Related papers: Explicit Exactly Energy-conserving Methods for Ham…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
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…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems, via their blended formulation. We also discuss the case of separable problems,…
Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy conservation law in…
In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…
We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods,…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation, when a Fourier expansion is considered for the space discretization. The obtained semi-discrete problem is then solved in…
Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…
In a recent series of papers, the class of energy-conserving Runge-Kutta methods named Hamiltonian BVMs (HBVMs) has been defined and studied. Such methods have been further generalized for the efficient solution of general conservative…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…