Recent advances in Krylov-subspace solvers for linear systems and applications in device simulation

The computational cost of many simulations is dominated by the solution of large, sparse systems of linear equations. Krylov-subspace methods, especially when combined with suitable preconditioning, are powerful algorithms for the iterative solution of such linear systems. One of the features of Krylov-subspace methods is that the matrix of the linear system is only used in the form of matrix-vector products, and thus sparsity is naturally exploited. In recent years, there have been many advances in Krylov-subspace methods for the solution of large, sparse, nonsymmetric linear systems. In this paper, we survey some of these recent advances especially in the area of Lanczos-based methods. We also discuss the use of state-of-the-art Krylov-subspace methods in device simulation.