Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data

DOI10.1088/1361-6420/ab750bzbMath1478.65106arXiv1909.06460OpenAlexW3104215129WikidataQ118126684 ScholiaQ118126684MaRDI QIDQ5000606

Liliana Borcea, Vladimir Druskin, Shari Moskow, Alexander V. Mamonov, Mikhail Zaslavsky

Publication date: 14 July 2021

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06460

zbMATH Keywords

inversionSchrödingerreduced order modelinternal data

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Boundary value problems for second-order elliptic equations (35J25) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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Uses Software

• Loewner

Cites Work

• Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models
• A discrete Liouville identity for numerical reconstruction of Schrödinger potentials
• Solution of the Time-Domain Inverse Resistivity Problem in the Model Reduction Framework Part I. One-Dimensional Problem with SISO Data
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• A model reduction approach to numerical inversion for a parabolic partial differential equation
• Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements
• Optimal finite difference grids for direct and inverse Sturm$ndash$Liouville problems
• Direct, Nonlinear Inversion Algorithm for Hyperbolic Problems via Projection-Based Model Reduction
• Circular resistor networks for electrical impedance tomography with partial boundary measurements
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• Optical tomography: forward and inverse problems
• Electrical impedance tomography and Calderón's problem
• Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation
• Untangling the nonlinearity in inverse scattering with data-driven reduced order models
• A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection
• Electrical impedance tomography
• Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain
• Resistor network approaches to electrical impedance tomography