94 citations · 98 across the 3 of their papers we have counts for
7 papers
A single LU~factorization approach to model reduction for linear system families with a quadratic matrix pencil
Mikhail A. Botchev, Leonid Knizhnerman, Nikolai L. Zamarashkin +1
To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivati…
Are implicit schemes needed in adaptive time stepping for PDEs?
Mikhail A. Botchev
Implicit time integration is the standard way to overcome the tight CFL time step restriction when solving nonstationary PDEs numerically. However, within an adaptive time accurate…
Accuracy and stability of the hyperbolic model time integration scheme revisited
Mikhail A. Botchev
The hyperbolic model (HM) time integration scheme tackles parabolic problems by adding a small artificial second order time derivative term. Described by Samarskii in his 1971 book…
Efficient and stable time integration of Cahn-Hilliard equations: explicit, implicit and explicit iterative schemes
M. A. Botchev, I. A. Fahurdinov, E. B. Savenkov
To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modifie…
Exponential time integrators for unsteady advection-diffusion problems on refined meshes
M. A. Botchev
Time integration of advection dominated advection-diffusion problems on refined meshes can be a challenging task, since local refinement can lead to a severe time step restriction,…
Predicting dynamical system evolution with residual neural networks
Artem Chashchin, Mikhail Botchev, Ivan Oseledets +1
Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems …
Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection
Gijs L. Kooij, Mikhail A. Botchev, Edo M. A. Frederix +7
Computational codes for direct numerical simulations of Rayleigh-Bénard (RB) convection are compared in terms of computational cost and quality of the solution. As a benchmark case…