Hello Mark,
the point why I ask all this questions is that my final goal is to enhance the SPME algorithm in Gromacs. As it is well know, that SPME is not momentum conserving in case the forces are derived with analytical differentiation, that means the reciprocal forces stem from the derivative of the reciprocal sum after performing the FFTs in reciprocal space and back again. This just requires 2FFTs per step. In contrast the ik differentiation allows to obtain forces that conserve the momentum. However in this case 4FFT are required: 1 into reciprocal space and 3 back to gather every component of the force. We have tested this two implementations of the SPME and realized that under the condition of a certain accuracy, the analytical differentiation is not always the cheaper one as expected due to the lessnumber of FFTs. Sometimes the higher number of FFTs is balanced out by the smaller interpolation order or
reciprocal space cut-off required to reach the accuracy the same accuracy as in case of analytical differentiation. It is also sad, that the PPPM algorithm is not working correctly, because this would be the "best" way of calculation electrostatic forces. The authors showed that the GreenFunction that is determined by the interpolation scheme and used for their derivation of the PPPM is mathematically the
optimal one. So I also would like to correct the implementation of the PPPM algorithm to provide a correct implementation of the virial calculation. And by the way, the error of the RMSF depens on the charge density, beta, interpolation order and cutoffs in real and reciprocal space. This means as soon as you have the optimal set for a given charge density. So you can apply this parameters to all systems with the same charge density independent of its actual size and chargedistribution, only the charge density has to match.
Flo * Mark Abraham <[email protected]> [2009-06-17 16:11:14 +1000]:
Florian Dommert wrote:* Mark Abraham <[email protected]> [2009-06-17 15:31:43 +1000]:Florian Dommert wrote:* Mark Abraham <[email protected]> [2009-06-17 14:14:22 +1000]:Florian Dommert wrote:However I am very confident and in case of success, that there will besoon an error estimate for the Ewald Sum available, which will be the first step to the an implementation a tuning routine for the SPME paramters to achieve optimalbalance between performance and accuracy ;)I've already implemented a version of mdrun that actually computes the RMS error in the force components under PME, and am planning to release it soon.That is very nice to hear, how do you compute the error ? By comparing to anEwald Sum ?Holding beta fixed, I compare force components with those from a converged real-space summation and high Fourier grid density & interpolation order.So you have to perform a very costly simulation for every system, when you gather the reference force ?Actually, both the reference force run and the parameter scan runs are invocations of "mdrun -rerun". I haven't notice the former to be very costly, but there's a trade-off involved. To converge the components to machine precision might indeed be very costly, but one doesn't need to go to that extreme to estimate that the average RMS force error over the test trajectory is 1e-4 (or whatever).And which beta do you choose, because if you take the right choice you can decrease the computational cost extremely.Yep. Having chosen a desired accuracy, you have to scan beta (with ewald_rtol and rcoulomb) and then scan the grid densities to find point(s) with acceptable accuracy and minimal cost. This is not such an extreme problem once you have some guidance from previous optimizations.So theoretically at first you have to find the right beta by sampling through the corresponding parameter space with a fixed Interpolation order and grid size. In the optimal range a change of beta within 0.1 will yield a difference in the error of about 10-1 this trend continues around +/- 0.5 of the optimal value for beta.OK, I'll have to take your word for that, since I haven't looked at the maths in that detail. It's certainly well-known (e.g. original PME papers) that a correct choice of parameters can swing orders of magnitude of computational cost for given accuracy, or vice-versa.Mark _______________________________________________ gmx-users mailing list [email protected] http://lists.gromacs.org/mailman/listinfo/gmx-users Please search the archive at http://www.gromacs.org/search before posting!Please don't post (un)subscribe requests to the list. Use the www interface or send it to [email protected].Can't post? Read http://www.gromacs.org/mailing_lists/users.php
-- Florian Dommert Dipl.-Phys. Institute for Computational Physics University Stuttgart Pfaffenwaldring 27 70569 Stuttgart Tel: +49 - 711 / 6856-3613 Fax: +49 - 711 / 6856-3658 EMail: [email protected] Home: http://www.icp.uni-stuttgart.de/~icp/Florian_Dommert !! PGP-ENCODED emails preferred !!
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