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4 papers · 1 filter
Control theory and splitting methods
Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…
Machine Learning for highly oscillatory differential equations
Maxime Bouchereau
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been d…
Convergence analysis of a Crank-Nicolson scheme for strongly magnetized plasmas
Francis Filbet, L Miguel Rodrigues, Kim Han Trinh
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for t…
A modified Crank-Nicolson scheme for the Vlasov-Poisson system with a strong external magnetic field
Francis Filbet, L Miguel Rodrigues, Kim Han Trinh
We propose and study a Particle-In-Cell (PIC) method based on the Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic…