systems of nonlinear algebraic equations; semiconductor device equations
In this paper, two algorithms are proposed to solve systems of algebraic equations generated by a discretization procedure of the weak formulation of boundary value problems for systems of nonlinear elliptic equations. The first algorithm, Newton-CG-MG, is suitable for systems with gradient mappings, while the second, Newton-CE-MG, can be applied to more general systems. Convergence theorems are proved and application to the semiconductor device modelling is described.
[bank.cont] R.E. Bank, H.D. Mittelmann: Continuation and multi-grid for nonlinear elliptic systems. Multigrid Methods. Proceedings, Hackbusch, W. (ed.), Lect. Notes Math., Berlin, Heilderberg, New York, 1985.
[bank.rose.81] R.E. Bank,D.J. Rose: Global approximate Newton methods
. Numer. Math. 37 (1981), 279–295. MR 0623045
| Zbl 0442.65034
[bpx.sym] J.H. Bramble, J.E. Pasciak, J. Xu: The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms
. Math. Comp. 56 (1991), 1–34. MR 1052086
[brussino.sonnad] G. Brussino, V. Sonnad: A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations. Int. J. Numer. Meth. Eng. 28 (1989), 801–815.