Lagrangian submanifolds: open Gromov-Witten theory and Mirror Symmetry
Implementable VU-decomposition methods for composite optimization
Probabilistic and algebraic aspects of smooth dynamical systems
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Laval, Dept Math & Stat, 1045 Ave Med, Quebec City, PQ G1V 0A6 - Canada
[3] Univ Bari Aldo Moro, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari - Italy
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | FOUNDATIONS OF COMPUTATIONAL MATHEMATICS; v. 16, n. 2, p. 531-575, APR 2016. |
| Web of Science Citations: | 8 |
| Abstract | |
In this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn-Hilliard equation. (AU) | |
| FAPESP's process: | 10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/07460-7 - Rigorous computations for PDEs |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |