Spectrally Accurate Simulation of Axisymmetric Vesicle Dynamics
Computational Physics
2026-04-17 v1 Soft Condensed Matter
Abstract
We present a meshless numerical method for simulating the dynamics of axisymmetric vesicles in a viscous medium. Key innovations include: (1) adaptive reparameterization based on local length scales, reducing the number of required harmonics; (2) gauge dynamics for maintaining optimal parameterization; (3) error control near the symmetry axis; and (4) spectrally accurate quadrature schemes for singular integrals. The method achieves high accuracy and computational efficiency for simulating lipid bilayer dynamics and related problems in soft matter physics.
Keywords
Cite
@article{arxiv.2604.14926,
title = {Spectrally Accurate Simulation of Axisymmetric Vesicle Dynamics},
author = {M. A. Shishkin},
journal= {arXiv preprint arXiv:2604.14926},
year = {2026}
}