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arXiv · 2508.03992

Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation

Chaoyu Quan·Tao Tang·Dong Wang
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Abstract

The energy dissipation property of the Strang splitting method was first demonstrated for the matrix-valued Allen-Cahn (MAC) equation under restrictive time-step constraints [J. Comput. Phys. 454, 110985, 2022]. In this work, we eliminate this limitation through a refined stability analysis framework, rigorously proving that the Strang splitting method preserves the energy dissipation law unconditionally for arbitrary time steps. The refined proof hinges on a precise estimation of the double-well potential term in the modified energy functional. Leveraging this unconditional energy dissipation property, we rigorously establish that the Strang splitting method achieves global-in-time $H^1$-stability, preserves determinant boundedness, and maintains second-order temporal convergence for the matrix-valued Allen-Cahn equation. To validate these theoretical findings, we conduct numerical experiments confirming the method's energy stability and determinant bound preservation for the MAC equation.

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Chaoyu Quan, Tao Tang, Dong Wang. 2025-08-06. Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation. https://arxiv.org/abs/2508.03992

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