A Gauss-Seidel Projection Method for Micromagnetics Simulations

Xiao Ping Wang, Carlos J. García-Cervera, E. Weinan

Research output: Contribution to journalArticlepeer-review

136 Scopus citations


One of the main difficulties in micromagnetics simulation is the severe time step constraint introduced by the exchange field. Using standard explicit integrators leads to a physical time step of sub-pico seconds, which is often two orders of magnitude smaller than the fastest physical time scales. Direct implicit integrators require solving complicated, coupled systems. In this paper, we introduce an implicit method whose complexity is comparable to solving the scalar heat equation implicitly. This method is based on a combination of a Gauss-Seidel implementation of a fractional step implicit solver for the gyromagnetic term, and the projection method for the heat flow of harmonic maps. This method allows us to carry out fully resolved calculations for the switching of the magnetization in micron-sized elements.

Original languageEnglish (US)
Pages (from-to)357-372
Number of pages16
JournalJournal of Computational Physics
Issue number1
StatePublished - Jul 20 2001

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Implicit methods
  • Landau-Lifshitz equation
  • Micromagnetics
  • Projection method


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