Kontakt
Direktor
Geschäftsstelle
Gleichstellungsbeauftragte
Ombudsperson für Fragen der
Diskriminierung und der sexuellen Belästigung
IT-Beauftragte
Anschrift
Prof. Dr. Alexey Chernov
Institut für Mathematik
Carl von Ossietzky Universität Oldenburg
D-26111 Oldenburg
Tel.: +49-441-798 3944
(Sekr.: -3247, Fax: -3004)
alexey.chernov@uni-oldenburg.de
Büro: Campus Oldenburg-Wechloy,
Carl von Ossietzky Straße, W1 2-223
Sprechstunde: nach Vereinbarung
Forschungsinteressen / Research Interests
My research interests are in the fields of Numerical Analysis and Scientific Computing, in particular:
- Numerical methods for uncertainty quantification in problems with random parameters
- Finite Element Methods, high-order and spectral FEM
- Boundary Element Methods, discretization of nonlocal operators
- Numerical integration
- Numerical methods for high-dimensional problems
- Numerical methods for contact and obstacle problems
Forschungsgruppe / Research Group
Current members
PhD student
since 10/2017 | Nick Wulbusch, Topic: "Numerical methods for parametric PDE models in time-harmonic acoustics" |
Postdoctoral research fellow
since 03/2024 | Tùng Lê, Topic: "Parametric regularity for nonlinear partial differential equations" |
Alumni
Postdoctoral research fellows
10/2020 – 07/2022 | Erik M. Schetzke, Topic: "Numerical methods for covariance functions of elliptic problems under uncertainty" |
05/2010 – 10/2013 | Duong T. Pham, Topic: "Sparse spectral approximation for pseudodifferential operators" |
10/2008 – 02/2009 | Kersten Schmidt, Topic: "High order transmission conditions for thin conducting sheets" |
PhD students
04/2017 – 03/2024 | Tùng Lê, Topic: "Parametric regularity for nonlinear partial differential equations" (defended at the University of Oldenburg in March 2024) |
10/2014 – 09/2020 | Erik M. Schetzke, Topic: "Numerical methods for covariance functions of elliptic problems under uncertainty" (defended at the University of Oldenburg in September 2020) |
10/2015 – 02/2018 | Lorenzo Mascotto, Topic: "High order Virtual Element Methods" |
(defended at the Università degli Studi di Milano Statale and the University of Oldenburg in February 2018) | |
02/2012 – 03/2016 | Claudio Bierig, Topic: "Approximation of Central Moments and Probability Density |
Functions by MLMC with Application to Stochastic Variational Inequalities" | |
(defended at the University of Oldenburg in March 2016) | |
02/2012 – 08/2015 | Anne Reinarz, Topic: "Sparse space-time Boundary Element Methods for the heat |
equation" (defended at the University of Reading, UK in August 2015) |
Collaborators
- Lourenço Beirão da Veiga, University of Milano-Bicocca, Italy
- Claudio Bierig, Robert Bosch GmbH, Abstatt, Germany
- Dinh Dũng, Vietnam National University, Hanoi, Vietnam
- Herbert Egger, Universität Linz, Austria
- Frances Y. Kuo, University of New South Wales, Sydney, Australia
- Matthias Maischak, Brunel University, United Kingdom
- Lorenzo Mascotto, University of Milano-Bicocca, Italy
- Duong T. Pham, Vietnamese-German University, Vietnam
- Anne Reinarz, University of Durham, UK
- Alessandro Russo, University of Milano-Bicocca, Italy
- Erik M. Schetzke, Fraunhofer-Institute FKIE, Wachtberg, Germany
- Kersten Schmidt, TU Darmstadt, Germany
- Christoph Schwab, ETH Zurich, Switzerland
- Ian H. Sloan, University of New South Wales, Sydney, Australia
- Ernst P. Stephan, University of Hanover, Germany
- Thanh Tran, University of New South Wales, Sydney, Australia
- Tobias von Petersdorff, University of Maryland, College Park, USA
Publikationen / Publications
Preprints
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A. Chernov and T. Lê, Analytic and Gevrey class regularity for parametric elliptic eigenvalue problems and applications, SIAM J. Numer. Anal. (2024), accepted, Preprint
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N. Wulbusch, R. Roden, M. Blau and A. Chernov, Bayesian parameter identification in impedance boundary conditions for Helmholtz problems, SIAM J. Sci. Comput (2024), accepted, Preprint
Peer-reviewed Publications
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A. Chernov and T. Lê, Analytic and Gevrey class regularity for parametric semilinear reaction-diffusion problems and applications in uncertainty quantification, Comput. Math. Appl., 164 (2024), 116–130, DOI: 10.1016/j.camwa.2024.04.007, Preprint
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A. Chernov and E. M. Schetzke, A simple, bias-free approximation of covariance functions by the multilevel Monte Carlo method having nearly optimal complexity, SIAM/ASA J. Uncertain. Quantif., 11 (2023), no. 3, 941–969, DOI: 10.1137/22M1506845, Preprint
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N. Wulbusch, R. Roden, A. Chernov and M. Blau, Using a one-dimensional finite-element approximation of Webster's horn equation to estimate individual ear canal acoustic transfer from input impedances, J. Acoust. Soc. Am., 153 (2023), no. 5, 2826–2837, DOI: 10.1121/10.0019378, Preprint
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A. Chernov, C. Marcati and L. Mascotto, p- and hp-virtual elements for the Stokes problem, Adv. Comput. Math., 47 (2021), no. 2, Paper No. 24, 31 pp., DOI: 10.1007/s10444-020-09831-w, Preprint
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A. Chernov, H. Hoel, K. Law, F. Nobile and R. Tempone, Multilevel ensemble Kalman filtering for spatio-temporal processes, Numer. Math. 147 (2021), no. 1, 71–125, DOI: 10.1007/s00211-020-01159-3, Preprint
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F. Schöpfer and A. Chernov, Certified efficient global roundness evaluation, J. Optim. Theory Appl., 186 (2020), no.1, 169–190, DOI: 10.1007/s10957-020-01689-8
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D. T. Pham, T. Tran, D. Dũng and A. Chernov, Exterior Dirichlet and Neumann problems in domains with random boundaries, Bull. Malays. Math. Sci. Soc., 43 (2020), no. 2, 1311–1342, DOI: 10.1007/s40840-019-00741-9
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A. Chernov and A. Reinarz, Sparse grid approximation spaces for space-time boundary integral formulations of the heat equation, Comput. Math. Appl., 78 (2019), no. 11, 3605–3619, DOI: 10.1016/j.camwa.2019.06.036, Preprint
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A. Chernov and L. Mascotto, The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains, IMA J. Numer. Anal., 39 (2019), no. 4, 1787–1817, DOI: 10.1093/imanum/dry038, Preprint
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L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo, Exponential convergence of the hp virtual element method in presence of corner singularities, Numer. Math. 138 (2018), no. 3, 581–613, DOI: 10.1007/s00211-017-0921-7, Preprint
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L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo, Basic principles of hp Virtual Elements on quasiuniform meshes, Math. Models Methods Appl. Sci. 26 (2016), no. 8, 1567–1598, DOI: 10.1142/S021820251650038X, Preprint
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C. Bierig and A. Chernov, Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method, J. Comput. Physics 314 (2016), 661–681, DOI: 10.1016/j.jcp.2016.03.027, Preprint
A supplimentary MATLAB package is available here
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C. Bierig and A. Chernov, Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo Method, Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 1, 3–40, DOI: 10.1007/s40072-015-0063-9, Preprint
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A. Chernov and D. Dũng, New explicit-in-dimension estimates for the cardinality of high-dimensional hyperbolic crosses and approximation of functions having mixed smoothness, J. Complexity 32 (2016), no.1, 92–121, DOI: 10.1016/j.jco.2015.09.001, Preprint
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A. Chernov, T. von Petersdorff, and C. Schwab, Quadrature algorithms for high-dimensional singular integrands on simplices, Numer. Algorithms 70 (2015), no. 4, 847–874, DOI: 10.1007/s11075-015-9977-6, Preprint
The supplimentary Netlib package na39 (peer-reviewed) is avaliable at www.netlib.org/numeralgo
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A. Chernov, D. Pham and T. Tran, A shape calculus based method for a transmission problem with random interface, Comput. Math. Appl. 70 (2015), no. 7, 1401–1424, DOI: 10.1016/j.camwa.2015.06.021, Preprint
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C. Bierig and A. Chernov, Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems, Numer. Math. 130 (2015), no. 4, 579–613, DOI: 10.1007/s00211-014-0676-3, Preprint
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A. Chernov and D. Pham, Sparse spectral BEM for elliptic problems with random input data on a spheroid, Adv. Comput. Math. 41 (2015), no. 1, 77–104, DOI: 10.1007/s10444-014-9350-7, Preprint
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K. Schmidt and A. Chernov, Robust transmission conditions of high order for thin conducting sheets in two dimensions, IEEE Trans. Magn. 50 (2014), no. 2, 41–44, DOI: 10.1109/TMAG.2013.2285437, Preprint
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A. Chernov and A. Reinarz, Numerical quadrature for high-dimensional singular integrals over parallelotopes, Comput. Math. Appl. 66 (2013), no. 7, 1213–1231
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A. Chernov and C. Schwab, First order k-th moment Finite Element analysis of nonlinear operator equations with stochastic data, Math. Comp. 82 (2013), no. 284, 1859–1888
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K. Schmidt and A. Chernov, A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model, SIAM J. Appl. Math. 73 (2013), no. 6, 1980–2003
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A. Chernov and C. Schwab, Sparse space-time Galerkin BEM for the nonstationary heat equation, ZAMM Z. Angew. Math. Mech. 93 (2013), no. 6–7, 403–413
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A. Chernov, Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex, Math. Comp. 81 (2012), no. 278, 765–787
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A. Chernov and C. Schwab, Exponential convergence of Gauss-Jacobi quadratures for singular integrals over high dimensional simplices, SIAM J. Numer. Anal. 50 (2012), no. 3, 1433–1455
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A. Chernov, Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading, Appl. Numer. Math. 62 (2012), no. 4, 360–377
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D. T. Pham, T. Tran, and A. Chernov, Pseudodifferential equations on the sphere with spherical splines, Math. Models Methods Appl. Sci. 21 (2011), no. 9, 1933–1959
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A. Chernov, T. von Petersdorff, and C. Schwab, Exponential convergence of hp quadrature for integral operators with gevrey kernels, ESAIM Math. Model. Numer. Anal. 45 (2011), no. 3, 387–422
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A. Chernov and P. Hansbo, An hp-Nitsche’s method for interface problems with nonconforming unstructured finite element meshes, Vol. 76 of Lecture Notes in Computational Science and Engineering, pp. 153–162, Springer, 2011.
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A. Chernov and C. Schwab, Sparse p-version BEM for first kind boundary integral equations with random loading, Appl. Numer. Math. 59 (2009), no. 11, 2698–2712
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A. Chernov, Abstract sensitivity analysis for nonlinear equations and applications, in: Numerical Mathematics and Advanced Applications, ENUMATH 2007, pp. 407–414, Springer, Berlin, Heidelberg, 2008.
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A. Chernov, M. Maischak, and E.P. Stephan, hp-mortar boundary element method for two-body contact problems with friction, Math. Methods Appl. Sci. 31 (2008), no. 17, 2029–2054
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A. Chernov, M. Maischak, and E.P. Stephan, A priori error estimates for hp penalty BEM for contact problems in elasticity, Comput. Methods Appl. Mech. Engrg. 196 (2007), no. 37–40, 3871–3880
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A. Chernov and E.P. Stephan, Adaptive BEM for Contact Problems with Friction, in IUTAM Symposium on Computational Methods in Contact Mechanics, Vol. 3 of IUTAM Bookser., pp. 113–122, Springer, Dordrecht, 2007
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A. Chernov, S. Geyn, M. Maischak, and E. P. Stephan, Finite element/boundary element coupling for two-body elastoplastic contact problems with friction, in: Analysis and Simulation of Contact Problems, Lecture Notes in Applied and Computational Mechanics, Vol. 27, pp. 171–178, Springer, Berlin, Heidelberg, 2006, P. Wriggers, U. Nackenhorst (Eds.)
Publications in conference proceedings
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A. Chernov and A. Reinarz, Sparse grid approximation spaces for space-time boundary integral formulations of the heat equation, Oberwolfach Report 06/2022 ''Space-Time Methods for Time-Dependent Partial Differential Equations'', 320-322, DOI: 10.14760/OWR-2022-6
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C. Bierig, A. Chernov and E. M. Schetzke, Multilevel Monte Carlo approximation of moments, covariance functions and the maximum entropy reconstruction, Oberwolfach Report 12/2019 ''Uncertainty Quantification'', 714–717, DOI: 10.14760/OWR-2019-12
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K. Schmidt and A. Chernov, Robust transmission conditions of high-order for thin conducting sheets, proceeding of WAVES 2011, Vancouver, Canada, pp. 691–694
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A. Chernov and C. Schwab, Efficient solution of elliptic BIEs with random loading or on a random boundary, Oberwolfach Report 19/2008 ''Analysis of Boundary Element Methods'', 958–961, DOI: 10.14760/OWR-2008-19
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A. Chernov, p-Sparse BEM for weakly singular integral equation with random data, proceedings of ICIAM 2007, Zurich, Switzerland, 16–20 July 2007
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A. Chernov and E. P. Stephan, Adaptive hp-version of mortar BEM for two-body contact problems in elasticity. DtN and Uzawa algorithms, proceedings of IABEM 2006, Graz, Austria, 10–12 July 2006
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A. Chernov, M. Maischak and E. P. Stephan, hp-mortar boundary element method and FE/BE coupling for multibody contact problems with friction, proceedings of ECCM 2006, Lisbon, Portugal, 5–9 June 2006
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A. Chernov and A. Koldoba, Propagation of the gasless burning wave. Numerical and Mathematical Modeling, proceedings of scientific conference ''Lomonosov Readings'' Moscow, Russia, April 2003
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A. Chernov and A. Koldoba, Thermal-diffusive instability of the deflagration front, proceedings of XIV Conference ''Theoretical Basis and Construction of Numerical Algorithms for Problems of Mathematical Physics'', Durso, Russia, September 2002
Other publications
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A. Chernov, A. Debussche and F. Nobile, Numerical methods for random and stochastic partial differential equations, Editorial preface, Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 1, 1–2, DOI: 10.1007/s40072-016-0073-2
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A. Chernov and F. Nobile, Numerical methods for uncertainty quantification, Editorial preface, Int. J. Uncertain. Quantif. 5 (2015), no. 3, vi–vii, DOI: 10.1615/Int.J.UncertaintyQuantification.2015014190
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A. Chernov and C. Schwab, High-order finite element approximation for partial differential equations, Editorial preface, Comput. Math. Appl. 67 (2014), no. 4, 709–711, DOI: 10.1016/j.camwa.2014.01.012
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A. Chernov, Nonconforming boundary elements and finite elements for interface and contact problems with friction – hp-version for mortar, penalty and Nitsche's methods, PhD Thesis, University of Hannover, 2006
Software
- Implementation of the Maximum Entropy method by matching generalized moments is available here. An earlier version of this program have been used for numerical experiments published in the paper:
C. Bierig and A. Chernov, Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method, J. Comput. Physics 314 (2016), 661–681, DOI: 10.1016/j.jcp.2016.03.027, Preprint
- Netlib package na39 (peer-reviewed), avaliable at www.netlib.org/numeralgo. This is a supplementary program package for the paper:
A. Chernov, T. von Petersdorff, and C. Schwab, Quadrature algorithms for high-dimensional singular integrands on simplices, Numer. Algorithms 70 (2015), no. 4, 847–874, DOI: 10.1007/s11075-015-9977-6, Preprint
Kurzer Lebenslauf / Curriculum Vitae
since 04/2023 | Member of Senate, University of Oldenburg |
since 10/2023 | Oldenburg representative, Deutscher Hochschulverband |
04/2019 – 03/2021 | Vice Dean (Prodekan) of the School of Mathematics and Science, University of Oldenburg |
04/2017 – 03/2019 | Director of the Institute for Mathematics, Univ. Oldenburg (Vice Director 04/2019–03/2021) |
09/2015 – 08/2018 | Vice-Chair of the GAMM Activity Group on Uncertainty Quantification |
since 04/2015 | Full Professor (W3), Institute for Mathematics, University of Oldenburg, Germany |
09/2013 – 03/2015 | Associate Professor, Dep. of Mathematics and Statistics, University of Reading, UK |
10/2008 – 08/2013 | Professor (W2), Hausdorff Center for Mathematics, University of Bonn, Germany |
10/2006 – 09/2008 | Postdoc, Seminar for Applied Mathematics, ETH Zurich, Switzerland |
10/2003 – 09/2006 | PhD, Institute for Applied Mathematics, University of Hannover, Germany |
09/1998 – 06/2003 | Student, Depart. of Mechanics and Mathematics, Moscow State University, Russia |