A multigrid continuation method for elliptic problems with folds
SIAM Journal on Scientific and Statistical Computing
Solving large nonlinear systems of equations by an adaptive condensation process
Numerische Mathematik
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Numerical determination of an emanating branch of Hopf bifurcation points in a two-parameter problem
SIAM Journal on Scientific and Statistical Computing
Stable solvers and block elimination for bordered systems
SIAM Journal on Matrix Analysis and Applications
Conjugate gradient methods for continuation problems
ISCM '90 Proceedings of the International Symposium on Computation mathematics
Solution of bordered singular systems in numerical continuation and bifurcation
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Mathematics and Computers in Simulation
Iterative methods for large continuation problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
An Algebraic Multilevel Multigraph Algorithm
SIAM Journal on Scientific Computing
A new algorithm for continuation and bifurcation analysis of large scale free surface flows
A new algorithm for continuation and bifurcation analysis of large scale free surface flows
| Hi-index | 0.00 |
This paper presents a systematic investigation of the numerical continuation algorithms for bifurcation problems (simple turning points and Hopf bifurcation points) of 2D nonlinear elliptic equations. The continuation algorithms employed are based only on iterative methods (Preconditioned Generalized Conjugate Gradient, PGCG, and Multigrid, MG). PGCG is mainly used as coarse grid solver in the MG cycle. Numerical experiments were made with the MG continuation algorithms developed by Hackbusch [W. Hackbusch, Multi-Grid Solution of Continuation Problems, Lecture Notes in Math., vol. 953, Springer, Berlin, 1982], Meis et al. [T.F. Meiss, H. Lehman, H. Michael, Application of the Multigrid Method to a Nonlinear Indefinite Problem, Lecture Notes in Math., vol. 960, Springer, Berlin, 1982], and Mittelmann and Weber [H.D. Mittelmann, H. Weber, Multi-grid solution of bifurcation problems, SIAM J. Sci. Statist. Comput. 6 (1985) 49]. The mathematical models selected, as test problems, are well-known diffusion-reaction systems; non-isothermal catalyst pellet and Lengyel-Epstein model of the CIMA reaction. The numerical methods proved to be efficient and reliable so that computations with fine grids can easily be performed.