Local Approximation Study of Difference Operators by Means of REDUCE System. - Victor G. Ganzha; Mikhail Yu. Shashkov (ISSAC, 1990)

Algorithms for Difference Schemes construction on Non-Orthogonal Logically Rectangular Meshes. - Richard Liska; Mikhail Yu. Shashkov (ISSAC, 1991)

Numerical simulation of two-dimensional flows by the free Lagrangian method - Mikhail Yu. Shashkov; Andrey V. Solovjov (Forschungsberichte, TU Munich, 1991)

Optimization-Based Reference-Matrix Rezone Strategies for Arbitrary Lagrangian-Eulerian Methods on Unstructured Meshes. - Mikhail J. Shashkov; Patrick M. Knupp (IMR, 2001)

Convergence of mimetic finite difference discretizations of the diffusion equation. - Markus Berndt; Konstantin Lipnikov; J. David Moulton; Mikhail J. Shashkov (J. Num. Math., 2001)

Optimization of Surface Mesh Quality Using Local Parametrization. - Rao V. Garimella; Mikhail J. Shashkov; Patrick M. Knupp (IMR, 2002)

Multilevel Accelerated Optimization for Problems in Grid Generation. - Markus Berndt; Mikhail J. Shashkov (IMR, 2003)

Reference Jacobian Rezoning Strategy for Arbitrary Lagrangian - Eulerian Methods on Polyhedral Grids. - Vadim Dyadechko; Rao V. Garimella; Mikhail J. Shashkov (IMR, 2004)

Polygonal surface mesh optimization. - Rao V. Garimella; Mikhail J. Shashkov (Eng. Comput., 2004)

Analysis and optimization of inner products for mimetic finite difference methods on a triangular grid. - Richard Liska; Mikhail Yu. Shashkov; Victor G. Ganzha (Math. Comput. Simul., 2004)

Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations. - Rao V. Garimella; Vadim Dyadechko; Blair Swartz; Mikhail J. Shashkov (IMR, 2005)

A mortar mimetic finite difference method on non-matching grids. - Markus Berndt; Konstantin Lipnikov; Mikhail J. Shashkov; Mary F. Wheeler; Ivan Yotov (Numerische Mathematik, 2005)

Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals. - Markus Berndt; Konstantin Lipnikov; Mikhail J. Shashkov; Mary F. Wheeler; Ivan Yotov (SIAM J. Numer. Anal., 2005)

Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes. - Franco Brezzi; Konstantin Lipnikov; Mikhail J. Shashkov (SIAM J. Numer. Anal., 2005)

The internal consistency, stability, and accuracy of the discrete, compatible formulation of Lagrangian hydrodynamics. - Amy L. Bauer; Donald E. Burton; E. J. Caramana; Raphaël Loubère; Mikhail J. Shashkov; P. P. Whalen (J. Comput. Phys., 2006)

Geometric Algorithms for 3D Interface Reconstruction. - Hyung Taek Ahn; Mikhail J. Shashkov (IMR, 2007)

Multi-material interface reconstruction on generalized polyhedral meshes. - Hyung Taek Ahn; Mikhail J. Shashkov (J. Comput. Phys., 2007)

Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov; Daniil Svyatskiy; Yuri V. Vassilevski (J. Comput. Phys., 2007)

Reconstruction of multi-material interfaces from moment data. - Vadim Dyadechko; Mikhail J. Shashkov (J. Comput. Phys., 2008)

Volume consistency in a staggered grid Lagrangian hydrodynamics scheme. - Raphaël Loubère; Mikhail Yu. Shashkov; Burton Wendroff (J. Comput. Phys., 2008)

Adaptive moment-of-fluid method. - Hyung Taek Ahn; Mikhail J. Shashkov (J. Comput. Phys., 2009)

A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems. - Dmitri Kuzmin; Mikhail J. Shashkov; Daniil Svyatskiy (J. Comput. Phys., 2009)

Local flux mimetic finite difference methods. - Konstantin Lipnikov; Mikhail J. Shashkov; Ivan Yotov (Numerische Mathematik, 2009)

Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods. - David Bailey; Markus Berndt; Milan Kucharik; Mikhail J. Shashkov (J. Comput. Appl. Math., 2010)

A comparative study of interface reconstruction methods for multi-material ALE simulations. - Milan Kucharik; Rao V. Garimella; Samuel P. Schofield; Mikhail J. Shashkov (J. Comput. Phys., 2010)

Failsafe flux limiting and constrained data projections for equations of gas dynamics. - Dmitri Kuzmin; Matthias Möller; John N. Shadid; Mikhail Yu. Shashkov (J. Comput. Phys., 2010)

A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2010)

Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian-Eulerian methods. - Richard Liska; Mikhail Yu. Shashkov; Pavel Váchal; Burton Wendroff (J. Comput. Phys., 2010)

ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method. - Raphaël Loubère; Pierre-Henri Maire; Mikhail Yu. Shashkov; Jérôme Breil; Stéphane Galera (J. Comput. Phys., 2010)

Compatible, energy and symmetry preserving 2D lagrangian hydrodynamics in rz - cylindrical coordinates. - Andrew Barlow; Donald E. Burton; Mikhail J. Shashkov (ICCS, 2010)

Using the feasible set method for rezoning in ALE. - Markus Berndt; Milan Kucharik; Mikhail J. Shashkov (ICCS, 2010)

A mimetic tensor artificial viscosity method for arbitrary polyhedral meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (ICCS, 2010)

2nd workshop on new trends in numerical methods for multi-material compressible fluid flows. - Raphaël Loubère; Pierre-Henri Maire; Mikhail Yu. Shashkov (ICCS, 2010)

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods. - Markus Berndt; Jérôme Breil; Stéphane Galera; Milan Kucharik; Pierre-Henri Maire; Mikhail J. Shashkov (J. Comput. Phys., 2011)

Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian-Eulerian methods. - Pavel B. Bochev; Denis Ridzal; Guglielmo Scovazzi; Mikhail J. Shashkov (J. Comput. Phys., 2011)

One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods. - Milan Kucharik; Mikhail J. Shashkov (J. Comput. Phys., 2012)

Isogeometric analysis of Lagrangian hydrodynamics. - Yuri Bazilevs; I. Akkerman; D. J. Benson; Guglielmo Scovazzi; Mikhail J. Shashkov (J. Comput. Phys., 2013)

Fast optimization-based conservative remap of scalar fields through aggregate mass transfer. - Pavel B. Bochev; Denis Ridzal; Mikhail J. Shashkov (J. Comput. Phys., 2013)

The Symmetric Moment-of-Fluid interface reconstruction algorithm. - Ryan N. Hill; Mikhail J. Shashkov (J. Comput. Phys., 2013)

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries. - Shiv Kumar Sambasivan; Mikhail J. Shashkov; Donald E. Burton (J. Comput. Phys., 2013)

Symmetry- and essentially-bound-preserving flux-corrected remapping of momentum in staggered ALE hydrodynamics. - Jan Velechovský; Milan Kucharik; Richard Liska; Mikhail Yu. Shashkov; Pavel Váchal (J. Comput. Phys., 2013)

A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows. - Matthew Jemison; Eva Loch; Mark Sussman; Mikhail J. Shashkov; Marco Arienti; Mitsuhiro Ohta; Yaohong Wang (J. Sci. Comput., 2013)

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics. - Andrew Barlow; Ryan N. Hill; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates. - Yuri Bazilevs; C. C. Long; I. Akkerman; D. J. Benson; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates. - Mack Kenamond; Matthew T. Bement; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods. - Milan Kucharik; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Mimetic finite difference method. - Konstantin Lipnikov; Gianmarco Manzini; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Arbitrary Lagrangian Eulerian remap treatments consistent with staggered compatible total energy conserving Lagrangian methods. - J. Michael Owen 001; Mikhail J. Shashkov (J. Comput. Phys., 2014)

Adaptive reconnection-based arbitrary Lagrangian Eulerian method. - Wurigen Bo; Mikhail J. Shashkov (J. Comput. Phys., 2015)

Filament capturing with the Multimaterial Moment-of-Fluid method. - Matthew Jemison; Mark Sussman; Mikhail J. Shashkov (J. Comput. Phys., 2015)

Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows. - Andrew Barlow; Pierre-Henri Maire; William J. Rider; Robert N. Rieben; Mikhail J. Shashkov (J. Comput. Phys., 2016)

Optimization-based mesh correction with volume and convexity constraints. - Marta D'Elia; Denis Ridzal; Kara J. Peterson; Pavel B. Bochev; Mikhail J. Shashkov (J. Comput. Phys., 2016)

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient. - Konstantin Lipnikov; Gianmarco Manzini; J. David Moulton; Mikhail J. Shashkov (J. Comput. Phys., 2016)

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces. - Evgeny Kikinzon; Yuri A. Kuznetsov; Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2017)

Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients. - Gianmarco Manzini; Konstantin Lipnikov; J. David Moulton; Mikhail J. Shashkov (SIAM J. Numer. Anal., 2017)

Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics. - Andrew Barlow; Matej Klima; Mikhail J. Shashkov (J. Comput. Phys., 2018)

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics. - Milan Kucharik; Guglielmo Scovazzi; Mikhail J. Shashkov; Raphaël Loubère (J. Comput. Phys., 2018)

Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics. - Andrew Barlow; Nathaniel R. Morgan; Mikhail J. Shashkov (Comput. Math. Appl., 2019)

Second-invariant-preserving Remap of the 2D deviatoric stress tensor in ALE methods. - Matej Klima; Milan Kucharik; Jan Velechovský; Mikhail J. Shashkov (Comput. Math. Appl., 2019)

An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics. - Tong Wu 005; Mikhail J. Shashkov; Nathaniel R. Morgan; Dmitri Kuzmin; H. Luo (Comput. Math. Appl., 2019)

A higher order approximate static condensation method for multi-material diffusion problems. - Alexander Z. Zinchenko; Daniil Svyatskiy; Maxim A. Olshanskii; Evgeny Kikinzon; Mikhail J. Shashkov (J. Comput. Phys., 2019)

Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. - Mack Kenamond; Dmitri Kuzmin; Mikhail J. Shashkov (J. Comput. Phys., 2021)

A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes. - Mack Kenamond; Dmitri Kuzmin; Mikhail J. Shashkov (J. Comput. Phys., 2021)

Conservative remapping of material-dependent fields between possibly misaligned material regions. - Hoby Rakotoarivelo; Rao V. Garimella; Angela Herring; Mikhail J. Shashkov; Daniel W. Shevitz; Evgeny Kikinzon; Jan Velechovský; Konstantin Lipnikov; Navamita Ray (J. Comput. Phys., 2022)

Multi-material swept face remapping on polyhedral meshes. - Jan Velechovský; Evgeny Kikinzon; Navamita Ray; Hoby Rakotoarivelo; Angela Herring; Mack Kenamond; Konstantin Lipnikov; Mikhail Yu. Shashkov; Rao V. Garimella; Daniel W. Shevitz (J. Comput. Phys., 2022)

Conservative high-order data transfer method on generalized polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2023)

Moments-based interface reconstruction, remap and advection. - Mikhail Yu. Shashkov; Evgeny Kikinzon (J. Comput. Phys., 2023)

A moment-of-fluid interface reconstruction using polygon inscribed in ellipse in 2D. - Robert Chiodi; Mikhail J. Shashkov (J. Comput. Phys., 2025)