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

作者：Schloemer N^*; Vanroose W

来源：Journal of Computational Physics, 2013, 234: 560-572.

DOI：10.1016/j.jcp.2012.10.013

• Ginzburg-Landau equations
• Preconditioning
• Algebraic multigrid

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).

• 出版日期2013-2-1