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Mathematics

D-Index
47
Citations
6903
World Ranking
1297
National Ranking
74

Overview

Boris N. Khoromskij is affiliated with the Max Planck Institute for Mathematics in the Sciences in Germany. Their research spans key areas in computational mathematics, engineering, and physics, with a focus on numerical methods and tensor-based approaches to complex scientific problems.

Their scholarly output includes several papers published in notable venues. Recent publications include:

  • Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements (2020, Numerical Linear Algebra with Applications)
  • Regularization of Poisson--Boltzmann Type Equations with Singular Source Terms Using the Range-Separated Tensor Format (2021, SIAM Journal on Scientific Computing)
  • Prospects of Tensor-Based Numerical Modeling of the Collective Electrostatics in Many-Particle Systems (2021, Computational Mathematics and Mathematical Physics)
  • Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints (2020, Journal of Computational Physics)
  • Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients (2021, Numerical Linear Algebra with Applications)

Frequent coauthors collaborating with Khoromskij include:

  • Venera Khoromskaia
  • Peter Benner
  • Volker Schulz
  • Cleophas Kweyu
  • Britta Schmitt

The main publication venues where Khoromskij's work appears are:

  • arXiv (Cornell University)
  • Numerical Linear Algebra with Applications
  • SIAM Journal on Scientific Computing
  • Computational Mathematics and Mathematical Physics
  • Journal of Computational Physics

Their research fields encompass:

  • Engineering
  • Physics and Astronomy
  • Mathematics

Within these fields, Khoromskij focuses on several subfields, such as:

  • Computational Mathematics
  • Computational Mechanics
  • Atomic and Molecular Physics, and Optics
  • Computational Theory and Mathematics
  • Mechanics of Materials

Key topics covered in their work relate to tensor and matrix computations and applied mathematical modeling, specifically:

  • Tensor decomposition and applications
  • Advanced Numerical Methods in Computational Mathematics
  • Electromagnetic Scattering and Analysis
  • Composite Material Mechanics
  • Advanced Mathematical Modeling in Engineering
  • Matrix Theory and Algorithms
  • Protein Structure and Dynamics

Best Publications

  • A sparse H -matrix arithmetic. Part II: application to multi-dimensional problems

    W. Hackbusch;B. N. Khoromskij

  • O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling

    Boris N. Khoromskij

  • On H2-Matrices

    Wolfgang Hackbusch;Boris N. Khoromskij;Stefan A. Sauter

  • Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances

    Boris N. Khoromskij

  • Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

    Boris N. Khoromskij;Christoph Schwab

  • Hierarchical Kronecker tensor-product approximations

    Wolfgang Hackbusch;Boris N. Khoromskij;Eugene E. Tyrtyshnikov

  • Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions

    W. Hackbusch;N. Khoromskij

  • Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse

    Vladimir A. Kazeev;Boris N. Khoromskij

  • Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays

    B. N. Khoromskij;V. Khoromskaia

  • Approximate iterations for structured matrices

    Wolfgang Hackbusch;Boris N. Khoromskij;Eugene E. Tyrtyshnikov

  • A sparse H -matrix arithmetic: general complexity estimates

    W. Hackbusch;B. N. Khoromskij

  • Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices

    L. Grasedyck;W. Hackbusch;B. N. Khoromskij

  • Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation

    Sergey V. Dolgov;Boris N. Khoromskij;Ivan V. Oseledets

  • Hierarchical Matrices based on a Weak Admissibility Criterion

    Wolfgang Hackbusch;Boris N. Khoromskij;Ronald Kriemann

  • Application of hierarchical matrices for computing the Karhunen–Loève expansion

    B. N. Khoromskij;A. Litvinenko;H. G. Matthies

  • Low rank Tucker-type tensor approximation to classical potentials

    Boris N. Khoromskij;Venera Khoromskaia

  • Computation of extreme eigenvalues in higher dimensions using block tensor train format

    Sergey V. Dolgov;Sergey V. Dolgov;Boris N. Khoromskij;Ivan V. Oseledets;Ivan V. Oseledets;Dmitry V. Savostyanov;Dmitry V. Savostyanov

  • Tensor-product approximation to operators and functions in high dimensions

    Wolfgang Hackbusch;Boris N. Khoromskij

  • Numerical Solution of the Hartree-Fock Equation in Multilevel Tensor-Structured Format

    B. N. Khoromskij;V. Khoromskaia;H.-J. Flad

  • H-matrix approximation for the operator exponential with applications

    Ivan P. Gavrilyuk;Wolfgang Hackbusch;Boris N. Khoromskij

  • Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs

    Boris N. Khoromskij;Ivan V. Oseledets

Frequent Co-Authors

Wolfgang Hackbusch
Wolfgang Hackbusch Max Planck Institute for Mathematics in the Sciences
Ivan V. Oseledets
Ivan V. Oseledets Skolkovo Institute of Science and Technology
Eugene E. Tyrtyshnikov
Eugene E. Tyrtyshnikov Russian Academy of Sciences
Hermann G. Matthies
Hermann G. Matthies Technische Universität Braunschweig
Peter Benner
Peter Benner Max Planck Institute for Dynamics of Complex Technical Systems
Reinhold Schneider
Reinhold Schneider Technical University of Berlin
Stefan A. Sauter
Stefan A. Sauter University of Zurich
Felix Otto
Felix Otto Max Planck Institute for Mathematics in the Sciences
Bert Jüttler
Bert Jüttler Johannes Kepler University of Linz
Ulrich Langer
Ulrich Langer Johannes Kepler University of Linz

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