A Structure-Preserving Method of Fundamental Solutions for the Multi-Phase Mullins-Sekerka Flow
Abstract
A charge simulation method, a variant of the method of fundamental solutions, is applied to approximate the multi-phase Mullins--Sekerka flow in ℝ2 and in a half-plane bounded by a Neumann wall. In the underlying mathematical model, interfaces driven by their curvature are coupled through a harmonic chemical-potential field. Each chemical potential is represented by fundamental solutions centered at charge points off the curve, so no bulk mesh is required. The scheme treats curve networks separating several phases at triple junctions, including phases that occupy more than one region; on the half-plane boundary, the homogeneous Neumann condition is imposed exactly by image charges, and mobile contacts stay orthogonal to the wall. The discretization is structure-preserving in the sense that every bounded phase area is conserved to machine precision at the velocity level by a null-space projection of the discrete area constraints. The proposed scheme is assessed through a convergence test against an exact three-concentric-circle solution.
Related
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BibTeX
@misc{eto2026structurepreserving,
title = {{A Structure-Preserving Method of Fundamental Solutions for the Multi-Phase Mullins-Sekerka Flow}},
author = {Tokuhiro Eto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.12759},
eprint = {2607.12759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12759},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Structure-Preserving Method of Fundamental Solutions for the Multi-Phase Mullins-Sekerka Flow
AU - Tokuhiro Eto
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2607.12759
UR - https://arxiv.org/abs/2607.12759
AB - A charge simulation method, a variant of the method of fundamental solutions, is applied to approximate the multi-phase Mullins--Sekerka flow in ℝ^2 and in a half-plane bounded by a Neumann wall. In the underlying mathematical model, interfaces driven by their curvature are coupled through a harmonic chemical-potential field. Each chemical potential is represented by fundamental solutions centered at charge points off the curve, so no bulk mesh is required. The scheme treats curve networks separating several phases at triple junctions, including phases that occupy more than one region; on the half-plane boundary, the homogeneous Neumann condition is imposed exactly by image charges, and mobile contacts stay orthogonal to the wall. The discretization is structure-preserving in the sense that every bounded phase area is conserved to machine precision at the velocity level by a null-space projection of the discrete area constraints. The proposed scheme is assessed through a convergence test against an exact three-concentric-circle solution.
ER -