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PreprintCC BY-NC-ND 4.0arXiv

A Structure-Preserving Symmetric Galerkin Boundary Element Method for Anisotropic Multi-phase Mullins-Sekerka Flow

  • Tokuhiro Eto
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Abstract

A structure-preserving symmetric Galerkin boundary element method (SGBEM) is developed for the anisotropic multi-phase Mullins-Sekerka problem in ℝ2. The bulk harmonic problems are eliminated through a discrete Dirichlet-to-Neumann operator assembled from region-wise SGBEM discretization, leading to a boundary-only formulation coupled to the evolution of a polygonal curve network with triple junctions. The Galerkin approximation of the resulting boundary problem is shown to be uniquely solvable, and the fully discrete scheme is unconditionally stable with respect to the time step as long as the evolving polygonal network remains in an admissible class. The accuracy of the proposed method is demonstrated by a convergence test under coupled space--time refinement against a similarity-rescaled exact solution consisting of three concentric circles.

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Cite

BibTeXRIS
BibTeX
@misc{eto2026structurepreserving,
  title = {{A Structure-Preserving Symmetric Galerkin Boundary Element Method for Anisotropic Multi-phase Mullins-Sekerka Flow}},
  author = {Tokuhiro Eto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14742},
  eprint = {2609.14742},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14742},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A Structure-Preserving Symmetric Galerkin Boundary Element Method for Anisotropic Multi-phase Mullins-Sekerka Flow
AU  - Tokuhiro Eto
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.14742
UR  - https://arxiv.org/abs/2609.14742
AB  - A structure-preserving symmetric Galerkin boundary element method (SGBEM) is developed for the anisotropic multi-phase Mullins-Sekerka problem in ℝ^2. The bulk harmonic problems are eliminated through a discrete Dirichlet-to-Neumann operator assembled from region-wise SGBEM discretization, leading to a boundary-only formulation coupled to the evolution of a polygonal curve network with triple junctions. The Galerkin approximation of the resulting boundary problem is shown to be uniquely solvable, and the fully discrete scheme is unconditionally stable with respect to the time step as long as the evolving polygonal network remains in an admissible class. The accuracy of the proposed method is demonstrated by a convergence test under coupled space--time refinement against a similarity-rescaled exact solution consisting of three concentric circles.
ER  -