Publications

Articles in Peer-Reviewed Journals (with links to preprints)

Submitted

1. P. Joly, M. Kachanovska, Z. Moitier, High-order quadratures on self-affine sets

2. M. Halla, M. Kachanovska, M. Wess,  Radial perfectly matched layers and infinite elements for the anisotropic wave equation.

Published/Accepted

1. P. Ciarlet, Jr., M. Kachanovska, E. Peillon, Study of a degenerate non-elliptic equation to model plasma heating,  ESAIM:M2AN, in press

2. M. Kachanovska,  A new class of uniformly stable time-domain Foldy-Lax models for scattering by small particles. Acoustic sound-soft scattering by circles, SIAM:MMS, 2024

3. E. Bécache, M. Kachanovska, M. Wess,  Convergence analysis of time-domain PMLs for 2D electromagnetic wave propagation in dispersive waveguides, ESAIM:M2AN, 2023. Erratum: https://uma.ensta-paris.fr//var/files/publis/2023/2023-art-uma2200-erratum.pdf

4. P. Ciarlet, Jr., M. Kachanovska, A mathematical study of a hyperbolic metamaterial in free space.  SIMA, 2022

5. P. Joly, M. Kachanovska, Local transparent boundary conditions for wave propagation in fractal trees (II). Error and complexity analysis. SINUM, 2022

6. P. Joly, M. Kachanovska, Local transparent boundary conditions for wave propagation in fractal trees (I). Method and numerical implementation. SISC, 2021

7. E. Bécache, M. Kachanovska, Stability and convergence analysis of time-domain perfectly matched layers for the wave equation in waveguides.  SINUM 59 (4), 2004-2039, 2021. Erratum: https://uma.ensta-paris.fr//var/files/publis/2023/2023-art-uma2200-erratum.pdf

8. E. Bécache, S. Fliss, M. Kachanovska, M. Kazakova, On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy. Comptes Rendus. Mathématique, Tome 359 (2021) no. 3 p. 249-256.

9. P. Joly, M. Kachanovska, Transparent boundary conditions for wave propagation in fractal trees: convolution quadrature approach.  Numerische Mathematik, 2020. Link to an extended version

10. D. Baffet, M. Grote, S. Imperiale, M. Kachanovska, Energy decay and stability of a perfectly matched layer for the wave equation.  Journal of Scientific Computing, 2019

11. P. Joly, M. Kachanovska, A. Semin, Wave propagation in fractal trees. Mathematical and numerical issues. Networks and Heterogeneous Media, 2019

12. M. Cassier, P. Joly, M. Kachanovska, Mathematical models for dispersive electromagnetic waves: an overview. Computers and Mathematics with Applications, 2017

13. E. Bécache, M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability. ESAIM: M2AN,  2017. Erratum: https://uma.ensta-paris.fr/var/files/kachanovska//erratum.pdf. Link to an extended version

14. E. Bécache, P. Joly, M. Kachanovska, Stable perfectly matched layers for a cold plasma in a strong background magnetic field. JCOMP 2017

15. C. Caldini-Queiros, B. Després, L.-M. Imbert-Gérard, M. Kachanovska, A numerical study of the solution of x-mode equations around the hybrid resonance. ESAIM: Proceedings and Surveys, 2016, CEMRACS 2014 - Numerical Modelling in Plasmas

16. E. Bécache, P. Joly,  M. Kachanovska, V. Vinoles, Perfectly matched layers in negative index metamaterials and plasmas. ESAIM: Proceedings and Surveys, 2015, CANUM 42e Congrès National d'Analyse Numérique. 

17. L. Banjai, M. Kachanovska,  Fast convolution quadrature for the wave equation in three dimensions. JCOMP 2014.

18. L. Banjai, M. Kachanovska,  Sparsity of Runge-Kutta convolution weights for the three-dimensional wave equation, BIT 2014.

Theses

1. M. Kachanovska, Fast, Parallel Techniques for Time-Domain Boundary Integral Equations, PhD thesis, University of Leipzig, 2014. http://www.qucosa.de/fileadmin/data/qucosa/documents/13218/thesis.pdf

Articles in Short Conference Proceedings

1. E. Bécache, M. Kachanovska, M. Wess, Stability and convergence of time-domain perfectly matched layers in dispersive waveguides, Proceedings of WAVES 2022

2. M. Kachanovska, Asymptotic models for time-domain scattering by small particles, Proceedings of WAVES 2022 

3. M. Kachanovska, On time-domain Foldy-Lax models, Oberwolfach Report for Workshop 'Space-Time Methods for Time-Dependent Partial Differential Equations' (February 2022)

4. P. Joly, M. Kachanovska, A. Semin, Transparent boundary conditions in fractal trees, Oberwolfach Report for Mini-Workshop 'Self-Adjoint Extensions in New Settings' (October 2019)

5. E. Bécache, S. Fliss, M. Kachanovska, M. Kazakova, On the analysis of perfectly matched layers for electromagnetic waves propagation in anisotropic media, Proceedings of WAVES 2019

6. P. Joly, M. Kachanovska, Error analysis for transparent boundary conditions in fractal trees, Proceedings of WAVES 2019

7. E. Bécache, M. Kachanovska, Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Models, Proceedings of WAVES 2019

8. P. Ciarlet, M. Kachanovska, Frequency-domain wave propagation in hyperbolic metamaterials, Proceedings of WAVES 2019

9. E. Bécache, M. Kachanovska, Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Models, Oberwolfach Report for Workshop 'Space-time Methods for Time-dependent Partial Differential Equations' (March 2017)

10. P. Joly, M. Kachanovska, A. Semin,  Propagation of acoustic waves in fractal networks, Oberwolfach Report for Workshop 'Space-time Methods for Time-dependent Partial Differential Equations' (March 2017)

11. E. Bécache, P. Joly, M. Kachanovska, Stable Perfectly Matched Layers for a Simplified Anisotropic Model of Cold Plasma, Proceedings of WAVES 2015

12. L. Banjai, M. Kachanovska, Fast convolution quadrature for the wave equation in 3D, Proceedings of ECCOMAS 2012

Reports

1. M. Kachanovska, Hierarchical matrices and the High-Frequency Fast Multipole Method for the Helmholtz Equation with Decay (H-matrices and the High-Frequency Fast Multipole Method for the Helmholtz Equation with Decay). (Technical) Report, Max Planck Institute for Mathematics in the Sciences, Leipzig, 2014. Available online at http://www.mis.mpg.de/preprints/2014/preprint2014_13.pdf.

2. E. Bécache, M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability.  <hal-01356811>

3. M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part II: energy estimates. Preprint available at  https://hal.archives-ouvertes.fr/hal-01419682

4. M. Kachanovska, Limiting amplitude principle for a hyperbolic metamaterial in free space, https://hal.archives-ouvertes.fr/hal-03164307

Other Publications (in other fields or in Ukrainian)

1. M. Kachanovska, I. Zhdanova. Parallelization of the computations in the problem of control of the unilateral processes of diffusion and heat and mass transfer. Research Bulletin of National Technical University of Ukraine 'Kyiv Polytechnic Instititute'

2. O. Palagin, V. Romanov, I. Galelyuka, and M. Kachanovska. Virtual laboratory for computer-aided design of biosensors. International Journal of Computing, 6:68-76, 2007

3. V. Romanov, I. Galelyuka, M. Kachanovska, and A. Denysenko. Virtual laboratory for computer-aided design and its use in the educational process and scientific research. Informational Technologies and Computer Engineering, 1 (8):82-85, 2007. (in Ukrainian)

4. O. Palagin, V. Romanov, A. Sachenko, I. Galelyuka, V. Hrusha, M. Kachanovska and R. Kochan, Virtual Laboratory for Computer-Aided Design: Typical Virtual Laboratory Structure and Principles of Its Operation, Proceedings of the4th IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS'2007.