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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.20475 |
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| _version_ | 1866910157395460096 |
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| author | Garcia, Idoia Cortes Förster, Peter F. Jansen, Lennart Schilders, Wil Schöps, Sebastian |
| author_facet | Garcia, Idoia Cortes Förster, Peter F. Jansen, Lennart Schilders, Wil Schöps, Sebastian |
| contents | We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20475 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A topological decoupling of modified nodal analysis including controlled sources Garcia, Idoia Cortes Förster, Peter F. Jansen, Lennart Schilders, Wil Schöps, Sebastian Numerical Analysis Computational Engineering, Finance, and Science 65L80 (Primary) 05C85, 05C90 (Secondary) G.1.7; G.2.2; J.2; J.6 We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling. |
| title | A topological decoupling of modified nodal analysis including controlled sources |
| topic | Numerical Analysis Computational Engineering, Finance, and Science 65L80 (Primary) 05C85, 05C90 (Secondary) G.1.7; G.2.2; J.2; J.6 |
| url | https://arxiv.org/abs/2604.20475 |