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

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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. After a finite-volume-type discretization, numerical experiments are done for representative two- and three-dimensional domains. Strong numerical evidence is provided that the number of Krylov iterations is independent of the dimension n of the solution space, yielding an overall solver complexity of O(n).