Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911683672276992 |
|---|---|
| author | Sharma, Aashutosh Bartel, Andreas Schaller, Manuel |
| author_facet | Sharma, Aashutosh Bartel, Andreas Schaller, Manuel |
| contents | Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in discrete approximations is a fundamental challenge and often has been achieved by designing particular schemes such as discrete gradient methods. In this work, we propose an approach that controls the energy balance violation for port-Hamiltonian differential algebraic equations via time adaptivity using a posteriori grid refinement techniques based on the dual weighted residual method. In particular, we show how one may leverage the port-Hamiltonian structure to efficiently compute the error estimators using a dissipativity-exploiting block-Jacobi approximation. We illustrate the efficacy of the method by means of simulations of electrical circuit models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1 Sharma, Aashutosh Bartel, Andreas Schaller, Manuel Numerical Analysis 65L80, 65L50, 65L05, 93C05 Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in discrete approximations is a fundamental challenge and often has been achieved by designing particular schemes such as discrete gradient methods. In this work, we propose an approach that controls the energy balance violation for port-Hamiltonian differential algebraic equations via time adaptivity using a posteriori grid refinement techniques based on the dual weighted residual method. In particular, we show how one may leverage the port-Hamiltonian structure to efficiently compute the error estimators using a dissipativity-exploiting block-Jacobi approximation. We illustrate the efficacy of the method by means of simulations of electrical circuit models. |
| title | Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1 |
| topic | Numerical Analysis 65L80, 65L50, 65L05, 93C05 |
| url | https://arxiv.org/abs/2605.14082 |