3 papers
math.NA2026
Quadratic projectable Runge-Kutta methods
Ari Stern, Milo Viviani
Runge-Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, on…
math.NA2025
Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Ari Stern, Enrico Zampa
The success of symplectic integrators for Hamiltonian ODEs has led to a decades-long program of research seeking analogously structure-preserving numerical methods for Hamiltonian…
math.NA2025
Multisymplecticity in finite element exterior calculus
Ari Stern, Enrico Zampa
We consider the application of finite element exterior calculus (FEEC) methods to a class of canonical Hamiltonian PDE systems involving differential forms. Solutions to these syst…