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On efficient semi-implicit auxiliary variable methods for the six-order Swift–Hohenberg model

Published: 01 February 2023 Publication History

Abstract

The Swift–Hohenberg model is a very important phase field crystal model which can describe many crystal phenomena. This model with quadratic–cubic nonlinearity based on the H − 1-gradient flow approach is a sixth-order system which satisfies mass conservation and energy dissipation law. In this paper, we consider several linear, second-order and unconditionally energy stable schemes based on the traditional and modified scalar auxiliary variable (SAV) approaches. The two novel modified SAV approaches which called step-by-step solving scalar auxiliary variable (3S-SAV) and exponential scalar auxiliary variable (E-SAV) approaches have been proved to have several advantages than the traditional SAV method. We proved the unconditional energy stability for all the semi-discrete schemes carefully and rigorously. In calculation, we show that the novel semi-implicit schemes save many computational CPU time compared with the traditional SAV scheme. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.

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          Published In

          cover image Journal of Computational and Applied Mathematics
          Journal of Computational and Applied Mathematics  Volume 419, Issue C
          Feb 2023
          678 pages

          Publisher

          Elsevier Science Publishers B. V.

          Netherlands

          Publication History

          Published: 01 February 2023

          Author Tags

          1. 65M12
          2. 35K20
          3. 35K35
          4. 35K55
          5. 65Z05

          Author Tags

          1. Swift–Hohenberg model
          2. Scalar auxiliary variable
          3. Step by step
          4. Energy stability
          5. Numerical simulations

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