2 citations · 4 across the 6 of their papers we have counts for
7 papers
Symplectic GARK methods for partitioned Hamiltonian systems
Michael Günther, Adrian Sandu, Kevin Schäfers +1
Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work develo…
Discrete Variational Methods and Symplectic Generalized Additive Runge--Kutta Methods
Antonella Zanna
We consider a Lagrangian system , where the -variable is treated by a Generalized Additive Runge--Kutta (GARK) method. Applying…
Symplectic P-stable Additive Runge--Kutta Methods
Antonella Zanna
Symplectic partitioned Runge--Kutta methods can be obtained from a variational formulation where all the terms in the discrete Lagrangian are treated with the same quadrature formu…
A classification of volume preserving generating forms in R^3
Olivier Verdier, Huiyan Xue, Antonella Zanna
In earlier work, Lomeli and Meiss used a generalization of the symplectic approach to study volume preserving generating differential forms. In particular, for the c…
Symmetric spaces and Lie triple systems in numerical analysis of differential equations
Hans Z. Munthe-Kaas, Gilles Reinout W. Quispel, Antonella Zanna
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differen…
The Euler equation of quasi-geostrophic fluids and volume preserving numerical methods
Antonella Zanna
We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long…
Explicit Volume-Preserving Splitting Methods for Polynomial Divergence-Free Vector Fields
Huiyan Xue, Antonella Zanna
We present new, explicit, volume-preserving vector fields for polynomial divergence-free vector fields of arbitrary degree (both positive and negative). The main idea is to decompo…