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Publications of A. V. Shapeev
Submitted Articles
[1]Accuracy of computation of crystalline defects at finite temperature (M. Luskin, A.V. Shapeev). [bibtex] [arXiv]
Refereed Articles
[20]Active Learning of Linearly Parametrized Interatomic Potentials (E. V. Podryabinkin, A. V. Shapeev), Computational Materials Science, volume 140, pages 171-180, 2017. [bibtex] [doi] [arXiv]
[19]Accurate representation of formation energies of crystalline alloys with many components (A. Shapeev), Computational Materials Science, volume 139, pages 26-30, 2017. [bibtex] [doi] [arXiv]
[18]Moment Tensor Potentials: a class of systematically improvable interatomic potentials (A.V. Shapeev), Multiscale Model. Simul., volume 14, pages 1153-1173, 2016. [bibtex] [pdf] [doi] [arXiv]
[17]Analysis of an optimization-based atomistic-to-continuum coupling method for point defects (D. Olson, A. V. Shapeev, P. Bochev, M. Luskin), ESAIM: Mathematical Modelling and Numerical Analysis, volume 50, pages 1--41, 2016. [bibtex] [doi] [arXiv]
[16]Analysis of blended atomistic/continuum hybrid methods (X. H. Li, C. Ortner, A. V. Shapeev, B. Van Koten), Numerische Mathematik, Springer Berlin Heidelberg, volume 134, pages 275-326, 2016. [bibtex] [pdf] [doi] [arXiv]
[15]Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations (V. Ehrlacher, C. Ortner, A.V. Shapeev), volume 222, pages 1217-1268, 2016. [bibtex] [doi] [arXiv]
[14]An optimization based coupling method for multiscale problems (A. Abdulle, A. Shapeev O. Jecker), Multiscale Model. Simul., Society for Industrial and Applied Mathematics, volume 14, pages 1377-1416, 2016. [bibtex] [pdf] [doi]
[13]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, pages 763--781, 2014. [bibtex] [pdf] [doi] [arXiv]
[12](In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods (C. Ortner, A.V. Shapeev, L. Zhang), Multiscale Model. Simul., volume 12, pages 1258-1293, 2014. [bibtex] [pdf] [doi] [arXiv]
[11]An optimization-based atomistic-to-continuum coupling method (D. Olson, P. Bochev, M. Luskin, A. V. Shapeev), SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, volume 52, pages 2183--2204, 2014. [bibtex] [arXiv]
[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, pages 2191--2236, 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, pages 2357--2379, 2013. [bibtex] [doi] [arXiv]
[8]Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions (A. V. Shapeev), SIAM J. Sci. Comput., volume 34, pages B335--B360, 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, pages 744--765, 2012. [bibtex] [doi] [arXiv]
[6]Numerical Methods for Multilattices (A. Abdulle, P. Lin, A. V. Shapeev), Multiscale Model. Simul., volume 10, pages 696--726, 2012. [bibtex] [doi] [arXiv]
[5]Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions (A. V. Shapeev), Multiscale Model. Simul., volume 9, pages 905--932, 2011. [bibtex] [doi] [arXiv]
(Winner of 2013 SIAM Outstanding Paper Prize)
[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, pages 1874--1900, 2009. [bibtex] [pdf] [doi]
[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, pages 149--162, 2005. (in Russian) [bibtex]
[2]Unsteady self-similar flow of a viscous incompressible fluid in a plane divergent channel (A. V. Shapeev), Fluid Dynamics, volume 39, pages 36--41, 2004. [bibtex]
[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, pages 213--221, 2000. [bibtex]
Conference Proceedings
[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, pages 100--116, 2009. [bibtex] [pdf]
[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]
[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, pages 103--105, 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, pages 189--193, 2002. (in Russian) [bibtex]
[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, pages 175--179, 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, pages 62--66, 2001. (in Russian) [bibtex]
[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, pages 715--724, 2000. [bibtex]
Other Publications
[6]Development of an Optimization-Based Atomistic-to-Continuum Coupling Method (Derek Olson, Pavel Bochev, Mitchell Luskin, Alexander V. Shapeev), 2013. [bibtex] [arXiv]
[5]Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods (C. Ortner, A. V. Shapeev), 2012. (arXiv:1204.3705) [bibtex] [pdf]
[4]Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals (A. Abdulle, P. Lin, A. V. Shapeev), 2010. (arXiv:1006.0378) [bibtex] [pdf]
[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]
[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]