Randomized low-rank approximation methods for projection-based model order reduction of large nonlinear dynamical problems
DOI10.1002/nme.6009zbMath1548.65145MaRDI QIDQ6555374
Lijun Song, Christian W. Bach, Fabian M. E. Duddeck, D. Ceglia
Publication date: 14 June 2024
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
nonlinear dynamicslow-rank approximationnonlinear model order reductionrandomized SVDrandomized numerical linear algebraexplicit FEM
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element methods applied to problems in solid mechanics (74S05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for ordinary differential equations (65L99)
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Cites Work
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Tensor-Train Decomposition
- CUR matrix decompositions for improved data analysis
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- Low-rank incremental methods for computing dominant singular subspaces
- Analysis of a complex of statistical variables into principal components.
- Rang revealing QR factorizations
- Isogeometric shell analysis: the Reissner-Mindlin shell
- A priori hyperreduction method: an adaptive approach
- Matrix multiplication via arithmetic progressions
- A single surface contact algorithm for the post-buckling analysis of shell structures
- A fast randomized algorithm for the approximation of matrices
- Random projections for the nonnegative least-squares problem
- Explicit algorithms for the nonlinear dynamics of shells
- Gauss and the history of the fast Fourier transform
- An overview of parallel algorithms for the singular value and symmetric eigenvalue problems
- A Divide and Conquer method for the symmetric tridiagonal eigenproblem
- Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
- A theory of pseudoskeleton approximations
- Low-rank revealing \(UTV\) decompositions
- A contribution to the theory of Legendre polynomials.
- Latent semantic indexing: A probabilistic analysis
- Eigenvalue computation in the 20th century
- Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates
- Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction
- Energy preserving model order reduction of the nonlinear Schrödinger equation
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Reduced order modeling strategies for computational multiscale fracture
- Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
- Efficient algorithms for CUR and interpolative matrix decompositions
- Fast low-rank modifications of the thin singular value decomposition
- Numerical simulation of Taylor impact tests
- Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations
- On the a priori model reduction: overview and recent developments
- Singular value decomposition and least squares solutions
- Gaussian elimination is not optimal
- A principal axis transformation for non-Hermitian matrices.
- The approximation of one matrix by another of lower rank.
- Sequential Karhunen-Loeve basis extraction and its application to images
- Dimensional model reduction in non‐linear finite element dynamics of solids and structures
- A DEIM Induced CUR Factorization
- A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices
- Improved Matrix Algorithms via the Subsampled Randomized Hadamard Transform
- Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
- Hierarchical Matrices: Algorithms and Analysis
- Nonlinear model order reduction based on local reduced-order bases
- Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency
- Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models
- Adaptiveh-refinement for reduced-order models
- Projection‐based model reduction for contact problems
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Randomized algorithms for the low-rank approximation of matrices
- Hierarchical Singular Value Decomposition of Tensors
- A fast randomized algorithm for overdetermined linear least-squares regression
- IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
- SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
- New Fast and Accurate Jacobi SVD Algorithm. I
- New Fast and Accurate Jacobi SVD Algorithm. II
- A Randomized Algorithm for Principal Component Analysis
- Relative-Error $CUR$ Matrix Decompositions
- A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
- A Fast Adaptive Multipole Algorithm for Particle Simulations
- An Improved Algorithm for Computing the Singular Value Decomposition
- A Divide-and-Conquer Algorithm for the Bidiagonal SVD
- A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem
- ARPACK Users' Guide
- Recursive Calculation of Dominant Singular Subspaces
- Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen*).
- Compressed Nonnegative Matrix Factorization Is Fast and Accurate
- Numerical Methods for Computing Angles Between Linear Subspaces
- Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
- Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
- Numerical linear algebra in the streaming model
- The Fast Johnson–Lindenstrauss Transform and Approximate Nearest Neighbors
- On the Compression of Low Rank Matrices
- Randomized QR with Column Pivoting
- Reduced-Order Models for Electromagnetic Scattering Problems
- Fast monte-carlo algorithms for finding low-rank approximations
- Least squares, singular values and matrix approximations
- Calculating the Singular Values and Pseudo-Inverse of a Matrix
- Augmented Implicitly Restarted Lanczos Bidiagonalization Methods
- Householder QR Factorization With Randomization for Column Pivoting (HQRRP)
- RELATIONS BETWEEN TWO SETS OF VARIATES
- The principle of minimized iterations in the solution of the matrix eigenvalue problem
- On lines and planes of closest fit to systems of points in space.
- Accelerated mesh sampling for the hyper reduction of nonlinear computational models
- A multilevel projection-based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics
- Limited-memory adaptive snapshot selection for proper orthogonal decomposition
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