Compressed solving: a numerical approximation technique for elliptic PDEs based on compressed sensing

DOI10.1016/j.camwa.2015.07.015zbMath1443.65313OpenAlexW1166999322MaRDI QIDQ2006439

Simone Brugiapaglia, Simona Perotto, Stefano Micheletti

Publication date: 11 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.07.015

zbMATH Keywords

partial differential equationssparse approximationcompressed sensingPetrov-Galerkin discretizationunderdetermined linear systems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (6)

A priori error analysis of high-order LL* (FOSLL*) finite element methods ⋮ A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems ⋮ Robust recovery of a kind of weighted l1-minimization without noise level ⋮ Compressive isogeometric analysis ⋮ A Compressive Spectral Collocation Method for the Diffusion Equation Under the Restricted Isometry Property ⋮ Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

Uses Software

• Matlab
• PDCO
• SPGL1

Cites Work

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• Sparse and Redundant Representations
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• Atomic Decomposition by Basis Pursuit
• Stable and Robust Sampling Strategies for Compressive Imaging
• Matching pursuits with time-frequency dictionaries
• Compressive Sensing
• Mixed Finite Element Methods and Applications
• A reduced-basis element method
• Compressed sensing

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