ACM Transactions on Mathematical Software (TOMS)
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
ScaLAPACK user's guide
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
MPI: The Complete Reference
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
CFD parallel simulation using Getfem++ and mumps
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
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Streamers dynamics are characterized by the fast propagation of ionized shock waves at the nanosecond scale under very sharp space charge variations. The streamer dynamics modelling needs the solution of charged particle transport equations coupled to the elliptic Poisson's equation. The latter has to be solved at each time step of the streamers evolution in order to follow the propagation of the resulting space charge electric field. In the present paper, a full multi grid (FMG) and a multi grid (MG) methods have been adapted to solve Poisson's equation for streamer discharge simulations between asymmetric electrodes. The validity of the FMG method for the computation of the potential field is first shown by performing direct comparisons with analytic solution of the Laplacian potential in the case of a point-to-plane geometry. The efficiency of the method is also compared with the classical successive over relaxation method (SOR) and MUltifrontal massively parallel solver (MUMPS). MG method is then applied in the case of the simulation of positive streamer propagation and its efficiency is evaluated from comparisons to SOR and MUMPS methods in the chosen point-to-plane configuration. Very good agreements are obtained between the three methods for all electro-hydrodynamics characteristics of the streamer during its propagation in the inter-electrode gap. However in the case of MG method, the computational time to solve the Poisson's equation is at least 2 times faster in our simulation conditions.