#215: Driscoll&Healy integration for Multipole -------------------------+-------------------------------------------------- Reporter: eschnett | Owner: Type: enhancement | Status: new Priority: major | Milestone: Component: Cactus | Version: Keywords: | -------------------------+-------------------------------------------------- The attached patch implements a more accurate integration over the sphere, using an algorithm by Driscoll & Healy. This algorithm uses Gaussian integration weights, leading (almost) to exponential convergence.
#215: Driscoll&Healy integration for Multipole --------------------------+------------------------------------------------- Reporter: eschnett | Owner: hinder Type: enhancement | Status: assigned Priority: major | Milestone: Component: Cactus | Version: Resolution: | Keywords: --------------------------+------------------------------------------------- Changes (by eschnett):
* owner: => hinder * status: new => assigned
#215: Driscoll&Healy integration for Multipole --------------------------+------------------------------------------------- Reporter: eschnett | Owner: hinder Type: enhancement | Status: review Priority: major | Milestone: Component: Cactus | Version: Resolution: | Keywords: --------------------------+------------------------------------------------- Changes (by hinder):
* status: assigned => review
#215: Driscoll&Healy integration for Multipole ------------------------------------+--------------------------------------- Reporter: eschnett | Owner: hinder Type: enhancement | Status: review Priority: major | Milestone: Component: EinsteinToolkit thorn | Version: Resolution: | Keywords: Multipole ------------------------------------+--------------------------------------- Changes (by hinder):
* keywords: => Multipole * component: Cactus => EinsteinToolkit thorn
#215: Driscoll&Healy integration for Multipole ------------------------------------+--------------------------------------- Reporter: eschnett | Owner: hinder Type: enhancement | Status: review Priority: major | Milestone: Component: EinsteinToolkit thorn | Version: Resolution: | Keywords: Multipole ------------------------------------+---------------------------------------
Comment (by rhaas):
this seems to be buggy. The results differ by what looks like Pi from the results of test_simpson.par which is otherwise an identical parfile. Testing this with a constant value fr[i]=1.0*sin(th) in utils.cc also yields an answer 3.14 times too large when driscoll&Healy is used as compared to Simpson (which gives the correct 4*Pi result).
I don't know how to fix this since I have no idea where the extra Pi creeps in.
Do not apply in this form. :-)
#215: Driscoll&Healy integration for Multipole ------------------------------------+--------------------------------------- Reporter: eschnett | Owner: hinder Type: enhancement | Status: reopened Priority: major | Milestone: Component: EinsteinToolkit thorn | Version: Resolution: | Keywords: Multipole ------------------------------------+--------------------------------------- Changes (by knarf):
* status: review => reopened
#215: Driscoll&Healy integration for Multipole ------------------------------------+--------------------------------------- Reporter: eschnett | Owner: eschnett Type: enhancement | Status: assigned Priority: major | Milestone: Component: EinsteinToolkit thorn | Version: Resolution: | Keywords: Multipole ------------------------------------+--------------------------------------- Changes (by eschnett):
* owner: hinder => eschnett * status: reopened => assigned
#215: Driscoll&Healy integration for Multipole ------------------------------------+--------------------------------------- Reporter: eschnett | Owner: eschnett Type: enhancement | Status: closed Priority: major | Milestone: Component: EinsteinToolkit thorn | Version: Resolution: fixed | Keywords: Multipole ------------------------------------+--------------------------------------- Changes (by eschnett):
* status: assigned => closed * resolution: => fixed
Comment:
I found the missing factor pi. This factor is actually present in the (unnumbered!) equations in the Driscoll&Healy paper. In my tests, I left it out because I implicitly assumed that theta ranges [0...1], whereas of course it ranger [0...pi]. This made the results too large by a factor of pi.
There was also an error in the index bounds. Driscoll&Healy want a point on the equator, which corresponds to even ntheta, not odd ntheta as previously in the code.
Applied.
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