For the elastodynamic simulation of a geometrically exact beam, a variational integrator is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (unit quaternions for the representation of rotational degrees of freedom), it intrinsically preserves the group structure withou...

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating ...

We implement a second-order exponential integrator for semidiscretized advectiondiffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by Finite Differences or Finite Elements, show that the Leja-Euler-Midpoint ...

We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and electron spin accumulation in magnetic and nonmagnetic multilayer structures. Despite the strong nonlinearity of the overall PDE system, the proposed integrator re...

In molecular dynamics simulations, an integrator-induced resonance is observed for conservative molecular system subject to the classical equations of motion when a Verlet integrator or Implicit Midpoint scheme is used. In this report, an existing variational integrator with adaptive timesteps is introduced to handle resonance. This Symplectic-Energy-Momentum (SEM) preserving algorithm is first...

In this paper, we address the problem of globally stabilizing a linear time-invariant (LTI) system by means of a static feedback law whose amplitude and successive time derivatives, up to a prescribed order p, are bounded by arbitrary prescribed values. We solve this problem for two classes of LTI systems, namely integrator chains and skew-symmetric systems with single input. For the integrator...

We introduce a time-integrator to sample with high order of accuracy the invariant distribution for a class of semilinear SPDEs driven by an additive space-time noise. Combined with a postprocessor, the new method is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. We first provide an analysis of the integrator when applied for SDEs (finite dime...

We investigate a variant of dense-time Duration Calculus which permits model checking using timed/hybrid automata. We define a variant of the Duration Calculus, called Interval Duration Logic, (IDL), whose models are timed state sequences [1]. A subset LIDL of IDL consisting only of located time constraints is presented. As our main result, we show that the models of an LIDL formula can be capt...

This paper invites the reader to learn more about time integrators for Molecular Dynamics simulation through a simple MATLAB implementation. An overview of methods is provided from an algorithmic viewpoint that emphasizes long-time stability and finite-time dynamic accuracy. The given software simulates Langevin dynamics using an explicit, second-order (weakly) accurate integrator that exactly ...

This paper addresses the non-linear noise and dynamic-range properties of bipolar and MOS (both in weak and in strong inversion) translinear integrators, following a systematic top-down approach. Several design principles to achieve an optimal dynamic range are derived. A qualitative comparison of a bipolar or weakinversion class-AB translinear integrator and the well-known linear gm ÿ C integr...