Alexander V. SHAPEEV - List of Publications

A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et�al 2003 Science 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100�1700 K is unique.

2020
[2]	Active Learning and Uncertainty Estimation (Alexander Shapeev, Konstantin Gubaev, Evgenii Tsymbalov, Evgeny Podryabinkin), Chapter in Machine Learning Meets Quantum Physics, Springer, pages 309--329, 2020. [bibtex]
2019
[1]	Applications of Machine Learning for Representing Interatomic Interactions (Alexander V. Shapeev), Chapter in Computational Materials Discovery (Artem R Oganov, Gabriele Saleh, Alexander G Kvashnin, eds.), The Royal Society of Chemistry, 2019. [bibtex]

2021
[68]	Modeling the high-temperature phase coexistence region of mixed transition metal oxides from ab initio calculations (Suzanne K Wallace, Ambroise van Roekeghem, Anton S Bochkarev, Javier Carrasco, Alexander Shapeev, Natalio Mingo), Physical Review Research, APS, volume 3, pages 013139, 2021. [bibtex]
[67]	Free energy of (Co x Mn 1- x)3 O4 mixed phases from machine-learning-enhanced ab initio calculations (Suzanne K Wallace, Anton S Bochkarev, Ambroise van Roekeghem, Javier Carrasco, Alexander Shapeev, Natalio Mingo), Physical Review Materials, APS, volume 5, pages 035402, 2021. [bibtex]
[66]	Machine learning for deep elastic strain engineering of semiconductor electronic band structure and effective mass (Evgenii Tsymbalov, Zhe Shi, Ming Dao, Subra Suresh, Ju Li, Alexander Shapeev), npj Computational Materials, Nature Publishing Group, volume 7, pages 1--10, 2021. [bibtex]
[65]	Efficient and accurate prediction of elastic properties of Ti0. 5Al0. 5N at elevated temperature using machine learning interatomic potential (Ferenc Tasnádi, Florian Bock, Johan Tidholm, Alexander V Shapeev, Igor A Abrikosov), Thin Solid Films, Elsevier, pages 138927, 2021. [bibtex]
[64]	Machine-learned interatomic potentials for alloys and alloy phase diagrams (Conrad W Rosenbrock, Konstantin Gubaev, Alexander V Shapeev, Livia B Pártay, Noam Bernstein, Gábor Csányi, Gus LW Hart), npj Computational Materials, Nature Publishing Group, volume 7, pages 1--9, 2021. [bibtex]
[63]	Assessing parameters for ring polymer molecular dynamics simulations at low temperatures: DH+ H chemical reaction (Ivan S Novikov, Yury V Suleimanov, Alexander V Shapeev), Chemical Physics Letters, Elsevier, volume 773, pages 138567, 2021. [bibtex]
[62]	Exceptional piezoelectricity, high thermal conductivity and stiffness and promising photocatalysis in two-dimensional MoSi2N4 family confirmed by first-principles (Bohayra Mortazavi, Brahmanandam Javvaji, Fazel Shojaei, Timon Rabczuk, Alexander V Shapeev, Xiaoying Zhuang), Nano Energy, Elsevier, volume 82, pages 105716, 2021. [bibtex]
[61]	Accelerating first-principles estimation of thermal conductivity by machine-learning interatomic potentials: A MTP/ShengBTE solution (Bohayra Mortazavi, Evgeny V Podryabinkin, Ivan S Novikov, Timon Rabczuk, Xiaoying Zhuang, Alexander V Shapeev), Computer Physics Communications, Elsevier, volume 258, pages 107583, 2021. [bibtex]
[60]	First-Principles Multiscale Modeling of Mechanical Properties in Graphene/Borophene Heterostructures Empowered by Machine-Learning Interatomic Potentials (Bohayra Mortazavi, Mohammad Silani, Evgeny V Podryabinkin, Timon Rabczuk, Xiaoying Zhuang, Alexander V Shapeev), Advanced Materials, Wiley Online Library, pages 2102807, 2021. [bibtex]
[59]	Bayesian learning of thermodynamic integration and numerical convergence for accurate phase diagrams (V. Ladygin, I. Beniya, E. Makarov, A. Shapeev), Physical Review B, APS, volume 104, pages 104102, 2021. [bibtex] [doi]
[58]	B2 ordering in body-centered-cubic AlNbTiV refractory high-entropy alloys (Fritz Körmann, Tatiana Kostiuchenko, Alexander Shapeev, Jörg Neugebauer), Physical Review Materials, APS, volume 5, pages 053803, 2021. [bibtex]
[57]	Finite-temperature interplay of structural stability, chemical complexity, and elastic properties of bcc multicomponent alloys from ab initio trained machine-learning potentials (Konstantin Gubaev, Yuji Ikeda, Ferenc Tasnádi, Jörg Neugebauer, Alexander V Shapeev, Blazej Grabowski, Fritz Körmann), Physical Review Materials, APS, volume 5, pages 073801, 2021. [bibtex]
[56]	Finite-temperature interplay of structural stability, chemical complexity, and elastic properties of bcc multicomponent alloys from ab initio trained machine-learning potentials (Konstantin Gubaev, Yuji Ikeda, Ferenc Tasnádi, Jörg Neugebauer, Alexander V Shapeev, Blazej Grabowski, Fritz Körmann), Physical Review Materials, APS, volume 5, pages 073801, 2021. [bibtex]
[55]	Ab initio simulations of the surface free energy of TiN (001) (Axel Forslund, Xi Zhang, Blazej Grabowski, Alexander V Shapeev, Andrei V Ruban), Physical Review B, APS, volume 103, pages 195428, 2021. [bibtex]
2020
[54]	Elinvar effect in beta-Ti simulated by on-the-fly trained moment tensor potential (Alexander V Shapeev, Evgeny V Podryabinkin, Konstantin Gubaev, Ferenc Tasnádi, Igor A Abrikosov), New Journal of Physics, IOP Publishing, volume 22, pages 113005, 2020. [bibtex] [pdf] [doi][Abstract] A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et�al 2003 Science 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100�1700 K is unique.
[53]	Performance and Cost Assessment of Machine Learning Interatomic Potentials (Yunxing Zuo, Chi Chen, Xiangguo Li, Zhi Deng, Yiming Chen, Jörg Behler, Gábor Csányi, Alexander V Shapeev, Aidan P Thompson, Mitchell A Wood, others), The Journal of Physical Chemistry A, ACS Publications, volume 124, pages 731--745, 2020. [bibtex]
[52]	Predicting the propensity for thermally activated $\beta$ events in metallic glasses via interpretable machine learning (Qi Wang, Jun Ding, Longfei Zhang, Evgeny Podryabinkin, Alexander Shapeev, Evan Ma), npj Computational Materials, Nature Publishing Group, volume 6, pages 1--12, 2020. [bibtex]
[51]	Metallization of diamond (Zhe Shi, Ming Dao, Evgenii Tsymbalov, Alexander Shapeev, Ju Li, Subra Suresh), Proceedings of the National Academy of Sciences, National Acad Sciences, volume 117, pages 24634--24639, 2020. [bibtex]
[50]	High thermal conductivity in semiconducting Janus and non-Janus diamanes (Mostafa Raeisi, Bohayra Mortazavi, Evgeny V Podryabinkin, Fazel Shojaei, Xiaoying Zhuang, Alexander V Shapeev), Carbon, Elsevier, 2020. [bibtex]
[49]	The MLIP package: Moment tensor potentials with mpi and active learning (Ivan S Novikov, Konstantin Gubaev, Evgeny Podryabinkin, Alexander V Shapeev), Machine Learning: Science and Technology, IOP Publishing, 2020. [bibtex]
[48]	Nanoporous C3N4, C3N5 and C3N6 nanosheets; novel strong semiconductors with low thermal conductivities and appealing optical/electronic properties (Bohayra Mortazavi, Fazel Shojaei, Masoud Shahrokhi, Maryam Azizi, Timon Rabczuk, Alexander V Shapeev, Xiaoying Zhuang), Carbon, Elsevier, 2020. [bibtex]
[47]	Machine-learning interatomic potentials enable first-principles multiscale modeling of lattice thermal conductivity in graphene/borophene heterostructures (Bohayra Mortazavi, Evgeny V Podryabinkin, Stephan Roche, Timon Rabczuk, Xiaoying Zhuang, Alexander V Shapeev), Materials Horizons, Royal Society of Chemistry, volume 7, pages 2359--2367, 2020. [bibtex]
[46]	Exceptional piezoelectricity, high thermal conductivity and stiffness and promising photocatalysis in two-dimensional MoSi2N4 family confirmed by first-principles (Bohayra Mortazavi, Brahmanandam Javvaji, Fazel Shojaei, Timon Rabczuk, Alexander V Shapeev, Xiaoying Zhuang), Nano Energy, Elsevier, volume 82, pages 105716, 2020. [bibtex]
[45]	Exploring phononic properties of two-dimensional materials using machine learning interatomic potentials (Bohayra Mortazavi, Ivan S Novikov, Evgeny V Podryabinkin, Stephan Roche, Timon Rabczuk, Alexander V Shapeev, Xiaoying Zhuang), Applied Materials Today, Elsevier, volume 20, pages 100685, 2020. [bibtex]
[44]	Efficient machine-learning based interatomic potentials for exploring thermal conductivity in two-dimensional materials (Bohayra Mortazavi, Evgeny Podryabinkin, Ivan S Novikov, Stephan Roche, Timon Rabczuk, Xiaoying Zhuang, Alexander Shapeev), Journal of Physics: Materials, IOP Publishing, 2020. [bibtex] [doi]
[43]	Lattice dynamics simulation using machine learning interatomic potentials (VV Ladygin, P Yu Korotaev, AV Yanilkin, AV Shapeev), Computational Materials Science, Elsevier, volume 172, pages 109333, 2020. [bibtex] [pdf] [doi]
[42]	Short-range order in face-centered cubic VCoNi alloys (Tatiana Kostiuchenko, Andrei V Ruban, Jörg Neugebauer, Alexander Shapeev, Fritz Körmann), Physical Review Materials, APS, volume 4, pages 113802, 2020. [bibtex]
[41]	Lattice dynamics of Yb x Co 4 Sb 12 skutterudite by machine-learning interatomic potentials: Effect of filler concentration and disorder (Pavel Korotaev, Alexander Shapeev), Physical Review B, APS, volume 102, pages 184305, 2020. [bibtex]
[40]	In operando active learning of interatomic interaction during large-scale simulations (Max Hodapp, Alexander Shapeev), arXiv preprint arXiv:2004.13158, 2020. [bibtex]
[39]	Ab initio analysis of structural and electronic properties and excitonic optical responses of eight Ge-based 2D materials (Ali Ghojavand, S Javad Hashemifar, Mahdi Tarighi Ahmadpour, Alexander V Shapeev, Amir Alhaji, Qaem Hassanzada), Journal of Applied Physics, AIP Publishing LLC, volume 127, pages 214301, 2020. [bibtex]
[38]	Young�s modulus and tensile strength of Ti3C2 MXene nanosheets as revealed by in situ TEM probing, AFM nanomechanical mapping, and theoretical calculations (Konstantin L Firestein, Joel E von Treifeldt, Dmitry G Kvashnin, Joseph FS Fernando, Chao Zhang, Alexander G Kvashnin, Evgeny V Podryabinkin, Alexander V Shapeev, Dumindu P Siriwardena, Pavel B Sorokin, others), Nano Letters, ACS Publications, volume 20, pages 5900--5908, 2020. [bibtex]
2019
[37]	Deep elastic strain engineering of bandgap through machine learning (Zhe Shi, Evgenii Tsymbalov, Ming Dao, Subra Suresh, Alexander Shapeev, Ju Li), Proceedings of the National Academy of Sciences, National Acad Sciences, volume 116, pages 4117--4122, 2019. [bibtex] [pdf] [doi]
[36]	Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning (Evgeny V Podryabinkin, Evgeny V Tikhonov, Alexander V Shapeev, Artem R Oganov), Physical Review B, APS, volume 99, pages 064114, 2019. [bibtex] [pdf] [doi] [arXiv]
[35]	Machine-learned multi-system surrogate models for materials prediction (Chandramouli Nyshadham, Matthias Rupp, Brayden Bekker, Alexander V Shapeev, Tim Mueller, Conrad W Rosenbrock, Gábor Csányi, David W Wingate, Gus LW Hart), npj Computational Materials, Nature Publishing Group, volume 5, pages 51, 2019. [bibtex] [pdf] [doi] [arXiv]
[34]	Improving accuracy of interatomic potentials: more physics or more data? A case study of silica (Ivan S Novikov, Alexander V Shapeev), Materials Today Communications, Elsevier, volume 18, pages 74--80, 2019. [bibtex] [doi] [arXiv]
[33]	Ring polymer molecular dynamics and active learning of moment tensor potential for gas-phase barrierless reactions: Application to S + H2 (Ivan S Novikov, Alexander V Shapeev, Yury V Suleimanov), The Journal of Chemical Physics, AIP Publishing, volume 151, pages 224105, 2019. [bibtex] [pdf] [doi]
[32]	Prediction of C7N6 and C9N4: stable and strong porous carbon-nitride nanosheets with attractive electronic and optical properties (Bohayra Mortazavi, Masoud Shahrokhi, Alexander V Shapeev, Timon Rabczuk, Xiaoying Zhuang), Journal of Materials Chemistry C, Royal Society of Chemistry, 2019. [bibtex] [doi]
[31]	Sublattice formation in CoCrFeNi high-entropy alloy (E.A. Meshkov, I.I. Novoselov, A.V. Shapeev, A.V. Yanilkin), Intermetallics, Elsevier, volume 112, pages 106542, 2019. [bibtex] [pdf] [doi]
[30]	Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials (Tatiana Kostiuchenko, Fritz Koermann, Joerg Neugebauer, Alexander Shapeev), npj Computational Materials, Nature Publishing Group, volume 5, pages 55, 2019. [bibtex] [pdf] [doi] [arXiv]
[29]	Accessing thermal conductivity of complex compounds by machine learning interatomic potentials (Pavel Korotaev, Ivan Novoselov, Aleksey Yanilkin, Alexander Shapeev), Physical Review B, APS, volume 100, pages 144308, 2019. [bibtex] [pdf] [doi]
[28]	Applying a machine learning interatomic potential to unravel the effects of local lattice distortion on the elastic properties of multi-principal element alloys (M. Jafary-Zadeh, K.H. Khoo, R. Laskowski, P.S. Branicio, A. Shapeev), Journal of Alloys and Compounds, Elsevier, 2019. [bibtex] [pdf] [doi]
[27]	Ab initio vibrational free energies including anharmonicity for multicomponent alloys (Blazej Grabowski, Yuji Ikeda, Prashanth Srinivasan, Fritz Körmann, Christoph Freysoldt, Andrew Ian Duff, Alexander Shapeev, Jörg Neugebauer), npj Computational Materials, Nature Publishing Groupcat=IP, volume 5, pages 1--6, 2019. [bibtex] [pdf] [doi]
[26]	Moment tensor potentials as a promising tool to study diffusion processes (I.I. Novoselov, A.V. Yanilkin, A.V. Shapeev, E.V. Podryabinkin), Computational Materials Science, volume 165, pages 46--56, 2019. [bibtex] [pdf] [doi] [arXiv]
[25]	Accelerating high-throughput searches for new alloys with active learning of interatomic potentials (Konstantin Gubaev, Evgeny V. Podryabinkin, Gus L. W. Hart, Alexander V. Shapeev), Computational Materials Science, volume 156, pages 148--156, 2019. [bibtex] [pdf] [doi] [arXiv]
2018
[24]	Machine learning of molecular properties: Locality and active learning (Konstantin Gubaev, Evgeny V. Podryabinkin, Alexander V. Shapeev), The Journal of Chemical Physics, AIP Publishing, volume 148, pages 241727, 2018. [bibtex] [pdf] [doi] [arXiv]
[23]	Automated calculation of thermal rate coefficients using ring polymer molecular dynamics and machine-learning interatomic potentials with active learning (Ivan S Novikov, Yury V Suleimanov, Alexander V Shapeev), Physical Chemistry Chemical Physics, Royal Society of Chemistry, volume 20, pages 29503--29512, 2018. [bibtex] [doi] [arXiv]
[22]	Dropout-Based Active Learning for Regression (Evgenii Tsymbalov, Maxim Panov, Alexander Shapeev), in International Conference on Analysis of Images, Social Networks and Texts, pages 247--258, 2018. [bibtex] [doi] [arXiv]
2017
[21]	Approximation of Crystalline Defects at Finite Temperature (Alexander V. Shapeev, Mitchell Luskin), Multiscale Modeling & Simulation, Society for Industrial & Applied Mathematics (SIAM), volume 15, pages 1830--1864, 2017. [bibtex] [pdf] [doi] [arXiv]
[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]
2016
[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]
2014
[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]
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, 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]
2012
[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]
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, pages 905--932, 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, pages 1874--1900, 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, pages 149--162, 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, pages 36--41, 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, pages 213--221, 2000. [bibtex]

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, pages 100--116, 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, 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]
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, 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]
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, pages 715--724, 2000. [bibtex]

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]