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| 2003 | Diploma, Moscow State Lomonosov University | | 2006 | Dr. rer. nat., Hannover University | | 2006--2008 | Postdoctoral research fellow, Seminar for Applied Mathematics, ETH Zurich | | 2008-- | Professor (W2, Bonn Junior Fellow), Bonn University |
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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].
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[ 1] Alexey Chernov, Tobias von Petersdorff, Christoph Schwab
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
M2AN , 45: (3): 387-422
2011
DOI: 10.1051/m2an/2010061[ 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
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2008.12.023[ 3] Alexey Chernov
Abstract sensitivity analysis for nonlinear equations and applications
Numerical Mathematics and Advanced Applications
ENUMATH 2007 : 407--414
2008[ 4] Alexey Chernov
Optimal convergence estimates for the trace of the polynomial L^2-projection operator on a simplex
accepted
Mathematics of Computation
2011[ 5] Alexey Chernov, Peter Hansbo
An hp-Nitsche's method for interface problems with nonconforming unstructured finite element meshes
Spectral and high order methods for partial differential equations
of Lecture Notes in Computational Science and Engineering : 153--162
Publisher: Springer
2011[ 6] Thanh Duong Pham, Thanh Tran, Alexey Chernov
Pseudodifferential equations on the sphere with spherical splines
accepted
M3AS Math. Models Meth. Appl. Sci.
2011[ 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
ISSN: 0170-4214
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
ISSN: 0045-7825
DOI: 10.1016/j.cma.2006.10.044 |
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| 2003 | Honors Diploma in Mechanics and Applied Mathematics, Moscow State Lomonosov University | | 2003--2006 | Scholarship of German Research Foundation, GRK 615, Hanover University |
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| 2008 | Workshop “Analysis of Boundary Element Methods”, MFO Oberwolfach, Germany | | 2009 | “Advances in Boundary Integral Equations and Related Topics“, University of Delaware, USA | | 2011 | Workshop “High-Dimensional Aspects of Stochastic PDEs”, Bonn, Germany |
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Co-organizer of the HCM-Workshop ''High-Order Numerical Approximation for Partial Differential Equations'' (February 6–10, 2012, org. A. Chernov, C. Schwab)
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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. This 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  -polynomial projection operator on a simplex. This fundamental approximation result has applications in many areas of numerical analysis, e.g. in analysis of  -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 techniques compares favorably with alternative methods based on the Karhuhen-Loeve expansion, especially if the convergence of the Karhuhen-Loeve expansion is slow. |
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- Bachelor theses: 1
- Master theses currently: 1
- Diplom theses: 3, currently 1
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