Hi, I’m currently writing a Nbody simulation using the Barnes-Hut algorithm. In order to validate what i wrote, i want to compare it to the brute force calculation. (setting the theta parameter in BH makes it degenerate in a brute force calculation) However,for reason i dont fully understand there…

[image] staufenbach: However,for reason i dont fully understand there a discrepancy between the two result (at machine precision level) which end up accumulating and diverging. [image] PSA: floating-point arithmetic Offtopic Sometimes people are surprise…

[image] staufenbach: Except that the BH algorithm is written in a recursive form in a separate module, i see no reason why i shouldn’t get the same result. In particular, floating-point arithmetic is not associative, so even adding up the same numbers in a different order (e.g. recursively ) w…

[image] staufenbach: Except that the BH algorithm is written in a recursive form in a separate module, i see no reason why i shouldn’t get the same result. In addition to the links posted by @stevengj , the error is probably due to that - changing the order of operations when dealing with floa…

[image] staufenbach: Except that the BH algorithm is written in a recursive form in a separate module, i see no reason why i shouldn’t get the same result. Same as in == or in isapprox? And N-body is hard AFAIU. Edit: the BH algorithm gives an approximate solution? And you are comparing it t…

The problem may be ill-conditioned. I would try gradually increasing the precision used in each algorithm and see if the answers begin to converge.

oh, i forgot about the impact of the order of operations. its effectively not the same. @goerch yes BH is approximate but the level of approximation can be control. and you can make it so its exactly equivalent to a brute force approach. also isapprox is true for the ~20 first iterations. thanks f…

[image] staufenbach: i probably round of the acceleration after each iteration. You could also parameterize isapprox help?> isapprox search: isapprox isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function]) [...]

[image] staufenbach: which end up accumulating and diverging. Note that N-body dynamics are typical chaotic, so even tiny differences in roundoff errors will eventually lead to exponentially differing results . The usual rejoinder is that any quantity that is exponentially sensitive to initia…

[image] stevengj: Note that N-body dynamics are typical chaotic. Not sure about this, isn’t the solar system N-body? Edit: dangerously off topic…

[image] Is the Solar System Stable? The stability of the solar system is one of the oldest problems in theoretical physics, dating back to Isaac Newton. After Newton discovered his famous laws of motion and gravity, he used these to determine the motion of a single planet around the... …

For some arguments on the origin of the instabilities, see i.e. [image] On the Exponential Instability of N-Body Systems We reconsider the old problem of the growth of numerical errors in N-body integrations. We analyze the effects of successive encounters and show that these tend to ma…

Precision error in Nbody simulation

General Usage

stevengj April 5, 2022, 4:32pm 2

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Precision error in Nbody simulation

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