Nonsymmetric systems arising in the computation of invariant tori
- Simons Fraser Univ., Burnaby, British Columbia (Canada)
We introduce two new spectral implementations for computing invariant tori. The underlying nonlinear partial differential equation although hyperbolic by nature, has periodic boundary conditions in both space and time. In our first approach we discretize the spatial variable, and find the solution via a shooting method. In our second approach, a full two-dimensional Fourier spectral discretization and Newton`s method lead to very large, sparse, nonsymmetric systems. These matrices are highly structured, but the sparsity pattern prohibits the use of direct solvers. A modified conjugate gradient type iterative solver appears to perform best for this type of problems. The two methods are applied to the van der Pol oscillator, and compared to previous algorithms. Several preconditioners are investigated.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 433350
- Report Number(s):
- CONF-9604167-Vol.1; ON: DE96015306; TRN: 97:000720-0023
- Resource Relation:
- Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 1; PB: 422 p.
- Country of Publication:
- United States
- Language:
- English
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