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Numerical methods for simulating Ginzburg-Landau vortices. (English) Zbl 0908.65121

Summary: Numerical solution to the Ginzburg-Landau (GL) equation becomes infeasible as the GL parameter \(\kappa\) and the number of GL vortices increase to a physically interesting regime. It is in this regime that we focus our attention to design a simulated annealing approach for minimizing the associated renormalized energy to study the GL vortex configurations. This approach applied to a commonly used model produces vortex configurations which are of interest in recent studies.

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
82D55 Statistical mechanics of superconductors
90C27 Combinatorial optimization
65K05 Numerical mathematical programming methods

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