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PreprintCC BY-NC-ND 4.0arXiv

A new operator splitting method for coupled PDE problems, with an application to poromechanics

  • Francesca Marcon
  • Stefano Scialò
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Abstract

The present work proposes a new operator splitting technique. The method leverages ideas used in PDE-constrained domain decomposition, adapting them to the objective of decoupling equations defined on the same geometric domain. The methodology is applied here to the resolution of coupled flow and deformation in the linear quasi-static Biot problem. An overview of its main characteristics is provided, also in comparison with the well established fixed-stress split for poroelasticity.

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Cite

BibTeXRIS
BibTeX
@misc{marcon2026operator,
  title = {{A new operator splitting method for coupled PDE problems, with an application to poromechanics}},
  author = {Francesca Marcon and Stefano Scialò},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31320},
  eprint = {2609.31320},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31320},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A new operator splitting method for coupled PDE problems, with an application to poromechanics
AU  - Francesca Marcon
AU  - Stefano Scialò
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31320
UR  - https://arxiv.org/abs/2609.31320
AB  - The present work proposes a new operator splitting technique. The method leverages ideas used in PDE-constrained domain decomposition, adapting them to the objective of decoupling equations defined on the same geometric domain. The methodology is applied here to the resolution of coupled flow and deformation in the linear quasi-static Biot problem. An overview of its main characteristics is provided, also in comparison with the well established fixed-stress split for poroelasticity.
ER  -