3 papers
physics.comp-ph2024
A Hamiltonian structure-preserving discretization of Maxwell's equations in nonlinear media
William Barham, Yaman Güçlü, Philip J. Morrison +1
A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phen…
math.NA2024
A mimetic discretization of Westervelt's equation
William Barham, Philip J. Morrison
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This s…
physics.comp-ph2022
Dual PIC: a structure preserving method for discretizing Lie-Poisson brackets
William Barham, Philip J. Morrison
We consider a general discretization strategy for Hamiltonian field theories generated by Lie-Poisson brackets which we call dual PIC (DPIC). This method involves prescribing two d…