A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs
Abstract
We develop an energy-optimal generalized scalar auxiliary variable (EOP-GSAV) framework for nonlinear index-one port-Hamiltonian differential-algebraic equations (pH-DAEs). Exploiting the port-Hamiltonian structure, we separate the nonlinear effort, interconnection, and dissipation terms from a constant implicit core. The resulting BDF-1 and BDF-2 schemes require one linear solve per time step with a reusable factorization, while retaining discrete passivity and accurate tracking of the Hamiltonian. The schemes are compared with the implicit midpoint method equipped with full, modified, and frozen-Jacobian Newton iterations. Numerical experiments ranging from a strongly state-dependent nonlinear stress test to large-scale benchmarks demonstrate robust and competitive performance, with substantial efficiency gains in matched-accuracy regimes. A comparison with SUNDIALS IDA shows comparable work-precision behavior at equal order despite a non-specialized Python/SciPy implementation, while unrestricted variable-order adaptive IDA is faster in the high-accuracy regime.
Related
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BibTeX
@misc{sharma2026generalized,
title = {{A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs}},
author = {Aashutosh Sharma and Andreas Bartel and Manuel Schaller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05246},
eprint = {2609.05246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05246},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs
AU - Aashutosh Sharma
AU - Andreas Bartel
AU - Manuel Schaller
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05246
UR - https://arxiv.org/abs/2609.05246
AB - We develop an energy-optimal generalized scalar auxiliary variable (EOP-GSAV) framework for nonlinear index-one port-Hamiltonian differential-algebraic equations (pH-DAEs). Exploiting the port-Hamiltonian structure, we separate the nonlinear effort, interconnection, and dissipation terms from a constant implicit core. The resulting BDF-1 and BDF-2 schemes require one linear solve per time step with a reusable factorization, while retaining discrete passivity and accurate tracking of the Hamiltonian. The schemes are compared with the implicit midpoint method equipped with full, modified, and frozen-Jacobian Newton iterations. Numerical experiments ranging from a strongly state-dependent nonlinear stress test to large-scale benchmarks demonstrate robust and competitive performance, with substantial efficiency gains in matched-accuracy regimes. A comparison with SUNDIALS IDA shows comparable work-precision behavior at equal order despite a non-specialized Python/SciPy implementation, while unrestricted variable-order adaptive IDA is faster in the high-accuracy regime.
ER -