Related papers: Differential-algebraic systems with dissipative Ha…
We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
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.…
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…
The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying…
We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.
This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally establish…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other one on complete differential graded Lie algebras. As an…
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.…
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…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…