6 papers · 1 filter
Backward error analysis for matrix discretizations of 2-D Euler equations
Eugen Bronasco, Klas Modin
We introduce a formalism of Lie--Poisson reduction of Butcher series. The corresponding forest momentum map allows for describing backward error analysis of isospectral symplectic…
Symplectic Isospectral Runge--Kutta Methods as Lie group methods
Paolo Cifani, Klas Modin, Cecilia Pagliantini +1
We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cot…
A brief introduction to matrix hydrodynamics
Klas Modin, Milo Viviani
This survey gives a basic demonstration of matrix hydrodynamics; the field pioneered by V. Zeitlin, where 2-D incompressible fluids are spatially discretized via quantization theor…
Spatio-temporal Lie-Poisson discretization for incompressible magnetohydrodynamics on the sphere
Klas Modin, Michael Roop
We give a structure preserving spatio-temporal discretization for incompressible magnetohydrodynamics (MHD) on the sphere. Discretization in space is based on the theory of geometr…
On the numerical signature of blow-up in hydrodynamic equations
Erik Jansson, Klas Modin
The phenomenon of finite time blow-up in hydrodynamic partial differential equations is central in analysis and mathematical physics. While numerical studies have guided theoretica…
On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport
Klas Modin
The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric…