arXiv subjects

H. J. Zwart

Publications and source records attributed to H. J. Zwart.

4 recordsLinked to original sources

arXiv2026

Optimal Sensor Placement for Output Estimation Using an Artificial Bee Colony Algorithm with Pre-filter

Sensor placement for maximizing the estimation performance of the Kalman filter is an NP-hard optimization problem. Furthermore, its feasible set grows combinatorially with the candidate locations and the number of sensors. In this paper, we study this sensor placement problem for a 3D thermoelastic system modelled as a discrete-time linear stochastic model. We use the Novel Binary Artificial Bee Colony (NBABC) algorithm with a Gramian-based pre-filter to reduce the computational complexity. Our results show the efficiency and the fast convergence of the proposed approach.

math.OC↗

arXiv2023

Port-Hamiltonian formulations of the incompressible Euler equations with a free surface

In this paper, we present port-Hamiltonian formulations of the incompressible Euler equations with a free surface governed by surface tension and gravity forces, modelling e.g. capillary and gravity waves and the evolution of droplets in air. Three sets of variables are considered, namely $(v,Σ)$, $(η,ϕ_{\partial},Σ)$ and $(ω,ϕ_{\partial},Σ)$, with $v$ the velocity, $η$ the solenoidal velocity, $ϕ_{\partial}$ a potential, $ω$ the vorticity, and $Σ$ the free surface, resulting in the incompressible Euler equations in primitive variables and the vorticity equation. First, the Hamiltonian formulation for the incompressible Euler equations in a domain with a free surface combined with a fixed boundary surface with a homogeneous boundary condition will be derived in the proper Sobolev spaces of differential forms. Next, these results will be extended to port-Hamiltonian formulations allowing inhomogeneous boundary conditions and a non-zero energy flow through the boundaries. Our main results are the construction and proof of Dirac structures in suitable Sobolev spaces of differential forms for each variable set, which provides the core of any port-Hamiltonian formulation. Finally, it is proven that the state dependent Dirac structures are related to Poisson brackets that are linear, skew-symmetric and satisfy the Jacobi identity.

math.AP↗

arXiv2022

Port-Hamiltonian Discontinuous Galerkin Finite Element Methods

A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical systems that have a non-zero energy flow through the boundaries. In this paper we propose a novel framework for discontinuous Galerkin (DG) discretizations of pH-systems. Linking DG methods with pH-systems gives rise to compatible structure preserving finite element discretizations along with flexibility in terms of geometry and function spaces of the variables involved. Moreover, the port-Hamiltonian formulation makes boundary ports explicit, which makes the choice of structure and power preserving numerical fluxes easier. We state the Discontinuous Finite Element Stokes-Dirac structure with a power preserving coupling between elements, which provides the mathematical framework for a large class of pH discontinuous Galerkin discretizations. We also provide an a priori error analysis for the port-Hamiltonian discontinuous Galerkin Finite Element Method (pH-DGFEM). The port-Hamiltonian discontinuous Galerkin finite element method is demonstrated for the scalar wave equation showing optimal rates of convergence.

math.AP↗

arXiv2021

Structure Preserving Discretization of 1D Nonlinear Port-Hamiltonian Distributed Parameter Systems

This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional port-Hamiltonian element is defined that enables a structure preserving discretization of the infinite dimensional model that inherits the Dirac structure, the underlying energy balance and matches the Hamiltonian function on any, possibly nonuniform mesh of the spatial geometry.

math.NA↗