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    • Several versions

    Quantitative photoacoustic imaging in radiative transport regime

    Mamonov, Alexander, Ren, Kui
    arXiv.org, Jul 19, 2012 [Peer Reviewed Journal]

    • Several versions

    Point source identification in non-linear advection-diffusion-reaction systems

    Mamonov, Alexander, Yen-Hsi, Richard
    arXiv.org, Mar 1, 2013 [Peer Reviewed Journal]

    • Several versions

    A discrete Liouville identity for numerical reconstruction of Schrödinger potentials

    Borcea, Liliana, Mamonov, Alexander
    arXiv.org, Jan 27, 2016

    • Several versions

    Study of noise effects in electrical impedance tomography with resistor networks

    Borcea, Liliana, Mamonov, Alexander
    arXiv.org, Dec 12, 2011

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    S-fraction multiscale finite-volume method for spectrally accurate wave propagation

    Druskin, Vladimir, Mamonov, Alexander V., Zaslavsky, Mikhail
    Cornell University
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    Title: S-fraction multiscale finite-volume method for spectrally accurate wave propagation
    Author: Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail
    Subject: Mathematics - Numerical Analysis ; 35q86, 86-08, 65m08, 65m55, 65m70
    Description: 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 in mind that implies a high level of parallelism and greatly reduced communication requirements compared to the traditional high-order finite-difference time-domain (FDTD) methods. The approach is inherently multiscale, with a reference fine grid model being split into subdomains. For each subdomain the coarse scale reduced order models (ROMs) are precomputed off-line in a parallel manner. The ROMs approximate the Neumann-to-Dirichlet (NtD) maps with high (spectral) accuracy and are used to couple the adjacent subdomains on the shared boundaries. The on-line part of the method is an explicit time stepping with the coupled ROMs. To lower the on-line computation cost the reduced order spatial operator is sparsified by transforming to a matrix Stieltjes continued fraction (S-fraction) form. The on-line communication costs are also reduced due to the ROM NtD map approximation properties. Another source of performance improvement is the time step length. Properly chosen ROMs substantially improve the Courant-Friedrichs-Lewy (CFL) condition. This allows the CFL time step to approach the Nyquist limit, which is typically unattainable with traditional schemes that have the CFL time step much smaller than the Nyquist sampling rate. Comment: 5 pages, 3 figures
    Identifier: 1406.6923 (ARXIV ID)

    • Several versions

    Multi-scale S-fraction reduced-order models for massive wavefield simulations

    Druskin, Vladimir, Mamonov, Alexander, Zaslavsky, Mikhail
    arXiv.org, Oct 16, 2016 [Peer Reviewed Journal]

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    Resistor network approaches to electrical impedance tomography

    Borcea, Liliana, Druskin, Vladimir, Mamonov, Alexander
    arXiv.org, Jul 1, 2011
    © ProQuest LLC All rights reserved, Engineering Database, Publicly Available Content Database, ProQuest Engineering Collection, ProQuest Technology Collection, ProQuest SciTech Collection, Materials Science & Engineering Database, ProQuest Central (new), ProQuest Central Korea, SciTech Premium Collection, Technology Collection, ProQuest Central Essentials, ProQuest One Academic, Engineering Collection (ProQuest)
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    Title: Resistor network approaches to electrical impedance tomography
    Author: Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander
    Contributor: Mamonov, Alexander (pacrepositoryorg)
    Subject: Tomography ; Inverse Problems ; Electrical Impedance ; Inverse Problems ; Dirichlet Problem ; Tomography
    Description: We review a resistor network approach to the numerical solution of the inverse problem of electrical impedance tomography (EIT). The networks arise in the context of finite volume discretizations of the elliptic equation for the electric potential, on sparse and adaptively refined grids that we call optimal. The name refers to the fact that the grids give spectrally accurate approximations of the Dirichlet to Neumann map, the data in EIT. The fundamental feature of the optimal grids in inversion is that they connect the discrete inverse problem for resistor networks to the continuum EIT problem.
    Is part of: arXiv.org, Jul 1, 2011
    Identifier: 2331-8422 (E-ISSN)

    • Several versions

    A nonlinear method for imaging with acoustic waves via reduced order model backprojection

    Druskin, Vladimir, Mamonov, Alexander, Zaslavsky, Mikhail
    arXiv.org, Aug 11, 2017 [Peer Reviewed Journal]

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    S-fraction multiscale finite-volume method for spectrally accurate wave propagation

    Druskin, Vladimir, Mamonov, Alexander, Zaslavsky, Mikhail
    arXiv.org, Jun 26, 2014
    © ProQuest LLC All rights reserved, Engineering Database, Publicly Available Content Database, ProQuest Engineering Collection, ProQuest Technology Collection, ProQuest SciTech Collection, Materials Science & Engineering Database, ProQuest Central (new), ProQuest Central Korea, SciTech Premium Collection, Technology Collection, ProQuest Central Essentials, ProQuest One Academic, Engineering Collection (ProQuest)
    Available
    More…
    Title: S-fraction multiscale finite-volume method for spectrally accurate wave propagation
    Author: Druskin, Vladimir; Mamonov, Alexander; Zaslavsky, Mikhail
    Contributor: Zaslavsky, Mikhail (pacrepositoryorg)
    Subject: Propagation ; Time Domain Analysis ; Mathematical Models ; Finite Volume Method ; Wave Propagation ; Reduced Order Models ; Mathematical Analysis ; Multiscale Methods ; Maps ; Dirichlet Problem ; Finite Difference Time Domain Method ; Model Reduction
    Description: 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 in mind that implies a high level of parallelism and greatly reduced communication requirements compared to the traditional high-order finite-difference time-domain (FDTD) methods. The approach is inherently multiscale, with a reference fine grid model being split into subdomains. For each subdomain the coarse scale reduced order models (ROMs) are precomputed off-line in a parallel manner. The ROMs approximate the Neumann-to-Dirichlet (NtD) maps with high (spectral) accuracy and are used to couple the adjacent subdomains on the shared boundaries. The on-line part of the method is an explicit time stepping with the coupled ROMs. To lower the on-line computation cost the reduced order spatial operator is sparsified by transforming to a matrix Stieltjes continued fraction (S-fraction) form. The on-line communication...
    Is part of: arXiv.org, Jun 26, 2014
    Identifier: 2331-8422 (E-ISSN)

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    Distance preserving model order reduction of graph-Laplacians and cluster analysis

    Druskin, Vladimir, Mamonov, Alexander V., Zaslavsky, Mikhail
    Cornell University
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    Title: Distance preserving model order reduction of graph-Laplacians and cluster analysis
    Author: Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail
    Subject: Computer Science - Machine Learning ; Statistics - Machine Learning ; I.5.3
    Description: Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral embedding provides a low-dimensional parametrization of the data manifold which makes the subsequent task (e.g., clustering) much easier. However, despite reducing the dimensionality of data, the overall computational cost may still be prohibitive for large data sets due to two factors. First, computing the partial eigendecomposition of the graph-Laplacian typically requires a large Krylov subspace. Second, after the spectral embedding is complete, one still has to operate with the same number of data points. For example, clustering of the embedded data is typically performed with various relaxations of k-means which computational cost scales poorly with respect to the size of data set. In this work, we switch the focus from the entire data set to... Comment: 28 pages, 10 figures
    Identifier: 1809.03048 (ARXIV ID)