Olivier Dubois: my personal webpage

Research

Here are some research projects I am currently involved in:

Finding efficient transmission conditions in domain decomposition methods - Optimized Schwarz methods. (Jointly with Martin J. Gander.)
Studying coarse space corrections that are appropriate for optimized Schwarz methods. (With Martin J. Gander, Sébastien Loisel, Amik St-Cyr and Daniel Szyld.)
Using multiscale and energy minimizing basis functions in the context of domain decomposition and multigrid preconditioners, with applications to reservoir simulation. (Joint work with Ilya D. Mishev and Ludmil Zikatanov.)
Proving convergence estimates for optimized Schwarz methods that are valid for subdomains of general shapes. (With Shaun H. Lui.)
Theoretical analysis of the convergence of multigrid methods applied to hybridized discontinuous Galerkin discretizations. (With collaborators Bernardo Cockburn and Jaydeep Gopalakrishnan.)

Papers, preprints, theses and other research documents are available below.

Springer Journal, Numerical Algorithms

O. Dubois and S. H. Lui, Convergence Estimates for an Optimized Schwarz Method for PDEs with Discontinuous Coefficients, Numerical Algorithms, vol. 51, no. 1, p. 115-131, 2009. http://dx.doi.org/10.1007/s11075-009-9268-1

Society for Petroleum Engineers (SPE), Reservoir Simulation Symposium
February 2-4, 2009, in Houston.

O. Dubois, I. D. Mishev and L. Zikatanov, Energy Minimizing Bases for Efficient Multiscale Modelling and Linear Solvers in Reservoir Simulation, paper SPE-119137, 2009.

18th International Conference on Domain Decomposition Methods (DD18)
January 2008, in Jerusalem, Israel.

O. Dubois and M. J. Gander, Convergence Behavior of a Two-Level Optimized Schwarz Preconditioner, Domain Decomposition Methods in Science and Engineering XVIII, Lecture Notes in Computational Science and Engineering, vol. 70, p. 177-184, Springer, 2009.

PhD thesis, June 2007:

17th International Conference on Domain Decomposition Methods (DD17)
July 2006, in Strobl, Austria.

Article submitted for the proceedings that will be published by Springer:
O. Dubois, Optimized Schwarz Methods for a Diffusion Problem with Discontinuous Coefficient.
Here is the 20-minute talk that I gave, about optimized Schwarz methods for problems with discontinuous coefficients.

16th International Conference on Domain Decomposition Methods (DD16)
January 2005, at Courant Institute, NYU.

Article for the proceedings that were published by Springer in 2006:
O. Dubois, Optimized Schwarz Methods with Robin Conditions for the Advection-Diffusion Equation.
Here is the 20-minute talk that I gave. I talked about the work I did for my masters.

Master's thesis, October 2003:

Poster for the SIAM Annual Meeting (in Montreal), June 2003:

IPSW7 (Industrial Problem Solving Workshop), May 2003, in Calgary:

Preprint: Modelling the cost of quality and warranty. With N. Nigam (main author), C.S. Bohun, H. Guo, V. Mendiratta, V. Stepankevych and T. Vassilev. To appear, v. 12, n.1, Canadian Applied Mathematics Quarterly.
Full proceedings of the conference.

GIMMC6 (Graduate Industrial Mathematical Modeling Camp), May 2003, in Banff (BIRS):

IPSW6 (Industrial Problem Solving Workshop), May 2002, in Vancouver (UBC):

GIMMC5 (Graduate Industrial Mathematical Modeling Camp), May 2002, in Vancouver (Simon Fraser):