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Paper: inexact GMRES with fast multipole method and low-p relaxation
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What were criteria used for far, near-singular, singular integration? #11

Closed labarba closed 9 years ago

labarba commented 9 years ago

There is no mention anywhere in the thesis (that I can find) of the distances used to define the domains where different integration methods were applied. I want to know what was the criterion for the "far" targets, where Gauss quadrature with <4 quadrature points was used, and what was the criterion for "near-singular" targets, where ~20 points were used. For "singular" targets: is the only case here where the collocation point is on the source panel itself? Or does it apply to any other case?

None of the results indicate this bit of information, as far as I can tell.

slayton58 commented 9 years ago

Singular is only when source panel == target panel

Then for semi-analytical the criteria I use is based on the area of the src panel and the distance between the panels (I’m not 100% sure where this expression came from, pretty certain it came from Chris though…):

if (sqrt(2*src_area)/d >= 0.5) { AnalyticalIntegral:: …; }

On Jun 5, 2015, at 3:57 AM, Lorena A. Barba notifications@github.com wrote:

There is no mention anywhere in the thesis (that I can find) of the distances used to define the domains where different integration methods were applied. I want to know what was the criterion for the "far" targets, where Gauss quadrature with <4 quadrature points was used, and what was the criterion for "near-singular" targets, where ~20 points were used. For "singular" targets: is the only case here where the collocation point is on the source panel itself? Or does it apply to any other case?

None of the results indicate this bit of information, as far as I can tell.

— Reply to this email directly or view it on GitHub https://github.com/barbagroup/inexact-gmres/issues/11.

cdcooper84 commented 9 years ago

Not sure how it is implemented in the code (where is it?), but according to the text you only use the semi-analytical integrals for singular integrals.

In the near-singular region we use high order quadrature (K~20). We got that 0.5 threshold from testing, and has been pretty consistent. I've only modified it for cases where we need extremely good accuracy, with GMRES tolerances in the order of 10^-9.

slayton58 commented 9 years ago

Yeah, that’s my error in the wording:

The criteria determines near-singular or far integrals, and then singular is checked previously. Each regime can use any type of integral (analytical, semi-analytical, quadrature).

My thesis results for Stokes were with:

Singular: Analytical Near-singular: High-k Gauss quadrature Far: Low-k Gauss quadrature

On Jun 5, 2015, at 8:55 AM, cdcooper84 notifications@github.com wrote:

Not sure how it is implemented in the code (where is it?), but according to the text you only use the semi-analytical integrals for singular integrals.

In the near-singular region we use high order quadrature (K~20). We got that 0.5 threshold from testing, and has been pretty consistent. I've only modified it for cases where we need extremely good accuracy, with GMRES tolerances in the order of 10^-9.

— Reply to this email directly or view it on GitHub https://github.com/barbagroup/inexact-gmres/issues/11#issuecomment-109284340.

labarba commented 9 years ago

OK, in summary: when the target is beyond 2 x √2A —> low-K Gauss If closer —> high-K Gauss. If on the source panel —> analytical

@slayton58 Pls confirm this is right.