i want to use a cubic kernel for a fast multipole method for a smoothedparticle magnetohydrodynamics simulation.
so i put the triple integral
(dx*dy*dz)/[(xa)(xa)+(yb)(yb)+(zc)(zc)]
into wolfram alpha, and it can't solve it:
https://www.wolframalpha.com/input/?i=integrate%201/[(xa)(xa)%2B(yb)(yb)%2B(zc)(zc)]%20dx%20dy%20dz
can anyone help?
thanks.
help with kernel for fast multipole method.

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

 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)/[(xa)(xa)+(yb)(yb)+(zc)(zc)r]
(dx*dy*dz)/[(xa)(xa)+(yb)(yb)+(zc)(zc)r]

 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...
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.
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 rescaled easily.
Carter

 Posts: 1435
 Joined: Wed Jul 14, 2010 5:27 pm
Re: help with kernel for fast multipole method.
excellent idea! and then i can do a simple trilinear interpolation from there if i want more accuracy. thanks!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 rescaled easily.