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We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining…

Numerical Analysis · Mathematics 2017-10-05 Michael Kraus , Katharina Kormann , Philip J. Morrison , Eric Sonnendrücker

In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…

Numerical Analysis · Mathematics 2018-06-26 Qi Hong , Jialing Wang , Yuezheng Gong

We consider the issue of strict, fully discrete \emph{local} energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms…

Numerical Analysis · Mathematics 2024-10-23 Luis Chacon , Guangye Chen

This paper presents a novel decision-focused framework integrating the physical energy storage model into machine learning pipelines. Motivated by the model predictive control for energy storage, our end-to-end method incorporates the prior…

Systems and Control · Electrical Eng. & Systems 2024-12-06 Ming Yi , Saud Alghumayjan , Bolun Xu

This paper presents a port-Hamiltonian formulation of hysteretic energy storage elements. First, we revisit the passivity property of backlash-driven storage elements by presenting a family of storage functions associated to the…

Systems and Control · Electrical Eng. & Systems 2026-03-30 Jurrien Keulen , Bayu Jayawardhana , Arjan van der Schaft

Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian…

Mathematical Physics · Physics 2015-05-13 O. T. Kosmas , D. S. Vlachos

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…

Numerical Analysis · Mathematics 2017-06-28 Elena Celledoni , Eirik Hoel Høiseth

In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover,…

Numerical Analysis · Mathematics 2018-12-31 Bin Wang

Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.

Symplectic Geometry · Mathematics 2009-10-31 J. Grabowski , G. Marmo , P. W. Michor

In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…

Numerical Analysis · Mathematics 2020-03-11 Tsubasa Sakai , Shuhei Kudo , Hiroto Imachi , Yuto Miyatake , Takeo Hoshi , Yusaku Yamamoto

This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…

Numerical Analysis · Mathematics 2025-05-20 Kunal Bahuguna , Ramesh Kolluru , S. V. Raghurama Rao

Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly performing long-time simulations. For this purpose, we here propose…

Numerical Analysis · Mathematics 2020-05-26 Luigi Brugnano , Felice Iavernaro , Ruili Zhang

Since proportional-integral-derivative (PID) controllers absolutely dominate the control engineering, numbers of different control structures and theories have been developed to enhance the efficiency of PID controllers. Thus, it is…

Systems and Control · Computer Science 2018-06-04 Jie Yuan , Abdullah Ates , Sina Dehghan , Yang Zhao , Shumin Fei , YangQuan Chen

We introduce a novel particle-in-Fourier (PIF) scheme that extends its applicability to non-periodic boundary conditions. Our method handles free space boundary conditions by replacing the Fourier Laplacian operator in PIF with a mollified…

Numerical Analysis · Mathematics 2024-09-18 Changxiao Nigel Shen , Antoine Cerfon , Sriramkrishnan Muralikrishnan

This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…

Machine Learning · Computer Science 2025-08-08 Hannes Waclawek , Stefan Huber

We propose a class of numerical integration methods for stochastic Poisson systems (SPSs) of arbitrary dimensions. Based on the Darboux-Lie theorem, we transform the SPSs to their canonical form, the generalized stochastic Hamiltonian…

Numerical Analysis · Mathematics 2021-02-03 Jialin Hong , Jialin Ruan , Liying Sun , Lijin Wang

We derive variational integrators for stochastic Hamiltonian systems on Lie groups using a discrete version of the stochastic Hamiltonian phase space principle. The structure-preserving properties of the resulting scheme, such as…

Numerical Analysis · Mathematics 2024-12-30 François Gay-Balmaz , Meng Wu

A grid-feeding converter system is added to a novel power system transient simulation scheme based on frequency response optimized integrators considering second order derivative. The converter system and its implementation in the…

Systems and Control · Electrical Eng. & Systems 2021-02-23 Sheng Lei , Alexander Flueck

Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…

Dynamical Systems · Mathematics 2015-06-26 G. Giachetta , L. Mangiarotti , G. Sardanashvily

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…

Numerical Analysis · Mathematics 2024-03-19 Murat Uzunca , Bülent Karasözen