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

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

2012-04-23

arxiv.org/abs/1204.5125v1

Physics

Computational Physics

Scientific paper

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).

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