31 citations · 239 across the 29 of their papers we have counts for
26 papers · 1 filter
Data generated internal solutions for the plasma wave equation: error bounds and numerical experiments in two dimensions
Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky
We consider the computation of internal solutions for a time domain plasma wave equation with an unknown potential from boundary response data. The internal solutions are compu…
On optimality and bounds for internal solutions generated from boundary data-driven Gramians
V. Druskin, S. Moskow, M. Zaslavsky
We consider the computation of internal solutions for a time domain plasma wave equation with unknown coefficients from the data obtained by sampling its transfer function at the b…
A Krylov projection algorithm for large symmetric matrices with dense spectra
Vladimir Druskin, Jörn Zimmerling
We consider the approximation of for large s.p.d. with dense spectrum and , . We target the com…
ROM inversion of monostatic data lifted to full MIMO
V. Druskin, S. Moskow, M. Zaslavsky
The Lippmann--Schwinger--Lanczos (LSL) algorithm has recently been shown to provide an efficient tool for imaging and direct inversion of synthetic aperture radar data in multi-sca…
Monotonicity, bounds and extrapolation of Block-Gauss and Gauss-Radau quadrature for computing
Jörn Zimmerling, Vladimir Druskin, Valeria Simoncini
In this paper, we explore quadratures for the evaluation of where is a symmetric positive-definite (s.p.d.) matrix in , is a tall matr…
Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain
Justin Baker, Elena Cherkaev, Vladimir Druskin +2
Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) m…
Solving inverse scattering problems via reduced-order model embedding procedures
Jörn Zimmerling, Vladimir Druskin, Murthy Guddati +2
We present a reduced-order model (ROM) methodology for inverse scattering problems in which the reduced-order models are data-driven, i.e. they are constructed directly from data g…
Reduced order modeling inversion of mono static data in a multi-scattering environment
V. Druskin, S. Moskow, M. Zaslavsky
The data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of the inverse scattering problems with applications to seismic and sonar im…
Model order reduction of layered waveguides via rational Krylov fitting
Vladimir Druskin, Stefan Güttel, Leonid Knizhnerman
Rational approximation recently emerged as an efficient numerical tool for the solution of exterior wave propagation problems. Currently, this technique is limited to wave media wh…
On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays
Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited…
Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky
Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin p…
Reduced Order Model Approach to Inverse Scattering
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +2
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (so…
Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +2
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schrödinger equation in the spectral domain given boundary data at a few frequencie…
Fast finite-difference convolution for 3D problems in layered media
Vladimir Druskin, Mikhail Zaslavsky
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the gr…
Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +1
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algor…
Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces
Vladimir Druskin, Rob Remis, Mikhail Zaslavsky +1
Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield p…
Untangling the nonlinearity in inverse scattering with data-driven reduced order models
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov +1
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. T…
A nonlinear method for imaging with acoustic waves via reduced order model backprojection
Vladimir Druskin, Alexander V. Mamonov, Mikhail Zaslavsky
We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoust…
Multi-scale S-fraction reduced-order models for massive wavefield simulations
Vladimir Druskin, Alexander V. Mamonov, Mikhail Zaslavsky
We developed a novel reduced-order multi-scale method for solving large time-domain wavefield simulation problems. Our algorithm consists of two main stages. During the first "off-…
Direct, nonlinear inversion algorithm for hyperbolic problems via projection-based model reduction
Vladimir Druskin, Alexander Mamonov, Andrew E. Thaler +1
We estimate the wave speed in the acoustic wave equation from boundary measurements by constructing a reduced-order model (ROM) matching discrete time-domain data. The state-variab…
Near-optimal perfectly matched layers for indefinite Helmholtz problems
Vladimir Druskin, Stefan Güttel, Leonid Knizhnerman
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rationa…
Exponential Convergence through Linear Finite Element Discretization of Stratified Subdomains
Murthy N. Guddati, Vladimir Druskin, Ali Vaziri Astaneh
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in expo…
Nonlinear seismic imaging via reduced order model backprojection
Alexander V. Mamonov, Vladimir Druskin, Mikhail Zaslavsky
We introduce a novel nonlinear seismic imaging method based on model order reduction. The reduced order model (ROM) is an orthogonal projection of the wave equation propagator oper…
S-fraction multiscale finite-volume method for spectrally accurate wave propagation
Vladimir Druskin, Alexander V. Mamonov, Mikhail Zaslavsky
We develop a method for numerical time-domain wave propagation based on the model order reduction approach. The method is built with high-performance computing (HPC) implementation…