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help with kernel for fast multipole method.
Posted: Mon Nov 25, 2013 5:10 pm
by happyjack27
i want to use a cubic kernel for a fast multipole method for a smoothed-particle magneto-hydrodynamics simulation.
so i put the triple integral
(dx*dy*dz)/[(x-a)(x-a)+(y-b)(y-b)+(z-c)(z-c)]
into wolfram alpha, and it can't solve it:
https://www.wolframalpha.com/input/?i=integrate%201/[(x-a)(x-a)%2B(y-b)(y-b)%2B(z-c)(z-c)]%20dx%20dy%20dz
can anyone help?
thanks.
Re: help with kernel for fast multipole method.
Posted: Mon Nov 25, 2013 5:15 pm
by happyjack27
would also like same with slight modification (for liquids and solids):
(dx*dy*dz)/[(x-a)(x-a)+(y-b)(y-b)+(z-c)(z-c)-r]
Re: help with kernel for fast multipole method.
Posted: Mon Nov 25, 2013 5:21 pm
by happyjack27
i just tried it in 2 dimensions (took out the z)...
https://www.wolframalpha.com/input/?i=i ... 9%5D+dx+dy
yikes! times to consider a different kernel...
Re: help with kernel for fast multipole method.
Posted: Wed Dec 04, 2013 8:27 pm
by kcdodd
You might consider doing it numerically and store the result in the most general way possible for lookup. I try to formulate them in dimensionless parameters so it can be re-scaled easily.
Re: help with kernel for fast multipole method.
Posted: Mon Dec 09, 2013 4:22 pm
by happyjack27
kcdodd wrote:You might consider doing it numerically and store the result in the most general way possible for lookup. I try to formulate them in dimensionless parameters so it can be re-scaled easily.
excellent idea! and then i can do a simple tri-linear interpolation from there if i want more accuracy. thanks!