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

Abstract

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).

References in corpus (1)

• Numerical bifurcation study of superconducting patterns on a square

Cited by in corpus (2)

• Preconditioned Recycling Krylov subspace methods for self-adjoint problems
• Automatic exploration techniques for the numerical bifurcation study of the Ginzburg-Landau equation