Related papers: A novel energy-based modeling framework
Energy system models underpin decisions by energy system planners and operators. Energy system modelling faces a transformation: accounting for changing meteorological conditions imposed by climate change. To enable that transformation, a…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…
The energy transition has recently experienced a further acceleration. In order to make the integration of renewable energies as cost-effective, secure and sustainable as possible and to develop new paradigms for the energy system, many…
Tulipa Energy Model aims to optimise the investment and operation of the electricity market, considering its coupling with other sectors, such as hydrogen and heat, that can also be electrified. The problem is analysed from the perspective…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
First, two examples of 1D distributed port-Hamiltonian systems with dissipation, given in explicit (descriptor) form, are considered: the Dzekster model for the seepage of underground water and a nanorod model with non-local viscous…
We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution…
The quest to develop a general framework for thermodynamics, suitable for the regime of strong coupling and correlations between subsystems of an autonomous quantum "universe," has entailed diverging definitions for basic quantities,…
In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…
An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this ``inherent…
We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is…
In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…