Work

Self-avoiding fluid deformable surfaces

Year: 2026

Type: article

Abstract: We propose a numerical method for fluid deformable surfaces governed by surface Stokes flow and Helfrich bending energy under active growth, aiming to model shape evolution of the epithelium in developmental processes. To prevent self-intersections, which commonly arise under large deformations or low enclosed volume-to-area ratios, we incorporate the nonlocal tangent-point energy to penalize non-embedded configurations. The resulting formulation is discretized using higher-order surface finite elements, with a parallelizable assembly strategy for the nonlocal terms. To tailor mesh quality to the geometric evolution, we propose a curvature-adaptive mesh redistribution strategy that improves mesh resolution in regions of high curvature. Numerical examples include the discocyte-to-stomatocyte transition and the inversion of a sphere within a spherical confinement. Both demonstrate the robustness of the method in capturing large deformations, self-avoidance, symmetry-breaking and growth-induced morphology changes.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/583

Authors: Maik Porrmann, Sören Bartels, Axel Voigt

Institutions: Technische Universität Dresden, University of Freiburg, Center for Systems Biology Dresden

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7083710120

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