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Thread divergence and memory traffic were identified as the main limiters of GPU integrator performance, and techniques to mitigate these issues were discussed.
Use of a finite-difference Jacobian on the GPU in place of the analytical Jacobian provided by pyJac greatly decreased integrator performance due to thread divergence, resulting in maximum slowdowns of 7.11−240.96×; in comparison, the corresponding slowdowns on the CPU were just 1.39−2.61×, underscoring the importance of use of an analytical Jacobian for efficient GPU integration.
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With a high performance integrator to generate a ramp signal as the reference for INL tests, the number of reference voltages can be greatly reduced such that the chip area overhead can be saved.
For Figure 7, the norm is constant within a percentage error of 3%. Figure 6 Norm conservation performance of integrator (14) for (16) μ = 1.
The optimal tracking performance for integrator and dead time plant in the case where plant uncertainty and control energy constraints are to be considered jointly is inrestigated.
Figure 7 Norm conservation performance of integrator (14) for (16) μ = 2. Norm conservation Norm k 2 of the nonstandard finite difference variational integrator (14) for the NLSE with variable coefficients (16) ( μ = 2 ), from t = 0 to t = 60 with Δ t = 0.1 and Δ x = 0.1.
In recent years, splitting methods have been extensively used as geometric numerical integrators showing excellent performances (both qualitatively and quantitatively) when applied on many problems.
To show the performance of our integrator (14) on this aspect, we plot the norm conservation Norm k 2 in Figure 6 and Figure 7.
In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator.
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We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
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