Energy quadratization Runge-Kutta method for the modified phase field crystal equation
- 주제(키워드) energy quadratization Runge-Kutta method , mass conservation , modified phase field crystal equation , unconditional energy stability
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 IOP Publishing Ltd
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000190366
- 본문언어 영어
- Published As https://doi.org/10.1088/1361-651X/ac466c
초록/요약
In this paper, we propose high order and unconditionally energy stable methods for a modified phase field crystal equation by applying the strategy of the energy quadratization Runge-Kutta methods. We transform the original model into an equivalent system with auxiliary variables and quadratic free energy. The modified system preserves the laws of mass conservation and energy dissipation with the associated energy functional. We present rigorous proofs of the mass conservation and energy dissipation properties of the proposed numerical methods and present numerical experiments conducted to demonstrate their accuracy and energy stability. Finally, we compare long-term simulations using an indicator function to characterize the pattern formation. © 2022 IOP Publishing Ltd.
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