Finite element simulations of window Josephson junctions

Authors:
Manolis Vavalis;Mo Mu;Giorgos Sarailidis
Affiliations:
Department of Computer & Communication Engineering, University of Thessaly, Glavani Str 37, GR 382 21 Volos, Greece and Mechatronics Institute, CERETETH, Technology Park of Thessaly, 1st Industria ...;Department of Mathematics,The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computer & Communication Engineering, University of Thessaly, Glavani Str 37, GR 382 21 Volos, Greece and Mechatronics Institute, CERETETH, Technology Park of Thessaly, 1st Industria ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

This paper deals with the numerical simulation of the steady state two dimensional window Josephson junctions by finite element method. The model is represented by a sine-Gordon type composite PDE problem. Convergence and error analysis of the finite element approximation for this semilinear problem are presented. An efficient and reliable Newton-preconditioned conjugate gradient algorithm is proposed to solve the resulting nonlinear discrete system. Regular solution branches are computed using a simple continuation scheme. Numerical results associated with interesting physical phenomena are reported. Interface relaxation methods, which by taking advantage of special properties of the composite PDE, can further reduce the overall computational cost are proposed. The implementation and the associated numerical experiments of a particular interface relaxation scheme are also presented and discussed.