Timeline for Symplectic (or alike) integrator for system with Coulomb singularity and time-dependent potentials
Current License: CC BY-SA 4.0
10 events
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| Mar 15, 2023 at 9:47 | comment | added | MPIchael | Another idea is to disregard the force of the electron on the ion as the weight ratio is ~1800, so ion orbit will effectively be decoupled from the electrons position. The idea goes back to the "Born–Oppenheimer (BO) approximation" That might serve you well to get a rough idea of the solution for a fraction of the computation power. | |
| Mar 15, 2023 at 7:01 | comment | added | MPIchael | I have worked with the "RK45" Method, where you can take the magnitude of the fifth Runge Kutta step as an error approximate, and if itis larger than a threshold you reduce the stepsize. en.wikipedia.org/wiki/… . | |
| Mar 15, 2023 at 6:59 | comment | added | Lutz Lehmann | Yes, or use the size of the ODE function, the first calculated derivatives vector in a step, to scale the step size, so that all steps have about the same length. This works nicely in some examples, removes the undersampling close to singularities, but might give too many steps in the more boring regions. | |
| Mar 15, 2023 at 1:31 | comment | added | michalt | @LutzLehmann Thank you for your comment. I will give it a try as it is quite simple thing to do. However, in my initial experiments with this problem, I first tried RK45 with completely disasterous results. Maybe the methods of higher order will work better. Is it worth introducing a "universal time" transformation so that d/dt=(1/r) d/ds, where r is the distance from the singulatiry? | |
| Mar 15, 2023 at 1:26 | comment | added | michalt | @MPIchael Hi and thank you for your comment. Would you mind mentioning an example of such variable-time-step method please? Just to help me to start some reading. So far, I was disregarding these schemes due to the reason mentioned by Lutz Lehmann. Thank you. | |
| Mar 14, 2023 at 10:12 | comment | added | Lutz Lehmann | With variable time steps you lose the advantage of symplectic methods, as each time step preserves a different perturbed energy. In that case it is better to employ variable-step RK 78 or higher order methods from the start | |
| Mar 14, 2023 at 9:30 | comment | added | MPIchael | Welcome to Scicomp! When dealing with Orbits you will have quite rapid dynamics when the electron and ion are close to each other and slow and smoth dynamics when they are apart. You may gain significant performance increases when simulating with variable timesteps. Also you may alleviate some of the problems with your singularity, as time dependent schemes can be tuned to have sufficient precision in the vicinity of it. | |
| Mar 14, 2023 at 1:18 | history | edited | Daniel Shapero | CC BY-SA 4.0 |
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| S Mar 13, 2023 at 23:48 | review | First questions | |||
| Mar 20, 2023 at 1:37 | |||||
| S Mar 13, 2023 at 23:48 | history | asked | michalt | CC BY-SA 4.0 |