Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916883350945792 |
|---|---|
| author | Quan, Chaoyu Tang, Tao Wang, Dong |
| author_facet | Quan, Chaoyu Tang, Tao Wang, Dong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation Quan, Chaoyu Tang, Tao Wang, Dong Numerical Analysis 65M12, 65M15 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. |
| title | Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation |
| topic | Numerical Analysis 65M12, 65M15 |
| url | https://arxiv.org/abs/2508.03992 |