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(at)uni-oldenburg.de 

Büro: Campus Oldenburg-Wechloy,
Carl von Ossietzky Straße, W1 2-223

Sprechstunde: nach Vereinbarung

Ankündigungen / News

Die Vortragsfolien zur Fachvorstellung Mathematik Bachelor finden Sie hier.

Visit the web site of the GAMM Activity Group Uncertainty Quantification

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 students

since 04/2017 Tùng Lê, Topic: "Numerical methods for nonlinear problems under uncertainty"
since 10/2015 Lorenzo Mascotto, Topic: "High order Virtual Element Methods"
since 10/2014 Erik M. Schetzke, Topic: "Adaptive error control for elliptic problems under uncertainty"

Alumni

Postdoctoral research fellows

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

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

Publikationen / Publications

Preprints

  1. A. Chernov, H. Hoel, K. Law, F. Nobile and R. Tempone, Multilevel ensemble Kalman filtering for spatially extended models, August 2016, submitted, available online: Preprint

Peer-reviewed Publications

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. A. Chernov and A. Reinarz, Numerical quadrature for high-dimensional singular integrals over parallelotopes, Comput. Math. Appl. 66 (2013), no. 7, 1213–1231

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. D. 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

  18. 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

  19. 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.

  20. 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

  21. 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.

  22. 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

  23. 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

  24. 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

  25. 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

  1. K. Schmidt and A. Chernov, Robust transmission conditions of high-order for thin conducting sheets, proceeding of WAVES 2011, Vancouver, Canada, pp. 691–694

  2. 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'', 6–9

  3. A. Chernov, p-Sparse BEM for weakly singular integral equation with random data, proceedings of ICIAM 2007, Zurich, Switzerland, 16–20 July 2007

  4. 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

  5. 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

  6. 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

  7. 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

  1. 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

  2. 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

  3. 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

  4. 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

  1. 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

  2. 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

Lehre / Recent Teaching

In Oldenburg

WS 2016/175.01.141 Einführung in die Numerik (Bachelor)
5.01.104 Proseminar zur Analysis (Numerische Mathematik) (Bachelor)
SS 20165.01.141 Numerik gewöhnlicher Differentialgleichungen (Bachelor)
5.01.596 Numerik partieller Differentialgleichungen (Master)
WS 2015/165.01.141 Einführung in die Numerik (Bachelor)
5.01.598 Numerische Methoden für partielle Differentialgleichungen mit Unsicherheiten (Master)
SS 20155.01.596 Numerik partieller Differentialgleichungen (Bachelor / Master)

In Reading

Spring 2015ICM299 Numerical Methods for Financial Engineering (MSc Financial Eng., ICMA & Henley BS)
Autumn 2014MA3NA2 Numerical Analysis II (BSc Mathematics)
Spring 2014ICM293 Numerical Methods for Finance (MSc Financial Eng., ICMA & Henley Business School)

Kurzer Lebenslauf / Curriculum Vitae

since 04/2017 Director of the Institute for Mathematics, University of Oldenburg
since 09/2015 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