A programming language for the FEM : FreeFem++
CASTS-LJLL workshop on Applied Mathematics and Mathematical Sciences
LJLL, CASTS & TWSIAM activity group
May 27-28, 2014, 3pm—6:45pm
Organizers: Marc Thiriet, Yannick Deleuze, Tony W.H. Sheu
Contact: Yannick Deleuze
Venue: Mathematics Research Center Building, NTU
(map)
Day 1: Tuesday, May 27th 2014
Part 1: Talk, 2 pm—2:45 pm
Speaker: F. Hecht
This talk focuses on:- the latest capabilities of FreeFem++ to solve PDEs using finite element methods,
- academic examples,
- how an academic solver could be used for advanced and industrial applications.
Part 2: Expert tutorial, 4:45 pm—6:45 pm
Speaker: F. Hecht
This discussion session is held to help researchers to develop their own applications using FreeFem++.
Day 2: Wednesday, May 28th 2014
Part 1: Talk, 2 pm—2:45 pm
Title: Scalable Domain Decomposition Preconditioners in FreeFem++
Authors: F. Hecht, P. Jolivet, F. Nataf
Speaker: F. Hecht
Abstract:
Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this presentation,a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of core, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom.
Such problems arise in computational science and engineering, in solid and fluid mechanics.
While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as Krylov methods.
Part 2: Basic tutorial, 3 pm–4:30 pm
Speaker: Yannick Deleuze
This basic tutorial will provide useful information to generate a mesh, solve a linear PDE, use a formulation with matrices and solve examples with steady and time evolution model PDEs.
This session is very useful for undergraduate students in studying numerical method and engineering mathematics courses.