10 citations · 16 across the 14 of their papers we have counts for
14 papers
Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods
Mike A. Botchev
The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attra…
Polygon-based unified Fourier-modal approach for diffractive optics simulations
K. V. Nikolaev, V. Soltwisch, M. A. Botchev +4
In this article, we derive a theoretical formalism that unifies the rigorous coupled wave analysis and the dynamical diffraction theory. Based on this formalism, we design a comput…
On convergence of waveform relaxation for nonlinear systems of ordinary differential equations
Mike A. Botchev
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindelöf i…
Krylov subspace residual and restarting for certain second order differential equations
M. A. Botchev, L. A. Knizhnerman, M. Schweitzer
We propose algorithms for efficient time integration of large systems of oscillatory second order ordinary differential equations (ODEs) whose solution can be expressed in terms of…
Coarse grid corrections in Krylov subspace evaluations of the matrix exponential
Mike A. Botchev
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and matrix function evaluations. The approach is intended for iterative…
A residual concept for Krylov subspace evaluation of the matrix function
Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
An efficient Krylov subspace algorithm for computing actions of the matrix function for large matrices is proposed. This matrix function is widely used in exponential time inte…