The efficient spectral Galerkin method to the phase-field models in polar geometry
Year: 2025
Type: article
Abstract: We construct in this paper an efficient spectral Galerkin approximation in combination with scalar auxiliary variable (SAV) method to the Allen–Cahn model and Cahn–Hilliard model in polar geometry. Since the spectral methods cannot be directly applied to the non-rectangular regions, the disk region is firstly mapped to the rectangular region by the polar transformation that will lead to singularity at the pole, then providing appropriate pole conditions and basis functions are fundamental for constructing efficient algorithms. Moreover, the accuracy and stability of the proposed approximation are verified by numerical experiments.
Source: Applied Mathematics Letters
Author: Yingying Xie
Institution: Southwestern University of Finance and Economics
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,800
OpenAlex ID: W4407596545