137/18M1207430OpenAlexW3090500529WikidataQ114074293 ScholiaQ114074293MaRDI QIDQ5132000
Stephen J. Wright, Ke Chen, Qin Li, Jian-feng Lu
Publication date: 9 November 2020
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.08848
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Asymptotic behavior of solutions to PDEs (35B40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
Generalized Multiscale Finite Element Method for Highly Heterogeneous Compressible Flow, Numerical homogenization beyond scale separation, Manifold Learning and Nonlinear Homogenization, A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps, Angles between subspaces and nearly optimal approximation in GFEM, An Adaptive Preconditioner for Three-Dimensional Single-Phase Compressible Flow in Highly Heterogeneous Porous Media, A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks, Small collaboration: Modeling phenomena from nature by hyperbolic partial differential equations. Abstracts from the small collaboration held April 11--17, 2021 (hybrid meeting), A Low-Rank Schwarz Method for Radiative Transfer Equation With Heterogeneous Scattering Coefficient, A reduced basis method for radiative transfer equation
Cites Work
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Generalized multiscale finite element methods (GMsFEM)
- Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
- Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics
- Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
- Fast construction of hierarchical matrix representation from matrix-vector multiplication
- Convergence rates in \(L ^{2}\) for elliptic homogenization problems
- The heterogeneous multiscale methods
- The penetration function and its application to microscale problems
- A fast randomized algorithm for the approximation of matrices
- A multiscale finite element method for elliptic problems in composite materials and porous media
- A theory of pseudoskeleton approximations
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
- A numerical method for computing asymptotic states and outgoing distributions for kinetic linear half-space problems.
- A concurrent global-local numerical method for multiscale PDEs
- Uncertain loading and quantifying maximum energy concentration within composite structures
- Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix
- Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. II
- Unconditionally stable and robust adjacent-cell diffusive preconditioning of weighted-difference particle transport methods is impossible
- Geometric correction for diffusive expansion of steady neutron transport equation
- Validity and regularization of classical half-space equations
- Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics
- Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
- A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
- Randomized Oversampling for Generalized Multiscale Finite Element Methods
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- The AL Basis for the Solution of Elliptic Problems in Heterogeneous Media
- Asymptotic-Preserving Schemes for Fluid Models of Plasmas
- Hierarchical Matrices: Algorithms and Analysis
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- Eliminating the pollution effect in Helmholtz problems by local subscale correction
- Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- Randomized algorithms for the low-rank approximation of matrices
- Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit
- Exponential Runge–Kutta Methods for Stiff Kinetic Equations
- Randomized Algorithms for Matrices and Data
- Analysis of the heterogeneous multiscale method for elliptic homogenization problems
- Randomized Local Model Order Reduction
- An analysis of a class of variational multiscale methods based on subspace decomposition
- Localization of elliptic multiscale problems
- A Fast Randomized Algorithm for Computing a Hierarchically Semiseparable Representation of a Matrix
- Multiscale Finite Element Methods
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- Homogenization and Two-Scale Convergence
- Asymptotic analysis of transport processes
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Fully-discrete numerical transfer in diffusive regimes
- THE PARTITION OF UNITY METHOD
- First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
- An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
- Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
- Randomized algorithms in numerical linear algebra
- A convergent method for linear half-space kinetic equations
- Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces
- Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
- Diffusion Approximation and Computation of the Critical Size
- Can a finite element method perform arbitrarily badly?
- Convergence of a Nonconforming Multiscale Finite Element Method
- Implicit Asymptotic Preserving Method for Linear Transport Equations
- A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit
- Bayesian Numerical Homogenization
- Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition
- Heterogeneous multiscale methods for stiff ordinary differential equations
- AnLptheory for stationary radiative transfer
- Fast monte-carlo algorithms for finding low-rank approximations
- A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
- An Adaptive Multiscale Method for Simulation of Fluid Flow in Heterogeneous Porous Media