Approximate Matrix Factorization and W-methods for the time integration of multidimensional parabolic problems (Domingo Hernández Abreu, Universidad de La Laguna)

25.06.2024 14:00

This talk deals with the time-integration of space-discretised parabolic problems subject to Dirichlet boundary conditions on a rectangular m-dimensional domain.
We consider the combination of linearly implicit methods (W-methods) along with Approximate Matrix Factorization based on an alternating direction implicit approach, which allows to reduce the algebra cost to the level of 1D problems. Optimal results on PDE-convergence will be presented for linear problems, the Euclidean norm and arbitrary spatial dimensions m ≥ 2. Some techniques aimed at mitigating the order reduction phenomenon due to time-dependent boundary conditions are also presented and numerically illustrated in two and three spatial dimensions.

This talk is based on joint work with S. González-Pinto, E. Hairer and S. Pérez-Rodríguez.

Lieu

Conseil Général 7-9, Room 1-15 (unusual room!), Séminaire d'analyse numérique

entrée libre