Events
DMS Applied and Computational Mathematics Seminar |
| Time: Sep 01, 2023 (02:00 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Cao Kha Doan (Auburn University)
Title: Low regularity integrators for the classical and conservative Allen-Cahn equations with maximum bound principles
Abstract: This talk is concerned with conditionally structure-preserving, low regularity time integration methods for both classical and conservative Allen–Cahn equations. Important properties of such equations include the maximum bound principle (MBP) and energy dissipation law. By iteratively using Duhamel’s formula, first- and second-order low regularity integrators (LRIs) are constructed for time discretization. The proposed LRI schemes are proved to preserve the MBP and energy stability, and are shown to conserve mass for the conservative Allen-Cahn equation. Furthermore, their temporal error estimates are also successfully derived under a low regularity requirement that the exact solution is only assumed to be continuous in time. Numerical results show that the proposed LRI schemes are more accurate and have better convergence rates than the exponential time differencing schemes, especially when the interfacial parameter approaches zero.
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