Linearized Schemes For The Time-dependent Ginzburg-landau Equations In Superconductivity

This thesis is devoted to the numerical solution of the time-dependent GinzburgLandau equations in superconductivity,which is derived by Ginzburg and Landau based on the phase field theory.The original time-dependent Ginzburg-Landau equations contain two unknows(,),which constitute a parabolic equation system with strong nonlinear coupling terms.In this thesis,we first simplify the original equation system into a single equation with one unknow .Then,we propose and analyze several linearized schemes for the simplified Ginzburg-Landau equation.In Chapter 1,we introduce the superconductivity model and some previous works on the Ginzburg-Landau equations,and simplify the Ginzburg-Landau equations.In Chapter 2,we provide a linear scheme for the simplified Ginzburg-Landau equation.In Chapter 3,the scheme is analyzed,in particular,the maximum principle,energy stability and error estimate are derived.In Chapter 4,we present an unconditional stable scheme based on the popular stabilization technique.In Chapter 5,we provide two ETD type schemes and give some theoretical results.In Chapter 6,extensive numerical experiments are conducted to verify the theoretical analysis.Finally,some concluding remarks are made and future works are discussed in Chapter 7.