[Dune] Notification from Dune

[Sreejith Pulloor Kuttanikkad]

Yes, I just found that one y-coord of an integ point in order 7 is
wrong. I couldnt find anything wrong with the data for order 6 though. I
shall try to fix it soon. 
thanks for pointing the bug.

cheers,
Sreejith

On Wed, Sep 06, 2006 at 02:16:04PM +0200, Flyspray wrote:
> THIS IS AN AUTOMATED MESSAGE, DO NOT REPLY.
> 
> A new Flyspray task has been opened.  Details are below.
> 
> User who did this: -  ()
> 
> Attached to Project - Dune
> Summary - Error in simplex quadrature rules of order 6 and 7
> Task Type - Bug Report
> Category - Quadrature
> Status - Unconfirmed
> Assigned To - 
> Operating System - All
> Severity - Medium
> Priority - Normal
> Reported Version - SVN
> Due in Version - 
> Due Date - Undecided
> Details - This is NOT a duplicate of FS#162!
> The triangle quadrature rules of order 6 and 7 produce wrong results.
> This is easily
> checked by integrating y^p:
> 
> #include <iostream>
> 
> #include "dune/config.h"
> #include "dune/grid/common/quadraturerules.hh"
> 
> int main() 
> {
>   using namespace Dune;
>   
>   for (int p=0; p<12; ++p) {
>     QuadratureRule<double,2> const& qr =
> QuadratureRules<double,2>::rule(GeometryType(GeometryType::simplex,2),p);
>     double integ = 0;
>     for (size_t g=0; g<qr.size(); ++g) {
>       FieldVector<double,2> const& x = qr[g].position();
>       double weight = qr[g].weight();
> 
>       // integrating x[0]^p instead yields correct result!
>       // Probably the y-coordinate of an integration point is wrong.
>       integ += weight*std::pow(x[1],p);
>     }
>     double exact = 1.0/((p+2)*(p+1));
>     std::cout.precision(16);
>     std::cout << "p=" << p << " integ=" << integ << " (should be " <<
> exact << ") error = " << integ-exact << "n";
>   }
>   return 0;
> }
> 
> This program produces the following output:
> 
> p=0 integ=0.5 (should be 0.5) error = 0
> p=1 integ=0.16666666665 (should be 0.1666666666666667) error =
> -1.666666804567285e-11
> p=2 integ=0.08333333333333331 (should be 0.08333333333333333) error =
> -1.387778780781446e-17
> p=3 integ=0.05 (should be 0.05) error = 0
> p=4 integ=0.03333333333333333 (should be 0.03333333333333333) error =
> 0
> p=5 integ=0.02380952380952381 (should be 0.02380952380952381) error =
> 3.469446951953614e-18
> p=6 integ=0.01788018253696759 (should be 0.01785714285714286) error =
> 2.303967982473024e-05
> p=7 integ=0.01389590970262738 (should be 0.01388888888888889) error =
> 7.020813738494933e-06
> p=8 integ=0.01111111111111111 (should be 0.01111111111111111) error =
> 1.734723475976807e-18
> p=9 integ=0.009090909090909089 (should be 0.00909090909090909) error =
> -1.734723475976807e-18
> p=10 integ=0.00757575757575758 (should be 0.007575757575757576) error
> = 4.336808689942018e-18
> p=11 integ=0.006410256410256407 (should be 0.00641025641025641) error
> = -2.602085213965211e-18
> 
> In particular, order 6 and 7 are quite wrong, but also order 1 seems
> to be less accurate than
> one should like.
> 
> Martin Weiser
> 
> 
> More information can be found at the following URL:
> http://hal.iwr.uni-heidelberg.de/flyspray/?do=details&id=174
> 
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-- 
Sreejith P. Kuttanikkad                       
IWR, University of Heidelberg       
Room:009, Im Neuenheimer Feld-348                         
69120 Heidelberg,Germany.                      
Ph :+49-6221-54-5689/4412(Office)
   :+49-(0)17624228904(Mob)
http://hal.iwr.uni-heidelberg.de/~sreejith/
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