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Volume 22, Issue 4
Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions

Marie-Claude Viallon

DOI: 10.4208/ijnam2025-1023

Int. J. Numer. Anal. Mod., 22 (2025), pp. 534-555.

Published online: 2025-04

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  • Abstract

A model parabolic linear partial differential equation in a geometrical multi-scale domain is studied. The domain consists of a two-dimensional central node, and several one-dimensional outgoing branches. The physical coupling conditions between the node and the branches are either continuity of the solution or continuity of the normal flux. An iterative Schwarz method based on Robin transmission conditions is adjusted to the problem in each case and formulated in substructured form. The convergence of the method is stated. Numerical results when the method is used as preconditioner for a Krylov method (GMRES) are provided.

  • Keywords

Finite volume scheme, parabolic problem, multi-scale domain, domain decomposition, stability and convergence of numerical methods, Schwarz methods, Robin interface condition.

  • AMS Subject Headings

35K05, 65F10, 65N08, 65N12, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-22-534, author = {Viallon , Marie-Claude}, title = {Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {4}, pages = {534--555}, abstract = {

A model parabolic linear partial differential equation in a geometrical multi-scale domain is studied. The domain consists of a two-dimensional central node, and several one-dimensional outgoing branches. The physical coupling conditions between the node and the branches are either continuity of the solution or continuity of the normal flux. An iterative Schwarz method based on Robin transmission conditions is adjusted to the problem in each case and formulated in substructured form. The convergence of the method is stated. Numerical results when the method is used as preconditioner for a Krylov method (GMRES) are provided.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1023}, url = {http://global-sci.org/intro/article_detail/ijnam/24039.html} }
TY - JOUR T1 - Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions AU - Viallon , Marie-Claude JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 534 EP - 555 PY - 2025 DA - 2025/04 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1023 UR - https://global-sci.org/intro/article_detail/ijnam/24039.html KW - Finite volume scheme, parabolic problem, multi-scale domain, domain decomposition, stability and convergence of numerical methods, Schwarz methods, Robin interface condition. AB -

A model parabolic linear partial differential equation in a geometrical multi-scale domain is studied. The domain consists of a two-dimensional central node, and several one-dimensional outgoing branches. The physical coupling conditions between the node and the branches are either continuity of the solution or continuity of the normal flux. An iterative Schwarz method based on Robin transmission conditions is adjusted to the problem in each case and formulated in substructured form. The convergence of the method is stated. Numerical results when the method is used as preconditioner for a Krylov method (GMRES) are provided.

Viallon , Marie-Claude. (2025). Schwarz Method in a Geometrical Multi-Scale Domain with Continuous or Discontinuous Junctions . International Journal of Numerical Analysis and Modeling. 22 (4). 534-555. doi:10.4208/ijnam2025-1023
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