## help with kernel for fast multipole method.

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happyjack27
Posts: 1435
Joined: Wed Jul 14, 2010 5:27 pm

### help with kernel for fast multipole method.

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.

happyjack27
Posts: 1435
Joined: Wed Jul 14, 2010 5:27 pm

### Re: help with kernel for fast multipole method.

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]

happyjack27
Posts: 1435
Joined: Wed Jul 14, 2010 5:27 pm

### Re: help with kernel for fast multipole method.

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...

kcdodd
Posts: 722
Joined: Tue Jun 03, 2008 3:36 am
Location: Austin, TX

### Re: help with kernel for fast multipole method.

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.
Carter

happyjack27
Posts: 1435
Joined: Wed Jul 14, 2010 5:27 pm

### Re: help with kernel for fast multipole method.

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!