Parallel realization of the finite difference method solution of the Poisson-Boltzmann equation
Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation
We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with...
Parallel SVD computation
Parallel, synchronous and asynchronous two-stage multisplitting methods.
Parallelization of artificial immune systems using a massive parallel approach via modern GPUs
Parallelization is one of possible approaches for obtaining better results in terms of algorithm performance and overcome the limits of the sequential computation. In this paper, we present a study of parallelization of the opt-aiNet algorithm which comes from Artificial Immune Systems, one part of large family of population based algorithms inspired by nature. The opt-aiNet algorithm is based on an immune network theory which incorporates knowledge about mammalian immune systems in order to create...
Parallelization of Random Number Generators and Long-Range Correlations.
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...
Perturbation of parallel asynchronous linear iterations by floating point errors.
QR factorizations using a restricted set of rotations.
Rehabilitation of the Gauss-Jordan Algorithm.
Resilient asynchronous primal Schur method
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...
Résolution de grands systèmes linéaires creux par méthodes itératives parallèles
Résolution parallèle de problèmes aux limites non linéaires
Scalable algebraic multigrid on 3500 processors.
Schwarz methods over the course of time.
Semicoarsening multigrid for systems.
Simulated annealing
Simulation of incompressible flows with heat and mass transfer using parallel finite element method.
Solving Differential Equations by Parallel Laplace Method with Assured Accuracy
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006We produce a parallel algorithm realizing the Laplace transform method for the symbolic solving of differential equations. In this paper we consider systems of ordinary linear differential equations with constant coefficients, nonzero initial conditions and right-hand parts reduced to sums of exponents with polynomial coefficients.