Splitting Techniques for DAEs with port-Hamiltonian Applications
arxiv(2024)
摘要
In the simulation of differential-algebraic equations (DAEs), it is essential
to employ numerical schemes that take into account the inherent structure and
maintain explicit or hidden algebraic constraints without altering them. This
paper focuses on operator-splitting techniques for coupled systems and aims at
preserving the structure in the port-Hamiltonian framework. The study explores
two decomposition strategies: one considering the underlying coupled subsystem
structure and the other addressing energy-associated properties such as
conservation and dissipation. We show that for coupled index-1 DAEs with and
without private index-2 variables, the splitting schemes on top of a
dimension-reducing decomposition achieve the same convergence rate as in the
case of ordinary differential equations. Additionally, we discuss an
energy-associated decomposition for index-1 pH-DAEs and introduce generalized
Cayley transforms to uphold energy conservation. The effectiveness of both
strategies is evaluated using port-Hamiltonian benchmark examples from electric
circuits.
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