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Finally, a numerical method with convergence monitoring is proposed to locate the solutions.
An Euler predictor corrector method with convergence check is used to solve for the oscillation of and the temperature distribution within each fluid plug.
Dynamics of OHPs is characterized using a newly developed time frequency analysis algorithm, and an Euler predictor corrector method with convergence check is used to solve for the temperature distribution within the fluid plug.
Moderate increases in the suction/injection velocities appear to have no effect on the precision of the method with convergence again achieved at the fourth order of the SLM series.
Finally, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom.
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Also a beneficial strategy to solve this optimization problem using Seeker Optimization Algorithm (SOA) based on Pareto optimum method with high convergence speed is presented.
These works motivate us to try to find another way to obtain another quasi-Newton method with better convergence based on the standard BFGS formula.
All compounds were minimized under the Tripos standard force field [14] with Gasteiger-Hückel atomic partial charges [15] by the Powell method with a convergence criterion of 0.01 kcal/mol Å.
Main results of the article are in Section 5, which contains a justification of the Chebyshev polynomial version of the introduced method with corresponding convergence analysis and error estimates.
For instance, the weakly penalized formulation combines the simplified structure of the penalty method with the convergence characteristics of the PL formulation.
The structures were initially optimized using the MM + molecular mechanics method and then were optimized using AM1 method employing the steepest-descent optimizer followed by conjugate gradient, Fletcher-Reeves and Polak-Ribiere methods consecutively with convergence limit of 0.0001 kcal/mol, and RMS gradient limit of 0.001 kcal/A-mol.
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