Organisation of Scientific Computing 2

1 Organisation of Scientific Computing 2

The course is an extension of Scientific Computing 1 (CS1) given the first semester of the 2nd year master. It uses some of the ingredients of CS1 and presents new ones in the context of the finite element software Life written in C++¹
We have 6 weeks from January 4th to February 9th, 2 days per week, 2 courses and 2 practical sessions.

Courses given by C. Prud'homme²
When/Where
- Mondays: (C) 11:30-13:00 Room F211
- Tuesdays: (C) 13:30-15:00 Room F211
Course notes in english will be provided.

Practical session given by M. Ismail³
When/Where
- Mondays: (P) 17:00-18:30 Room F212
- Tuesdays: (P) 11:30-13:00 Room F211
Will be in computer rooms with bi processors and 4Go of RAM
Must use the Linux OS (no windows), Debian or Ubuntu distros are preferred
Requirements: knowledge in C++ programming environment (compilation of large software, …).
A course on software tools is being developed by C. Prud'homme and F. Faure that may help you with this course. Check out this page http://course-scicomp.www.ljkforge.imag.fr Some of the slides/courses notes are already available
Visualisation will be done with Paraview⁴


Sessions	Course(h)	Practical(h)	Total(h eq TD)
Introduction	1		1.5
Intro Life	2	1.5	4.5
Mesh	3	1.5	6.
Large Sparse Systems	3	1.5	6.
Galerkin Methods	6	3	12.
Models	3	1.5	6.
Project	0	9	9.
Total	18	18.	45.

Course
- Session 1 : introduction (1h) + introduction life
- Session 2 : introduction life
Practical session
- Session 1 : introduction to life
- Session 2 : introduction to life + presentation of the project

Course
- Session 1 : Mesh
  - mesh generation
  - localisation, localize points in a mesh, see kd-trees and ann⁵
- Session 2 : Mesh
  - localisation,
  - adaptation
Practical session
- Session 1 : Use the Chain OpenCascade⁶, Gmsh⁷ and MadLib⁸
Use OpenCascade to define the geometry, import the geometry in Gmsh and adapt the mesh using Madlib according to a given metric (e.g. given by life, or something else)
- Session 2 : Project

Course
- Session 1 : Large sparse linear systems
- Session 2 : Large sparse linear and nonlinear systems
Practical session
- Session 1 : Manipulation and comparison of various methods
  - provide one linear example and one nonlinear example
  - exercise the solvers/preconditioners from the course
  - look for information on Trilinos⁹/Petsc¹⁰ websites to get help on the solver/preconditioner availability
  - test the code/solvers with respect to solver type, preconditioner type, dimension and polynomials order.
  - measure number of iterations and computing time. Report them in tables
- Session 2 : Project

The project is presented the first week at the second session. Every week, one of the practical session is dedicated to the project.
The project is the simulation of a cooling system for electronic components. This is a coupling between heat-transfer (heat equation) and fluid flow (poiseuille or Navier-Stokes flows). Ideally this problem will be treated fully nonlinearly using a Newton solver in both steady and unsteady cases. Alternatives approximation spaces may be used for comparisons. Performance indices will be computed to check the behavior of the system.

The course is validated as follows:

Report in LaTeX on the project with at least two of the practical sessions in an appendix
20 minutes of oral presentation where the students present the project and the associated results and one of the practical sessions they have written in the appendices
Grade is given as follows:
- quality of report
- quality of oral presentation
- advancement in the project
- answers to questions on the practical sessions and the project
- failing to write one of the two practical sessions will automatically reduce the grade
Students can be in groups of at most 2 persons