Sparse data-driven quadrature rules via \(\ell^p\)-quasi-norm minimization

DOI10.1515/cmam-2021-0131zbMath1485.65022arXiv2012.05264OpenAlexW4213170186MaRDI QIDQ2134455

Mattia Manucci, Domenico Borzacchiello, Jose Vicente Aguado

Publication date: 3 May 2022

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.05264

zbMATH Keywords

linear programmingparametrized PDEshyper-reduction\textsf{FOCUSS} algorithmparametrized integralssparse quadrature rules

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for integral transforms (65R10) Numerical quadrature and cubature formulas (65D32)

Related Items

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Uses Software

• Matlab
• GitHub

Cites Work

• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization
• Extensions of Gauss quadrature via linear programming
• Sparsest solutions of underdetermined linear systems via \( \ell _q\)-minimization for \(0<q\leqslant 1\)
• An LP empirical quadrature procedure for parametrized functions
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Presolving in linear programming
• An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs
• Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations
• A discretize-then-map approach for the treatment of parameterized geometries in model order reduction
• An offline/online procedure for dual norm calculations of parameterized functionals: empirical quadrature and empirical test spaces
• Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
• Certified reduced basis approximation for parametrized partial differential equations and applications
• Computing a quantity of interest from observational data
• The generalized simplex method for minimizing a linear form under linear inequality restraints
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models
• Nonlinear Model Reduction via Discrete Empirical Interpolation
• Hyper-reduction of mechanical models involving internal variables
• Sparse Approximate Solutions to Linear Systems
• Restricted Isometry Constants Where $\ell ^{p}$ Sparse Recovery Can Fail for $0≪ p \leq 1$