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Publications of A. V. Shapeev
Submitted Articles
[3]An Optimization-Based Atomistic-to-Continuum Coupling Method (D. Olson, P. Bochev, M. Luskin, A. V. Shapeev). [bibtex] [arXiv]
[2](In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods (C. Ortner, A.V. Shapeev, L. Zhang). [bibtex] [arXiv]
[1]Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations (V. Ehrlacher, C. Ortner, A.V. Shapeev). [bibtex] [arXiv]
Refereed Articles
2014
[11]Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method (Xingjie Li, Mitchell Luskin, Christoph Ortner, Alexander V. Shapeev), Computer Methods in Applied Mechanics and Engineering, volume 268, 2014. [bibtex] [doi] [arXiv]
2013
[10]Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice (C. Ortner, A. V. Shapeev), Math. Comp., volume 82, 2013. [bibtex] [doi] [arXiv]
[9]A Priori and A Posteriori $W^1,infty$ Error Analysis of a QC Method for Complex Lattices (A. Abdulle, P. Lin, A. Shapeev), SIAM J. Numer. Anal., volume 51, 2013. [bibtex] [doi] [arXiv]
2012
[8]Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions (A. V. Shapeev), SIAM J. Sci. Comput., volume 34, 2012. [bibtex] [doi] [arXiv]
[7]The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain (M. Dobson, C. Ortner, A. V. Shapeev), Multiscale Model. Simul., volume 10, 2012. [bibtex] [doi] [arXiv]
[6]Numerical Methods for Multilattices (A. Abdulle, P. Lin, A. V. Shapeev), Multiscale Model. Simul., volume 10, 2012. [bibtex] [doi] [arXiv]
2011
[5]Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions (A. V. Shapeev), Multiscale Model. Simul., volume 9, 2011. [bibtex] [doi] [arXiv]
(Winner of 2013 SIAM Outstanding Paper Prize)
2009
[4]An asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows (A. V. Shapeev, Ping Lin), SIAM J. Sci. Comput., volume 31, 2009. [bibtex] [pdf] [doi]
2005
[3]Investigation of mixed spectral and finite difference approximation on the basis of problem of viscous flow in a diffuser (A. V. Shapeev), Siberian Journal of Numerical Mathematics, volume 8, 2005. (in Russian) [bibtex]
2004
[2]Unsteady self-similar flow of a viscous incompressible fluid in a plane divergent channel (A. V. Shapeev), Fluid Dynamics, volume 39, 2004. [bibtex]
2000
[1]High-order accurate difference schemes for elliptic equations in a domain with a curvilinear boundary (A. V. Shapeev, V. P. Shapeev), Computational Mathematics and Mathematical Physics, volume 40, 2000. [bibtex]
Conference Proceedings
2009
[7]Polynomial Least-Squares Reconstruction for Semi-Lagrangian Cell-Centered Hydrodynamic Schemes (Gilles Carre, Stephane Del Pino, Kirill Pichon Gostaf, Emmanuel Labourasse, Alexander Shapeev), In ESAIM Proceedings, CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids, volume 28, 2009. [bibtex] [pdf]
2008
[6]A numerical-asymptotic method for computation of infinite number of eddies of viscous flows in domains with corners (A. V. Shapeev), In Computational Fluid Dynamics, 2008. [bibtex]
2002
[5]Numerical Simulation of 3D Motions of Locally Heated Liquid Films (A. V. Shapeev), In Proceedings of the Third Russian National Conference on Heat Transfer, 2002. (in Russian) [bibtex]
[4]Proof of Convergence of Numerical Methods of Solving Weakly Nonlinear Problems (A. V. Shapeev), In Problems of Continuous Media Mechanics: Proceedings of the 33rd Regional Youth Conference, 2002. (in Russian) [bibtex]
2001
[3]Unconditionally Stable Explicit High-Order Scheme for the Nonlinear Schrodinger Equation (A. V. Shapeev), In Proceedings of the Youth Scientific Conference dedicated to the 10th anniversary of Institute of Computational Technologies SB RAS, volume 2, 2001. (in Russian) [bibtex]
[2]Solution of Elliptical Problems with Singularities using High-Order Schemes (A. V. Shapeev, V. P. Shapeev), In Problems of Continuous Media Mechanics: Proceedings of the 32nd Regional Youth Conference, 2001. (in Russian) [bibtex]
2000
[1]High order approximation schemes (A. V. Shapeev, V. P. Shapeev), In Proceedings of the 3rd European Conference on Numerical Mathematics and Advanced Applications, World Scientific, 2000. [bibtex]
Other Publications
2013
[6]Development of an Optimization-Based Atomistic-to-Continuum Coupling Method (Derek Olson, Pavel Bochev, Mitchell Luskin, Alexander V. Shapeev), 2013. [bibtex] [arXiv]
2012
[5]Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods (C. Ortner, A. V. Shapeev), 2012. (arXiv:1204.3705) [bibtex] [pdf]
2010
[4]Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals (A. Abdulle, P. Lin, A. V. Shapeev), 2010. (arXiv:1006.0378) [bibtex] [pdf]
2009
[3]Viscous incompressible axisymmetric flows in cones (A. V. Shapeev), Technical report, Lavrentyev Institute of Hydrodynamics SB RAS, 2009. (In Russian) [bibtex]
[2]Energy-based ghost force removing techniques for the quasicontinuum method (P. Lin, A. V. Shapeev), 2009. (arXiv:0909.5437) [bibtex] [pdf]
2002
[1]Pattern Formation -- Group Theoretical and Numerical Points of View (G. Czichowski, A. V. Shapeev, V. P Shapeev), Technical report, Ernst-Moritz-Arndt-Universitat Greifswald, Institut fur Mathematik und Informatik, 2002. [bibtex]