11 research outputs found

    Plot of the percentage of messages in the event-triggered communication solver for various values of horizon <i>h</i> and decay <i>d</i>.

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    Note that a decay of 0 is used to represent 100% of the messages since an event of communication is triggered for this case at every iteration. We see that as the decay and horizon increases, the percentage of messages starts to decrease.</p

    Evolution of the Manhattan or L-1 norm of the top boundary of 4 randomly chosen PEs.

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    Note that the x axis starts from 2000 to wait for the large scale oscillations to die out.</p

    Corresponding thresholds in a semi-log plot for the boundaries shown in Fig 5.

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    It is seen that the thresholds overall decrease with iterations to reflect the decrease in slope of the norm of the boundaries in Fig 5.</p

    Comparison between synchronous and asynchronous solvers between two PEs.

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    The vertical axis is wall clock time. The variable ki refers to the iteration count at the i-th PE. In the synchronous solver, every PE will execute the same iteration number at a certain point in time. In contrast, every PE in the asynchronous solver independently executes its iterations and may execute different iteration numbers at a certain point in time.</p

    Bubbles in a liquid illustrating multiphase flows in a periodic 3-D domain.

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    Only a small section of the domain is shown here.</p

    Comparison between asynchronous solver and event-triggered solver as illustrated using two PEs.

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    The vertical axis is wall clock time. The asynchronous solver communicates at every iteration whereas the event-triggered solver communicates only when the event condition is satisfied. At other iterations, it avoids communication as shown by the red cross signs on the sender side.</p

    Parameters relevant to the simulation setup we consider in this paper.

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    Parameters relevant to the simulation setup we consider in this paper.</p

    Procedure for calculation of the threshold of event-triggered communication at the sending PE.

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    When the event E2 is triggered, a new threshold τ* is calculated by multiplying the local slope s between events E1 and E2 with the horizon h as shown in the left subfigure (a). Then the previously calculated threshold τ* is gradually decayed in the form τ = τ*dm where 0 d m is the number of iterations since the event E2 when τ* was calculated. This decay phenomenon, shown in subfigure (b), continues until the next event E3 triggers.</p

    Plot highlighting the number of messages sent by each of the 200 PEs to the left and right neighbors with the event-triggered communication algorithm considering horizon <i>h</i> = 750 and decay <i>d</i> = 0.8.

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    The number of iterations with the synchronous solver (Sync Iters in the plot legend) which is the same for all PEs is shown by the blue line for reference. In contrast, the number of iterations taken by each of the PEs in the event-triggered solver (Event Iters in the plot legend) is shown by the red asterisks. Further, the number of messages sent to the left neighbor and right neighbor (shown as Event Left Msgs and Event Right Msgs in the plot legend) by each of the PEs is shown respectively by the yellow star sign and the purple round sign. The number of messages for both the left and right neighbors for every PE are quite close. Hence the purple round signs overlap the corresponding yellow star signs for all the PEs. It is seen that the number of messages is considerably lesser than the number of iterations for any PE, thus illustrating the benefit of reduced messages in event-triggered communication.</p
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