Numerical Methods for the Landau--Lifshitz Equation
نویسندگان
چکیده
منابع مشابه
Numerical Methods for the Landau-Lifshitz Equation
We discuss numerical schemes for various forms of the Landau–Lifshitz equation. A new simple projection method is introduced and is shown to be unconditionally stable. The advantages over other schemes are also demonstrated numerically.
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In this paper we give an overview of the numerical methods for the solution of the Landau-Lifshitz-Gilbert equation. We discuss advantages of the presented methods and perform numerical experiments to demonstrate their performance. We also discuss the coupling with Maxwell’s equations.
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The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to giv...
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By using the geometric concept of PDEs with prescribed curvature representation, we prove that the 1+2 dimensional isotropic Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schrödinger-type system. From the nonlinear Schrödinger-type system, we construct blowing up H3(R2)-solutions to the Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2000
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142999352199