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Some results for the weak convergence of semi-implicit split-step methods

Burhaneddin Izgi, Berivan Ari
2019 New Trends in Mathematical Sciences  
In this paper, we obtain some results for the weak convergence of semi-implicit split-step (SISS) methods which are recently developed to solve a class of nonlinear stochastic differential equation with  ...  First, we present some moment estimates based on the actual and numerical solutions of stochastic Ginzburg-Landau equations by SISS methods.  ...  Semi implicit split-step methods for Ginzburg-Landau equation We consider the scalar version of the generalized stochastic Ginzburg-Landau equation dX(t) = (AX(t) − δ X r (t))dt + σ (X(t))dW (t), 0 < t  ... 
doi:10.20852/ntmsci.2019.336 fatcat:admavdeabvgl7dcofre2522eei

Solving generalized quintic complex Ginzburg–Landau equation by homotopy analysis method

Soheila Naghshband, Mohammad Ali Fariborzi Araghi
2016 Ain Shams Engineering Journal  
In this paper, the generalized quintic complex Ginzburg-Landau equation is considered to be solved, by means of the homotopy analysis method (HAM).  ...  Two examples are solved to illustrate the efficiency of the proposed method. By plotting the h-curve of the examples, the region of convergence is determined.  ...  Acknowledgements The authors would like to thank the reviewers of this paper for their valuable recommendations and also the Islamic Azad University, central Tehran branch, for their support during this  ... 
doi:10.1016/j.asej.2016.01.015 fatcat:ylxfj4dmorhvdi6ydndubzweqe

An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg–Landau problem

N. Schlömer, W. Vanroose
2013 Journal of Computational Physics  
This paper considers the extreme type-II Ginzburg--Landau equations, a nonlinear PDE model for describing the states of a wide range of superconductors.  ...  Based on properties of the Jacobian operator and an AMG strategy, a preconditioned Newton--Krylov method is constructed.  ...  We are also grateful to the Research Foundation Flanders (FWO) for financial support through the project G017408N.  ... 
doi:10.1016/j.jcp.2012.10.013 fatcat:dh442xohlzdlznotmwmdga55ma

Surface tension and kinetic coefficient for the normal/superconducting interface: Numerical results versus asymptotic analysis

James C. Osborn, Alan T. Dorsey
1994 Physical Review B (Condensed Matter)  
In this paper we calculate the surface tension and kinetic coefficient numerically by solving the one dimensional equilibrium Ginzburg-Landau equations for a wide range of κ values.  ...  The dynamics of the normal/superconducting interface in type-I superconductors has recently been derived from the time-dependent Ginzburg-Landau theory of superconductivity.  ...  II we review our numerical methods for solving the Ginzburg-Landau equations. In Sec.  ... 
doi:10.1103/physrevb.50.15961 pmid:9975964 fatcat:b6ir6gkv5zaqzcj4kgcc5yl2zu

A New Time Integration Scheme for Cahn-hilliard Equations

R. Schaefer, M. Smołka, L. Dalcin, M. Paszyński
2015 Procedia Computer Science  
We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional.  ...  The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step.  ...  Acknowledgments The work presented in this paper, in particular the visits of Lisandro Dalcin, PhD. at AGH has been supported by Polish National Science Center grant no. DEC-2012/07/B/ST6/01229.  ... 
doi:10.1016/j.procs.2015.05.244 fatcat:572q4gad7bd3rfsjpuhratdf7q

Minimization of the Ginzburg–Landau energy functional by a Sobolev gradient trust-region method

P. Kazemi, R.J. Renka
2013 Applied Mathematics and Computation  
We describe a generalized Levenberg-Marquardt method for computing critical points of the Ginzburg-Landau energy functional which models superconductivity.  ...  The algorithm is a blend of a Newton iteration with a Sobolev gradient descent method, and is equivalent to a trust-region method in which the trustregion radius is defined by a Sobolev metric.  ...  Conclusion We have described a new method for computing solutions to the Ginzburg-Landau equations.  ... 
doi:10.1016/j.amc.2012.12.038 fatcat:57bv7c4fmzfbziydcgltunv46e

Page 3438 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
A. (1-CMU; Pittsburgh, PA); Wu, Xiaonan (PRC-BAP; Kowloon) Analysis and convergence of a covolume approximation of the Ginzburg-Landau model of superconductivity. (English summary) SIAM J. Numer.  ...  The resulting system of linear equations is then solved using a Krylov subspace itera- tive method.  ... 

Local Discontinuous Galerkin Method for Nonlinear Ginzburg- Landau Equation [chapter]

Tarek Aboelenen
2018 Differential Equations - Theory and Current Research  
In this chapter, we develop a local discontinuous Galerkin method to solve the nonlinear Ginzburg-Landau equation.  ...  The nonlinear Ginzburg-Landau problem has been expressed as a system of low-order differential equations.  ...  Conclusions In this chapter, we developed and analyzed a local discontinuous Galerkin method for solving the nonlinear Ginzburg-Landau equation and have proven the stability of this method.  ... 
doi:10.5772/intechopen.75300 fatcat:ibb6z6hepvhb3kuf3sagnh6cye

TEMPORAL SOLITONS OF MODIFIED COMPLEX GINZBERG LANDAU EQUATION

Sahay Shwetanshumala
2008 Progress In Electromagnetics Research Letters  
In this paper we have reported soliton solution of one dimensional modified complex Ginzburg Landau equation. The parametric region where such soliton solution is possible is also identified.  ...  approach, we have found soliton solution of one dimensional modified complex Ginzburg Landau equation.  ...  Recently, based on variational iteration, a very simple yet effective method was proposed by He [21] which has the capacity to solve a large class of nonlinear problems.  ... 
doi:10.2528/pierl08010401 fatcat:4vqikliqqnaofmd6hflfdl5tpq

Photonic band structure of Abrikosov lattices in superconductors

Hesam Zandi, Alireza Kokabi, Aliakbar Jafarpour, Sina Khorasani, Mehdi Fardmanesh, Ali Adibi, Ali Adibi, Shawn-Yu Lin, Axel Scherer
2007 Photonic Crystal Materials and Devices VI  
The implemented numerical method is based on the extensive numerical solution of the Ginzburg-Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from  ...  We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic  ...  For solving the Ginzburg-Landau equation one has to minimize the free energy ( , ) mn mn f a b and find the stable answer in terms of Fourier coefficients.  ... 
doi:10.1117/12.725943 fatcat:nl5ex3ctgnhgrbhfy7dpy6pftq

Nonlinear optimization in Hilbert space using Sobolev gradients with applications [article]

Parimah Kazemi, Robert Renka
2011 arXiv   pre-print
We apply these results to the Ginzburg-Landau model of superconductivity.  ...  The corresponding discretized nonlinear least squares problem is an often met problem in the field of numerical optimization, and thus there exist a wide variety of methods for solving such problems.  ...  Acknowledgements The first author would like to thanks the Institute of Applied Analysis and the Institute of Quantum Physics at Ulm University for their hospitality during my time in Ulm.  ... 
arXiv:1112.3150v1 fatcat:ysirzqo2d5f7bdyb5pc3sdwo2a

Superheating field of superconductors within Ginzburg-Landau theory

Mark K. Transtrum, Gianluigi Catelani, James P. Sethna
2011 Physical Review B  
By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for an ordinary differential equation, we solve the problem numerically.  ...  We study the superheating field of a bulk superconductor within Ginzburg-Landau theory, which is valid near the critical temperature.  ...  Acknowledgments The authors would like to thank Hasan Padamsee, Georg Hoffstaetter, and Matthias Liepe for helpful discussion.  ... 
doi:10.1103/physrevb.83.094505 fatcat:emzdyh2k6fanhjfidqx5xkpj3e

Computationally efficient approach for the minimization of volume constrained vector-valued Ginzburg–Landau energy functional

Rouhollah Tavakoli
2015 Journal of Computational Physics  
A computationally efficient algorithm is presented to solve the space discretized form of the original optimization problem.  ...  The minimization of volume constrained vector-valued Ginzburg-Landau energy functional is considered in the present study.  ...  In the present study, a computationally efficient method is developed to solve the volume constrained L 2 gradient flow of the Ginzburg-Landau functional.  ... 
doi:10.1016/j.jcp.2015.04.020 fatcat:he6f3tg4fjfpbpaifme5oxrw3m

Page 8274 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
J. (4-OX-AM; Oxford) Asymptotic analysis of the bifurcation diagram for symmetric one- dimensional solutions of the Ginzburg-Landau equations. (English summary) European J. Appl.  ...  From the summary: “The bifurcation of symmetric supercon- ducting solutions from the normal solution is considered for the one-dimensional Ginzburg-Landau equation by the methods of formal asymptotics.  ... 

Page 45 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
There is a brief analysis of some iterative algo- rithms which can be used for the solution of the system.  ...  From the introduction: “In our note, the following Ginzburg- Landau equation with a variable coefficient in a bounded domain D CR?  ... 
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