Section: New Results

Parallel numerical algorithms

Parallel Adaptive GMRES with deflated restarting

Participant : Jocelyne Erhel.

Grants and projects: C2S@EXA 8.2.3 , JLPC 8.4.4

Software: DGMRES, AGMRES, GPREMS.

Publications: [17] , [26] .

Abstract: The GMRES iterative method is widely used as a Krylov subspace technique for solving sparse linear systems when the coefficient matrix is nonsymmetric and indefinite. The Newton basis implementation has been proposed on distributed memory computers as an alternative to the classical approach with the Arnoldi process. The aim of our work here is to introduce a modification based on deflation techniques. This approach builds an augmented subspace in an adaptive way to accelerate the convergence of the restarted formulation. In our numerical experiments, we show the benefits of using this implementation with hybrid direct/iterative methods to solve large linear systems.

Hybrid algebraic solvers for CFD problems

Participant : Jocelyne Erhel.

Grants and projects: C2S@EXA 8.2.3 , JLPC 8.4.4

Software: DGMRES, AGMRES, GPREMS.

Publications: [18] .

Abstract: Sparse linear systems arise from design optimization in computational fluid dynamics. In this approach, a linearization of the discretized compressible Navier-Stokes equations is built, in order to evaluate the sensitivity of the entire flow with respect to each design parameter. The goal is to reduce the memory requirements and indirectly, the computational cost at different steps of this scheme. Numerical results are presented with industrial test cases to show the benefits of our methodology.

Algebraic multilevel preconditioning

Participant : Thomas Dufaud.

Grants: C2S@EXA 8.2.3

Publications: [51] , [23] , [24] .

Conferences: [37] , [24] .

Abstract: The Schwarz domain decomposition method is a very attractive numerical method for parallel computing as it needs only to update the boundary conditions on the artificial interfaces generated by domain decomposition. Thus only local communications between the neighbouring sub-domains are required. We review the use of Aitken's acceleration applied to the Schwarz domain decomposition method.

Counting eigenvalues in domains of the complex field

Participant : Bernard Philippe.

Grants: momappli 8.4.2

Publications: [15] , [28] .

Conferences: [47] , [48] , [22] .

Abstract: A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument of the logarithm of a function. A strategy is proposed for selecting a path length that insures that the same branch of the logarithm is followed during the integration. Numerical tests are reported for matrices obtained from conventional matrix test sets.

Sliced-time computation method

Participant : Jocelyne Erhel.

Grants: MODNUM 8.4.5

Publications: [16] , [25] .

Abstract: We consider the mathematical framework of a sliced-time computation method for explosive solutions to systems of ordinary differential equations. We also derive an Adaptive Parallel-in-Time Method with application to a membrane problem.

Interacting particles systems

Participant : Lionel Lenôtre.

Grants: H2MNO4 8.2.1

Conferences: [31]

Abstract: We consider a variance reduction method for simulations with particles.