Convergence of an implicit–explicit midpoint scheme for computational micromagnetics. (1st March 2018)

• Record Type: Journal Article
• Authors: Praetorius, Dirk; Ruggeri, Michele; Stiftner, Bernhard
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 5(2018)
• Page Start: 1719
• Page End: 1738
• Publication Date: 2018-03-01
• Subjects: Micromagnetism -- Landau–Lifschitz–Gilbert equation -- Spin-transfer torque -- Finite elements -- Implicit–explicit time-integration; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.11.028
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Based on lowest-order finite elements in space, we consider the numerical integration of the Landau–Lifschitz–Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange field, the external field, and lower-order contributions such as the stray field. The latter requires the solution of an additional partial differential equation in full space. Following Bartels and Prohl (2006), we employ the implicit midpoint rule to treat the exchange field. However, in order to treat the lower-order terms effectively, we combine the midpoint rule with an explicit Adams–Bashforth scheme. The resulting integrator is formally of second-order in time, and we prove unconditional convergence towards a weak solution of LLG. Numerical experiments underpin the theoretical findings.