
List of speakers :
 Gabriele Ciaramella (Constance)
 Victorita Dolean (Nice)
 Martin J. Gander (Genève)
 Laurence Halpern (Paris XIII)
 Felix Kwok (Hong Kong)
 Veronique Martin (Amiens)
 Roland Masson (Nice)
 Tommaso Vanzan (Genève)
Timetable :

Tuesday 19 june 

Wednesday 20 june 

Thursday 21 june 

 9:0010:30 
Felix Kwok
 9:0010:30 
Veronique Martin



10:3011:00 
Coffee Break 
10:3011:00 
Coffee Break 


11:0012:30 
Laurence Halpern

11:0012:30 
Tommaso Vanzan



12:3014:00 
Lunch 
12:3013:30 
Lunch 
14:0015:30 
Martin Gander

14:0015:30 
Roland Masson

13:3015:00 
Victorita Dolean

15:3016:00 
Coffee Break 
15:3016:00 
Coffee Break 
15:0015:30 
Coffee Break 
16:0017:30 
Gabriele Ciaramella

16:0018:00 
TP1 (Tommaso Vanzan and Martin Gander)

15:3017:30 
TP2 (Gabriele Ciaramella and Felix Kwok)

17:3019:00 
Session poster





Slides available here.
Detailed program :
 Gabriele Ciaramella Classical Schwarz Methods
In this lecture, classical Schwarz methods are introduced and their convergence behavior discussed.
Using a Fourier analysis the main convergence properties of these methods are presented.
Moreover, some examples of modern applications of classical Schwarz methods are discussed underlying
their unusual scalability in certain situations.
If time permits, further classical techniques for convergence analysis, like maximum principle and
orthogonal projection, will be treated.
 Victorita Dolean Domain decomposition methods with Freefem++
The purpose of this lecture is to give a few examples of domain decomposition methods and their implementation using Freefem++.
We will start with a short introduction to Freefem++ on a simple boundary value problem defined on a square on which we will test the basic functionalities
such as the construction of the geometry, the treatment of different boundary conditions, discretisation matrices and plots.
Secondly we will illustrate the iterative version of Schwarz method and then its use as a preconditioner on uniform and METIS decompositions of the same geometry.
We will finish by the same kind of tests on the historical "Schwarz geometry" (the union of a disk and a rectangle) now the DD community logo.
Time permitting, we will also briefly address the notion of scalability by a few tests on twolevel methods (achieving a convergence independent of the number of domains) on the above geometries.
Freefem++ codes will be made available for testing to the participants.
 Martin J. Gander Homogeneous and Heterogeneous Domain Decomposition Methods.
I will first give an overview of classical domain decomposition
methods of Schwarz, DirichletNeumann and NeumannNeumann type. I
will then present the extension of these methods to time dependent
problems, which leads to waveform relaxation variants of these
methods. I will finally explain the difference between homogeneous
and heterogeneous domain decomposition methods, and define two
classes of heterogeneous domain decomposition problems.
 Laurence Halpern Schwarz waveform relaxation and best approximation problem.
For the heat equation, introduce rapidly the algorithm, give the behavior over long and short time intervals.
Then define the complex best approximation problem in $\mathbb{P}_n$, and give details on the existence, uniqueness and approximation results, for the real and complex problems.
I will show application to Robin and Ventcell transmission conditions.
 Felix Kwok DirichletNeumann and NeumannNeumann Methods.
In this lecture, we introduce the DirichletNeumann (DN) and NeumannNeumann (NN) methods, which are naturally formulated on nonoverlapping domain decompositions. We will discuss their convergence behaviour on two subdomains, first in 1D, then in 2D using Fourier techniques seen in Lecture 1. The influence of geometry and relaxation parameters will be discussed. If time
permits, we will explain how these methods can be extended to yield FETI and BDDC methods, which are very powerful methods that can be used for problems with complicated geometries.
 Veronique Martin Heterogeneous Methods for Homogeneous Problems.
In this talk we consider domain decomposition methods where different models are solved in different subdomains: we want to approximate a homogeneous object with different approximations
with the aim to reduce the global cost.
We will present a method based on the factorization of the operator, starting with a simple one dimensional case for advection reaction diffusion, then we will generalize to the spacetime equation.
 Roland Masson Heterogeneous Methods for drying problems.
Robin Robin domain decomposition methods are discussed to solve the nonlinear coupling between liquid gas Darcy and free gas flow and transport.
This type of drying models is of interest in various applications ranging from food processing, wood or paper production, salinization of agricultural land,
prediction of convective heat and moisture transfer at exterior building surfaces, to the study of the mass and energy exchanges at
the interface between a nuclear waste disposal and the ventilation galleries.
 Tommaso Vanzan Heterogeneous domain decomposition methods
The aim of the lecture is to introduce optimized Schwarz methods (OSM) which,
due to their favorable convergence properties in the absence of overlap and their
capability to take physical properties at the interfaces into account, are natural
domain decomposition methods for heterogeneous problems. We will use mainly
the StokesDarcy coupling as a model problem to present OSM and to investigate
the limit of the classical approach used to optimize the parameters.
Session poster :
 Joubine Aghili (Nice, LJADInria): Hybriddimensional twophase flow in fractured porous media with nonlinear elimination of interfacial unknowns
 Charhabil Ayoub (University Paris XIII, LAGA): Coupling model of superficial and underground flow
 Laurence Beaude (Nice, LJADInria): New methodology to combine VAG and HFV discretizations on hybrid meshes
 Konstantin Brenner (Nice, LJADInria): Nonlinear Jacobi preconditioning for Newton's method
 Yaguang Gu (Hong Kong Baptist University): RobinType RASPEN method for nonlinear steadystate diffusion equations
 Melanie Lipp (University of Stuttgart, IWS): Adaptive Staggered 2D Grids for DuMux  Plans/Ideas
 Giulia Lissoni (Nice, LJADInria): DDFV method for NavierStokes problem with outflow boundary conditions
 Weslley da Silva Pereira (Inria Sophia Antipolis and LNCC): MHM method for elastodynamics
 Joao Reis (Ecole Polytechnique  Inria Saclay): Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations
Organizing Committee:
Victorita Dolean, Martin J. Gander, Stella Krell, MarieCécile Lafont, Roland Masson and Chiara Soresi.
Contact
