Profile
Profile

Prof. Dr. Alexey Chernov

Former Bonn Junior Fellow
Current position: Professor (W3), University of Oldenburg

E-mail: alexey.chernov(at)uni-oldenburg.de
Homepage: https://www.uni-oldenburg.de/alexey-chernov
Institute: Institute for Numerical Simulation
Research Areas: Research Area G
Research Area J
Date of birth: 13.Aug 1981
Mathscinet-Number: 819420

Academic Career

2003

Diploma, Moscow State Lomonosov University, Russia

2006

Dr. rer. nat., University of Hannover

2006 - 2008

Postdoctoral Research Fellow, Seminar for Applied Mathematics, ETH Zürich, Switzerland

2008 - 2013

Professor (W2, Bonn Junior Fellow), University of Bonn

2013 - 2015

Associate Professor, Department of Mathematics and Statistics, University of Reading, England, UK

Since 2015

Professor (W3), Institute for Mathematics, University of Oldenburg

Research Profile

My primary research interests are in construction and analysis of numerical schemes for solutions of partial differential and integral equations with an emphasis on high-order numerical methods [4,5,6].
I am particularly interested in numerical analysis of problems with random data [2,3]; construction and analysis of efficient automatic integration algorithms, especially for high-dimensional singular integrands [1]; construction and analysis of numerical schemes for variational inequalities, in particular, for contact problems in elasticity [7,8,9].

Research Projects and Activities

HCM-Workshop “High-Order Numerical Approximation for Partial Differential Equations”
Co-organizer, February 6 - 10, 2012, org. A. Chernov, C. Schwab

Contribution to Research Areas

Research Area J
In [1], we constructed and analyzed a family of quadrature rules for approximate computation of high dimensional integrals with diagonal singularity over regular simplices. The approach is based on a family of regularizing coordinate transformations simplifying simultaneously the structure of the singularity and the integration domain and works in any dimension.
In [2], we developed a sparse spectral approximation theory with polynomials on finite intervals. These discretization techniques can be used to overcome the curse of dimensionality in numerical approximation of statistical moments of solutions of elliptic equations with a random loading term. After an appropriate linearization procedure [3], this approach is applicable to nonlinear problems as well.
In [4], we studied the approximation properties of the trace of the L^2-polynomial projection operator on a simplex. This fundamental approximation result has applications in many areas of numerical analysis, e.g. in analysis of hp-Discontinuous Galerkin Methods, Nitsche's methods [5].
In [6], we aim at an efficient numerical solution of elliptic pseudodifferential equations on the surface of the sphere with applications in geodesy.
Research Area G
The quadrature algorithms developed in [1] can be used in particular for pricing of financial options based on Levy-driven assets. The special difficulty here is that the singularity order is a model parameter which might take fractional values.
In [2], we work on numerical schemes for the statistical moment equation. This technique compares favorably with alternative methods based on the Karhuhen-Loeve expansion, especially if the convergence of the Karhuhen-Loeve expansion is slow.

Selected Publications

[2] Alexey Chernov, Christoph Schwab
Sparse p-version BEM for first kind boundary integral equations with random loading
Appl. Numer. Math. , 59: (11): 2698--2712
2009
DOI: 10.1016/j.apnum.2008.12.023
[7] Alexey Chernov, Matthias Maischak, Ernst P. Stephan
hp-mortar boundary element method for two-body contact problems with friction
Math. Methods Appl. Sci. , 31: (17): 2029--2054
2008
DOI: 10.1002/mma.1005
[8] Alexey Chernov, Ernst P. Stephan
Adaptive BEM for contact problems with friction
IUTAM Symposium on Computational Methods in Contact Mechanics
of IUTAM Bookser. : 113--122
Publisher: Springer, Dordrecht
2007
DOI: 10.1007/978-1-4020-6405-0_7
[9] A. Chernov, M. Maischak, E. P. Stephan
A priori error estimates for hp penalty BEM for contact problems in elasticity
Comput. Methods Appl. Mech. Engrg. , 196: (37-40): 3871--3880
2007
DOI: 10.1016/j.cma.2006.10.044

Publication List

Awards

2003

Honors Diploma in Mechanics and Applied Mathematics, Moscow State Lomonosov University, Russia

2003 - 2006

Scholarship of German Research Foundation, Research Training Group GRK 615, University of Hannover

Selected Invited Lectures

2008

Workshop “Analysis of Boundary Element Methods”, MFO Oberwolfach

2009

“Advances in Boundary Integral Equations and Related Topics”, University of Delaware, Newark, DE, USA

2011

Workshop “High-Dimensional Aspects of Stochastic PDEs”, Bonn

Supervised Theses

  • Master theses currently: 1
  • Diplom theses: 3, currently 1
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