Mikhail J. Shashkov

Publication Activity (10 Years)

Years Active: 2001-2023
Publications (10 Years): 15

Top Topics

Finite Difference Method

Constrained Optimization

Top Venues

J. Comput. Phys.

Comput. Math. Appl.

SIAM J. Numer. Anal.

J. Sci. Comput.

Publications

Konstantin Lipnikov, Mikhail J. Shashkov
Conservative high-order data transfer method on generalized polygonal meshes. J. Comput. Phys. 474 (2023)
Hoby Rakotoarivelo, Rao V. Garimella, Angela Herring, Mikhail J. Shashkov, Daniel W. Shevitz, Evgeny Kikinzon, Jan Velechovský, Konstantin Lipnikov, Navamita Ray
Conservative remapping of material-dependent fields between possibly misaligned material regions. J. Comput. Phys. 466 (2022)
Mack Kenamond, Dmitri Kuzmin, Mikhail J. Shashkov
A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes. J. Comput. Phys. 435 (2021)
Mack Kenamond, Dmitri Kuzmin, Mikhail J. Shashkov
Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. J. Comput. Phys. 429 (2021)
Matej Klima, Milan Kucharik, J. Velechovský, Mikhail J. Shashkov
Second-invariant-preserving Remap of the 2D deviatoric stress tensor in ALE methods. Comput. Math. Appl. 78 (2) (2019)
Tong Wu, Mikhail J. Shashkov, Nathaniel R. Morgan, Dmitri Kuzmin, H. Luo
An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics. Comput. Math. Appl. 78 (2) (2019)
Alexander Z. Zinchenko, Daniil Svyatskiy, Maxim A. Olshanskii, Evgeny Kikinzon, Mikhail J. Shashkov
A higher order approximate static condensation method for multi-material diffusion problems. J. Comput. Phys. 395 (2019)
Andrew Barlow, Nathaniel R. Morgan, Mikhail J. Shashkov
Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics. Comput. Math. Appl. 78 (2) (2019)
Milan Kucharik, Guglielmo Scovazzi, Mikhail J. Shashkov, Raphaël Loubère
A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics. J. Comput. Phys. 354 (2018)
Andrew Barlow, Matej Klima, Mikhail J. Shashkov
Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics. J. Comput. Phys. 371 (2018)
Gianmarco Manzini, Konstantin Lipnikov, J. David Moulton, Mikhail J. Shashkov
Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients. SIAM J. Numer. Anal. 55 (6) (2017)
Evgeny Kikinzon, Yuri A. Kuznetsov, Konstantin Lipnikov, Mikhail J. Shashkov
Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces. J. Comput. Phys. 347 (2017)
Konstantin Lipnikov, Gianmarco Manzini, J. David Moulton, Mikhail J. Shashkov
The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient. J. Comput. Phys. 305 (2016)
Andrew Barlow, Pierre-Henri Maire, William J. Rider, Robert N. Rieben, Mikhail J. Shashkov
Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows. J. Comput. Phys. 322 (2016)
Marta D'Elia, Denis Ridzal, Kara J. Peterson, Pavel B. Bochev, Mikhail J. Shashkov
Optimization-based mesh correction with volume and convexity constraints. J. Comput. Phys. 313 (2016)
Wurigen Bo, Mikhail J. Shashkov
Adaptive reconnection-based arbitrary Lagrangian Eulerian method. J. Comput. Phys. 299 (2015)
Matthew Jemison, Mark Sussman, Mikhail J. Shashkov
Filament capturing with the Multimaterial Moment-of-Fluid method. J. Comput. Phys. 285 (2015)
Andrew Barlow, Ryan N. Hill, Mikhail J. Shashkov
Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics. J. Comput. Phys. 276 (2014)
J. Michael Owen, Mikhail J. Shashkov
Arbitrary Lagrangian Eulerian remap treatments consistent with staggered compatible total energy conserving Lagrangian methods. J. Comput. Phys. 273 (2014)
Milan Kucharik, Mikhail J. Shashkov
Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods. J. Comput. Phys. 258 (2014)
Konstantin Lipnikov, Gianmarco Manzini, Mikhail J. Shashkov
Mimetic finite difference method. J. Comput. Phys. 257 (2014)
Y. Bazilevs, C. C. Long, I. Akkerman, D. J. Benson, Mikhail J. Shashkov
Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates. J. Comput. Phys. 262 (2014)
Mack Kenamond, Matthew T. Bement, Mikhail J. Shashkov
Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates. J. Comput. Phys. 268 (2014)
Ryan N. Hill, Mikhail J. Shashkov
The Symmetric Moment-of-Fluid interface reconstruction algorithm. J. Comput. Phys. 249 (2013)
Y. Bazilevs, I. Akkerman, D. J. Benson, Guglielmo Scovazzi, Mikhail J. Shashkov
Isogeometric analysis of Lagrangian hydrodynamics. J. Comput. Phys. 243 (2013)
Matthew Jemison, Eva Loch, Mark Sussman, Mikhail J. Shashkov, Marco Arienti, Mitsuhiro Ohta, Yaohong Wang
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows. J. Sci. Comput. 54 (2-3) (2013)
Shiv Kumar Sambasivan, Mikhail J. Shashkov, Donald E. Burton
A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries. J. Comput. Phys. 237 (2013)
Pavel B. Bochev, Denis Ridzal, Mikhail J. Shashkov
Fast optimization-based conservative remap of scalar fields through aggregate mass transfer. J. Comput. Phys. 246 (2013)
Milan Kucharik, Mikhail J. Shashkov
One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods. J. Comput. Phys. 231 (7) (2012)
Pavel B. Bochev, Denis Ridzal, Guglielmo Scovazzi, Mikhail J. Shashkov
Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian-Eulerian methods. J. Comput. Phys. 230 (13) (2011)
Markus Berndt, Jérôme Breil, Stéphane Galera, Milan Kucharik, Pierre-Henri Maire, Mikhail J. Shashkov
Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods. J. Comput. Phys. 230 (17) (2011)
Konstantin Lipnikov, Mikhail J. Shashkov
A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes. J. Comput. Phys. 229 (20) (2010)
Konstantin Lipnikov, Mikhail J. Shashkov
A mimetic tensor artificial viscosity method for arbitrary polyhedral meshes. ICCS (1) (2010)
Markus Berndt, Milan Kucharik, Mikhail J. Shashkov
Using the feasible set method for rezoning in ALE. ICCS (1) (2010)
Milan Kucharik, Rao V. Garimella, Samuel P. Schofield, Mikhail J. Shashkov
A comparative study of interface reconstruction methods for multi-material ALE simulations. J. Comput. Phys. 229 (7) (2010)
Andrew Barlow, Donald E. Burton, Mikhail J. Shashkov
Compatible, energy and symmetry preserving 2D lagrangian hydrodynamics in rz - cylindrical coordinates. ICCS (1) (2010)
David Bailey, Markus Berndt, Milan Kucharik, Mikhail J. Shashkov
Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods. J. Comput. Appl. Math. 233 (12) (2010)
Dmitri Kuzmin, Mikhail J. Shashkov, Daniil Svyatskiy
A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems. J. Comput. Phys. 228 (9) (2009)
Konstantin Lipnikov, Mikhail J. Shashkov, Ivan Yotov
Local flux mimetic finite difference methods. Numerische Mathematik 112 (1) (2009)
Hyung Taek Ahn, Mikhail J. Shashkov
Adaptive moment-of-fluid method. J. Comput. Phys. 228 (8) (2009)
Vadim Dyadechko, Mikhail J. Shashkov
Reconstruction of multi-material interfaces from moment data. J. Comput. Phys. 227 (11) (2008)
Hyung Taek Ahn, Mikhail J. Shashkov
Multi-material interface reconstruction on generalized polyhedral meshes. J. Comput. Phys. 226 (2) (2007)
Hyung Taek Ahn, Mikhail J. Shashkov
Geometric Algorithms for 3D Interface Reconstruction. IMR (2007)
Konstantin Lipnikov, Mikhail J. Shashkov, Daniil Svyatskiy, Yuri V. Vassilevski
Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. J. Comput. Phys. 227 (1) (2007)
Amy L. Bauer, Donald E. Burton, E. J. Caramana, Raphaël Loubère, Mikhail J. Shashkov, P. P. Whalen
The internal consistency, stability, and accuracy of the discrete, compatible formulation of Lagrangian hydrodynamics. J. Comput. Phys. 218 (2) (2006)
Markus Berndt, Konstantin Lipnikov, Mikhail J. Shashkov, Mary F. Wheeler, Ivan Yotov
Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals. SIAM J. Numer. Anal. 43 (4) (2005)
Markus Berndt, Konstantin Lipnikov, Mikhail J. Shashkov, Mary F. Wheeler, Ivan Yotov
A mortar mimetic finite difference method on non-matching grids. Numerische Mathematik 102 (2) (2005)
Franco Brezzi, Konstantin Lipnikov, Mikhail J. Shashkov
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes. SIAM J. Numer. Anal. 43 (5) (2005)
Rao V. Garimella, Vadim Dyadechko, Blair Swartz, Mikhail J. Shashkov
Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations. IMR (2005)
Vadim Dyadechko, Rao V. Garimella, Mikhail J. Shashkov
Reference Jacobian Rezoning Strategy for Arbitrary Lagrangian - Eulerian Methods on Polyhedral Grids. IMR (2004)
Rao V. Garimella, Mikhail J. Shashkov
Polygonal surface mesh optimization. Eng. Comput. 20 (3) (2004)
Markus Berndt, Mikhail J. Shashkov
Multilevel Accelerated Optimization for Problems in Grid Generation. IMR (2003)
Rao V. Garimella, Mikhail J. Shashkov, Patrick M. Knupp
Optimization of Surface Mesh Quality Using Local Parametrization. IMR (2002)
Markus Berndt, Konstantin Lipnikov, J. David Moulton, Mikhail J. Shashkov
Convergence of mimetic finite difference discretizations of the diffusion equation. J. Num. Math. 9 (4) (2001)
Mikhail J. Shashkov, Patrick M. Knupp
Optimization-Based Reference-Matrix Rezone Strategies for Arbitrary Lagrangian-Eulerian Methods on Unstructured Meshes. IMR (2001)