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A posteriori error estimators and mesh adaptation

Master Thesis

Date: December 19 2006

Keywords : A posteriori error estimators, finite elements, mesh adaptation

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Description

The main goal of this project is to study and implement some a posteriori error estimators within the Life library, a C++ scientific computing library. The applicant will make a state of the art in the area of a posteriori error estimator and compare them on some standard examples using Life. The applicant will also couple Life with some mesh adaptation tools such as bamg or netgen. The applicant shall also make a few steps in the direction of h-p adaptation.

References:

Prerequisites

It is preferable that the applicants have some knowledge in the following areas:

Mass transport models in the context of the cardiovascular system

Master Thesis

Date: November 24 2006

Keywords : multi-physics coupling, Navier-Stokes, Darcy, Convection-diffusion-reaction, application in blood flow simulations

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Description

The main goal of this projet to develop and implement solvers for mass transport processes within the Life library a scientific computing library. We are mainly interested to model transport processes in large and medium sized arteries and we shall use macroscopic scale models. The blood flow in the arterial lumen is described by the Navier-Stokes equations and the plasma filtration in the arterial wall by Darcy's law. Regarding the mathematical model for the transport of molecules within the blood flow, it uses the convection- diffusion equation and the solid dynamics in a porous media is modelled by the macroscopic convection-diffusion-reaction equation.

Prerequisites

It is preferable that the applicants have some knowledge in the following areas:

Efficient computations of incompressible flows

Master Thesis

Date: November 24 2006

Keywords : 2D/3D incompressible Navier-Stokes equations, preconditioning, solver strategies, splitting

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Description

The main goal of this project is to study a few strategies for solving 3D incompressible Navier-Stokes equations and compare them in terms of accuracy and efficiency on some non-trivial models. We shall use the library Life to implement and test the strategies.

Reference: Howard C. Elman, David J. Silvester, Andrew J. Wathen,  Finite Elements And Fast Iterative Solvers: With Applications in  Incompressible Fluid Dynamics,  Editeur: Oxford University Press (19 Mai 2005),  ISBN: 019852868X

Prerequisites

It is preferable that the applicants have some knowledge in the following areas:

Serialization, archiving and visualisation of large scale data structures for Life: a library for parallel scientific computing

Master Thesis

Date: November 24 2006

Keywords : large scale data structures, serialization, archiving, visualisation, parallelism, file formats, C++, Boost, MPI, HDF5

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Description

This project is driven by the development of a modern C++ library for the resolution of partial differential equations called Life. The main goal is to create a framework for the management, archiving and visualisation of the data structures coming from large scale simulations. To this end, we will establish a state of the art in this area and study the possibilities given by the libraries boost.serialisation, boost.archive et hdf5.

The applicant will gain knowledge and experience in the following areas:

Prerequisites

It is preferable that the applicants have some knowledge in the following areas:


Contact:
The project will be supervised by Prof. Christophe Prud'homme  christophe.Prudhomme@ujf-grenoble.fr, Tel: +33 4 76 63 54 97

Dates
  Application deadline: No deadline,
  Positions start: as early as possible,

Conditions for applicants

Related links
  LMC Lab,
  IMAG,
  Université Joseph Fourier.