A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations

A parallel Navier–Stokes solver for the rotating flow problem

“…A sufficiently large grid will allow this to happen; in our specific case we are interested when the ratio M/N is large, since that will maximize the amount of local computation for a given p while keeping small (relative to the local computation) the communication time. This approach has been successfully applied in other parallel applications (see [16][17][18][19]). However, there are two penalties brought about by the parallel computation of Equations (20)- (23): 1. the amount of time needed to set up the asynchronous sends and the retrieval of data from the local communications buffer into the appropriate memory locations of the user's program; 2. the computation of reductions, needed to obtain the norms used in the stopping criteria of the iterations.…”

“…Also, note that the initial condition for w is the solution of Equation (14); as it is solved in the form of (17) the computation can be organized such that one data exchange is suppressed, since for the first iterations (i.e. for k = 0 at t = 0) a processor will have already received columns w :,m and w :,1 from its left and right neighbouring processors, which is done in the last iteration prior to convergence using (17).…”

An implicit pseudo‐spectral multi‐domain method for the simulation of incompressible flows

“…When evaluating the matrix-vector products with A or solving the systems with Q, the special form of Equation (13) can be exploited in order to minimize the computational e ort. A detailed explanation of the corresponding implementation of the restarted GMRES method can be found in Reference [20].…”

Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations

“…(7), which provides a fast and monotonically decreasing con- vergence [6][7][8]. However, the restarted GMRES suffers from the poor scalability in parallelization [18] and hence, is replaced by a CG based method such as the stabilized biconjugate gradient (BiCGSTAB) method in this work for a cheaper memory usage, a comparable convergence, and a better parallel scalability. When applying the BiCGSTAB method to the iterative solution of the interface Eq.…”