Publications of A. V. Shapeev

Submitted Articles

[3] | An Optimization-Based Atomistic-to-Continuum Coupling Method . [bibtex] [arXiv] |

[2] | (In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods . [bibtex] [arXiv] |

[1] | Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations . [bibtex] [arXiv] |

Refereed Articles

2014 | |

[11] | Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method , 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 , 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 , 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 , SIAM J. Sci. Comput., volume 34, 2012. [bibtex] [doi] [arXiv] |

[7] | The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain , Multiscale Model. Simul., volume 10, 2012. [bibtex] [doi] [arXiv] |

[6] | Numerical Methods for Multilattices , 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 , 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 , 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 , 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 , Fluid Dynamics, volume 39, 2004. [bibtex] |

2000 | |

[1] | High-order accurate difference schemes for elliptic equations in a domain with a curvilinear boundary , Computational Mathematics and Mathematical Physics, volume 40, 2000. [bibtex] |

Conference Proceedings

2009 | |

[7] | Polynomial Least-Squares Reconstruction for Semi-Lagrangian Cell-Centered Hydrodynamic Schemes , 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 , In Computational Fluid Dynamics, 2008. [bibtex] |

2002 | |

[5] | Numerical Simulation of 3D Motions of Locally Heated Liquid Films , 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 , 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 , 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 , In Problems of Continuous Media Mechanics: Proceedings of the 32nd Regional Youth Conference, 2001. (in Russian) [bibtex] |

2000 | |

[1] | High order approximation schemes , 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 , 2013. [bibtex] [arXiv] |

2012 | |

[5] | Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods , 2012. (arXiv:1204.3705) [bibtex] [pdf] |

2010 | |

[4] | Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals , 2010. (arXiv:1006.0378) [bibtex] [pdf] |

2009 | |

[3] | Viscous incompressible axisymmetric flows in cones , Technical report, Lavrentyev Institute of Hydrodynamics SB RAS, 2009. (In Russian) [bibtex] |

[2] | Energy-based ghost force removing techniques for the quasicontinuum method , 2009. (arXiv:0909.5437) [bibtex] [pdf] |

2002 | |

[1] | Pattern Formation -- Group Theoretical and Numerical Points of View , Technical report, Ernst-Moritz-Arndt-Universitat Greifswald, Institut fur Mathematik und Informatik, 2002. [bibtex] |