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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.NA2024
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.NA2023
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…