Related papers: Goal-oriented time adaptivity for port-Hamiltonian…
We present an adjoint-based optimization method to invert for stress and frictional parameters used in earthquake modeling. The forward problem is linear elastodynamics with nonlinear rate-and-state frictional faults. The misfit functional…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
In this work we present an a posteriori error indicator for approximation schemes of Runge-Kutta-discontinuous-Galerkin type arising in applications of compressible fluid flows. The purpose of this indicator is not only for mesh adaptivity,…
The short-term operation of a power system is usually planned by solving a day-ahead unit commitment problem. Due to historical reasons, the commitment of the power generating units is decided over a time horizon typically consisting of the…
In this paper, we consider the energy-bandwidth allocation for a network of multiple users, where the transmitters each powered by both an energy harvester and conventional grid, access the network orthogonally on the assigned frequency…
This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…
The growth in variable renewables such as solar and wind is increasing the impact of climate uncertainty in energy system planning. Addressing this ideally requires high-resolution time series spanning at least a few decades. However,…
We propose and analyze two a posteriori error indicators for hybridizable discontinuous Galerkin (HDG) discretizations of the Helmholtz equation. These indicators are built to minimize the residual associated with a local superconvergent…
In this paper we extend the previously introduced class of boundary port-Hamiltonian systems to boundary control systems where the variational derivative of the Hamiltonian functional is replaced by a pair of reciprocal differential…
The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology…
We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions…