Happy New Year

2017

WAMS Workshop : Programs and Description of Courses

 

West Asia Mathematical Schools

WAMS

entitled

"Iterative methods for solving the boundary's data reconstruction problems"

 

Description of Courses

 

  • Introduction
  • Motivation : examples from industry and medicine
  • Resolution methods: state of the art
  • A review of analysis
  • Basic function spaces
  • Definitions Properties of Hilbert space
  • Green's representation formulas and applications
  • Distributions
  • Sobolev spaces
  • Motivation for Sobolev spaces
  • Definitions
  • Density of smooth functions and trace in dimension d
  • Sobolev embedding theorems
  • Poincare? inequality
  • General Sobolev inequalities
  • The variational formulation of elliptic PDEs
  • Abstract variational problems
  • General second order elliptic problems
  • Variational approximation methods for elliptic PDEs
  • The general abstract variational approximation scheme
  • The finite element method
  • Meshes in 2d
  • Iterative domain decomposition based methods for Cauchy problems
  • Overlapping methods
  • Methods without overlap
  • Accelerated convergence
  • Variational Steklov–Poincaré theory
  • Notions of parallelism

 

 

Program of the school-First Weak

14h30 hours Theoretical courses – 10h30 hours Programming courses

Date Sunday: 18 December 2016 No of hours
9:30-11:00 Abdeljalil Nachaoui, Introduction and motivations 1h30
11:00-11:30 Break  
11:30-13:00 Fatima Aboud, A review of analysis, Basic function spaces 1h30
13:00-14:00 Lunch  
14:00-16:00 Fatima Aboud, Hilbert space, Green's representation formulas and applications 2h
Date Monday: 19 December 2016  
9:30-11:00 Abdelkrim Chakib, Distributions, Sobolev spaces 1h30
11:00-11:30 Break  
11:30-13:00 Abdelkrim Chakib, Density of smooth functions and trace, Sobolev embedding theorems 1h30
13:00-14:00 Lunch  
14:00-16:00 Abdelkrim Chakib, application examples 2h
Date Tuesday: 20 December 2015  
9:30-11:00 Fatima Aboud, Poincare? inequality, General Sobolev inequalities 1h30
11:00-11:30 Break  
11:30-13:00 Fatima Aboud, application examples 1h30
13:00-14:00 Lunch  
14:00-16:00 Abdelkrim Chakib, Abstract variational problems, General second order elliptic problems 2h
Date Wednesday: 21 December 2016  
9:30-11:00 Abdeljalil Nachaoui, Variational approximation methods for elliptic PDEs 1h30
11:00-11:30 Break  
11:30-13:00 Abdeljalil Nachaoui, Introduction to finite element methods 1h30
13:00-14:00 Lunch  
14:00-16:00 Abdeljalil Nachaoui, Finite element method implementation Issue 2h
Date Thursday: 22 December 2016  
9:30-11:00 Abdeljalil Nachaoui, Introduction FreeFem++ 1h30
11:00-11:30 Break  
11:30-13:00 Fatima Aboud, FreeFem++: Meshes generation 1h30
13:00-14:00 Lunch  
14:00-16:00 Mourad Nachaoui, Programming with FreeFem++ 2h
Date Friday: 23 December 2016  
Social Program
Date Saturday: 24 December 2016  
9:30-12:30 Communications by participants 3h
12:30-13:30 Lunch  

3 hours of communications

 

 

Program of the school-Second Weak

8h30 hours Theoretical courses – 12h hours Programming courses

1h30 Semnar and 1h30 Theoretical and programming evaluations

 
Date Sunday: 25 December 2016 No. of hours  
9:30-11:00 Abdeljalil Nachaoui, Domain decomposition: Overlapping methods 1h30
11:00-11:30 Break  
11:30-13:00 Mourad Nachaoui, Domain decomposition: Methods without overlap 1h30
13:00-14:00 Lunch  
14:00-16:00 Abdeljalil Nachaoui, Domain decomposition: Programming with FreeFem++ 2h
Date Monday: 26 December 2016  
9:30-11:00 Mourad Nachaoui, Domain decomposition: Programming with FreeFem++ 1h30
11:30-11:30 Break  
11:00-13:00 Abdeljalil Nachaoui, domain decomposition: Accelerated convergence andimplementation with FreeFem++ 1h30
13:00-14:00 Lunch  
14:00-16:00 Abdelkrim Chakib, Domain decomposition: variational Steklov–Poincaré theory 2h
Date Tuesday: 27 December 2016  
9:30-11:00 Abdeljalil Nachaoui, Domain decomposition: Programming with FreeFem++ 1h30
11:00-11:30 Break  
11:30-13:00 Mourad Nachaoui, Domain decomposition: Programming with FreeFem++ 1h30
13:00-14:00 Lunch  
14:00-16:00 Mourad Nachaoui, Domain decomposition based methods for Cauchy problems: implementation with FreeFem++ 2h
Date Wednesday: 28 December 2016  
9:30-11:00 Abdeljalil Nachaoui, Domain decomposition based methods for Cauchy problems 1h30
11:00-11:30 Break  
11:30-13:00 Abdeljalil Nachaoui, Domain decomposition based methods for Cauchy problem : Notions of parallelism and implementation with FreeFem++ 1h30
13:00-14:00 Lunch  
14:00-16:00 Mourad Nachaoui, Domain decomposition based methods for Cauchy problem : implementation with FreeFem++ 2h
Date Thursday: 29 December 2016  
9:30-11:00 Abdeljalil Nachaoui: Recent research issue 1h30
11:30-11:30 Break  
11:00-13:00 Evaluations 1h30
13:00-14:00 Lunch  
14:00-16:00 Cloture of School 2h
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