Abstract
Operator splitting is a powerful method for numerical investigation of complex models. This method was successfully used for ordinary and partial differential equations (ODEs and PDEs). In constrained dynamical problems as electric circuits or energy transport networks, differential-algebraic equations (DAEs) arise. The constraints prevent a simple transfer of operator splitting from ODEs to DAEs. Here, we present an approach for splitting linear circuit DAEs of index 1 based on a port-Hamiltonian modeling that we derive from loop and cutset equations by a topological decoupling. Finally, we present convergence results for the proposed DAE operator splitting.
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Acknowledgements
This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 76504. Furthermore, we acknowledge financial support by DFG under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, ID 390685689).
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Diab, M., Tischendorf, C. (2021). Splitting Methods for Linear Circuit DAEs of Index 1 in port-Hamiltonian Form. In: van Beurden, M., Budko, N., Schilders, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-84238-3_21
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DOI: https://doi.org/10.1007/978-3-030-84238-3_21
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