Related papers: Variational integrators for non-autonomous systems…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
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…
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…
In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems,…
The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete…
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…
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…
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…