MPI implementation of parallel subdomain methods for linear and nonlinear convection–diffusion problems

Distributed Iterative Solution of Numerical Simulation Problems on Infiniband and Ethernet Clusters via the P2PSAP Self-Adaptive Protocol

“…The choice of scheme of computation has important consequences on the efficiency of the distributed iterative algorithm. The interest of asynchronous iterations for various problems including boundary value problems and optimization has been shown in [8], [15], [16], [17], [18], [19].…”

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

“…Various strategies of data exchange can be implemented (see [9]). Experiments show that the more data is exchanged, the faster the convergence is because the behaviour tends to multiplicative scheme.…”

“…Note that cancellation of send requests must occur before cancellation of receive requests; otherwise data exchange based on rendezvous mechanism may fail. For more details on the implementation of asynchronous iterative schemes of computation, the reader is referred to [9]. From a mathematical point of view, this implementation of the stopping criterion of the parallel asynchronous iterative process is based on the study presented in [18].…”

“…Denote α = τ 2h 2 ; note that, for the particular application concerning the study of image processing, the spatial discretization step size h is here mentioned for memory; in fact in image processing, h is defined implicitly by the distance between two pixels and can be fixed to the value one (see [19] and [24]); in the sequel, we will see that the value of h has no effect with respect to the behavior of the studied algorithms. Denote also by U (k) the vector of components u (k) i, j that approximates u(x i , y j , t k ); in the sequel U (0) is given by the components of u 0 (x i , y j ) of the initial condition arising in (9). Then, classically, the explicit scheme is given by…”

“…Thus, the implementation principle of the parallel asynchronous Schwarz alternating method needs a particular effort concerning the combination of the solution of very large scale algebraic systems with an efficient communication strategy. When the size of the subsystems is large, note that the asynchronous communications compared to the synchronous ones suppress more efficiently the idle times (see [9]). …”