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This approach uses more computational calculations in each iteration which can be handled by parallel-processing supporting hardware.
Open image in new window Fig. 3 Flowchart of the framework of the form-finding procedure (the right column shows the calculations in each iteration; the left column shows the updated state variables for calculation).
Those quantities need to be advanced by use of auxiliary equations, and thus the reconstruction requires more x-derivative calculations in each integration step as compared to the classical GS reconstruction.
Finally, applying the Runge-Kutta method to the given initial value problem, we carry out the intermediate calculations in each step to give figures after decimal point and round off the final results each at step to four such places.
Finally, applying the Runge-Kutta method to the given initial value problem, we carry out the intermediate calculations in each step to give figures after the decimal point and round off the final results at each step to four such places.Here F ( x, y ) = 2 x ( y + 1 ), x 0 = 0, y 0 = 0 and we are to use h = 0.2.
Finally, applying the Runge-Kutta method to the given initial value problem, we carry out the intermediate calculations in each step to give figures after the decimal point and round off the final results at each step to four such places.
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So, in the proposed algorithm, the amount of calculation in each iteration is mainly caused by calculating T(c k −b k ) and T −1 d k+1 whose calculation have been reduced to O(N 2log2N) through FFT and IFFT.
The power calculation in each scenario was performed using the "Genetic Power Calculator" which is public available (http://pngu.mgh.harvard.edu/̃purcell/gpc/).edu/̃purcell/gpc/
See Figure 2 figure supplement 1 2 for additional information on calculating drift-variance and Table 2. Also, see Methods section for transcriptional drift calculation in each figure panel.
So instead of doing a flash calculation in each time step of the simulation, we just generate a sparse grid approximation of all possible results of the flash calculation before the reservoir simulation.
We introduce a re-meshing algorithm which adapts the finite element mesh used for the field calculation in each iteration to the actual space charge distribution to keep it sufficiently fine in all areas with non-zero space charge.
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