Abstract dissipative Hamiltonian differential-algebraic equations are everywhere

2023/11/06 by Volker Mehrmann, Mehrmann, Volker, Hans Zwart +1 · 2 citations
Mathematics · Physics and Astronomy · Engineering · #Numerical methods for differential equations #Model Reduction and Neural Networks #Control and Stability of Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2311.03091

Abstract

In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there are constraints coming from the underlying physics, but many standard PDE models can be seen as an adHDAE on an extended state space. This reflects the fact that models often include closure relations and structural properties. We present a unifying operator theoretic approach to analyze the properties of such operator equations and illustrate this by several applications.

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• Differential algebraic system nodes
• Iterative solvers for partial differential equations with dissipative structure: Operator preconditioning and optimal control

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