4 citations · 16 across the 5 of their papers we have counts for
5 papers
On fast Fourier solvers for the tensor product high-order FEM for a generalized Poisson equation
Alexander Zlotnik, Ilya Zlotnik
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangula…
A direct fast FFT-based implementation for high order finite element method on rectangular parallelepipeds for PDE
Alexander Zlotnik, Ilya Zlotnik
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallel…
Some remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis
Alexander Zlotnik, Ilya Zlotnik
We consider the generalized time-dependent Schrödinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (…
On the Richardson Extrapolation in Time of Finite Element Method with Discrete TBCs for the Cauchy Problem for the 1D Schrödinger Equation
A. Zlotnik, I. Zlotnik
We consider the Cauchy problem for the 1D generalized Schrödinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method w…
The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip
Bernard Ducomet, Alexander Zlotnik, Ilya Zlotnik
We consider an initial-boundary value problem for a generalized 2D time-dependent Schrodinger equation (with variable coefficients) on a semi-infinite strip. For the Crank-Nicolso…