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.
[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. DOI 10.1002/nme.1620280406