Related papers: Variational Integrators for Maxwell's Equations wi…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
We present a novel variational derivation of the Maxwell-GLM system, which augments the original vacuum Maxwell equations via a generalized Lagrangian multiplier approach (GLM) by adding two supplementary acoustic subsystems and which was…
A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless…
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We propose and compare several projection methods applied to variational integrators for degenerate Lagrangian systems, whose Lagrangian is of the form $L = \vartheta(q) \cdot \dot{q} - H(q)$ and thus linear in velocities. While previous…
Variational integrators have traditionally been constructed from the perspective of Lagrangian mechanics, but there have been recent efforts to adopt discrete variational approaches to the symplectic discretization of Hamiltonian mechanics…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…