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  1. We develop an algorithm for solving the general grade-two model of non-Newtonian fluids which for the first time includes inflow boundary conditions. The algorithm also allows for both of the rheological parameters to be chosen independently. The proposed algorithm couples a Stokes equation for the velocity with a transport equation for an auxiliary vector-valued function. We prove that this model is well posed using the algorithm that we show converges geometrically in suitable Sobolev spaces for sufficiently small data. We demonstrate computationally that this algorithm can be successfully discretized and that it can converge to solutions for the model parameters of order one. We include in the appendix a description of appropriate boundary conditions for the auxiliary variable in standard geometries. 
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  2. Summary

    Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix‐vector multiplication. We clarify a folk theorem that this can only result in a speedup of 2× over the naive implementation. Examining many repeated runs, we show that stochastic noise also contributes to the latency, and we model this using an analytical probability distribution. Our analysis shows that speedups greater than 2× are possible with these algorithms. Copyright © 2016 John Wiley & Sons, Ltd.

     
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