Numerical integration of squares,cubes etc.

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2 total messages Started by Dr. D. Kidger Thu, 09 Apr 1992 11:53

#270

Author: Dr. D. Kidger
Date: Thu, 09 Apr 1992 11:53

9 lines
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Does anyone have any references to integration formulae for 2d/3d 'squares' 
other than the 'standard' product Gauss rules.
 I have 6,14 and 15 point rules for cubes (range -1--> +1) and a 
'better than 3x3x3 Gauss' 27 point rule for cubes.

In particular what are the optimal sampling points (and weights) for 9
integration points in 2d ?

--------- Dr. Dan Kidger ------ Dept. of Civ Eng. Manchester, UK ---------

Re: Numerical integration of squares,cubes etc.

#285

Author: Ronald Cools
Date: Tue, 14 Apr 1992 08:56

31 lines
2084 bytes

In article <4777@mccuts.uts.mcc.ac.uk>, mbgapdk@uts.mcc.ac.uk (Dr. D. Kidger) writes:
|> Does anyone have any references to integration formulae for 2d/3d 'squares' 
|> other than the 'standard' product Gauss rules.
|>  I have 6,14 and 15 point rules for cubes (range -1--> +1) and a 
|> 'better than 3x3x3 Gauss' 27 point rule for cubes.
|> 
|> In particular what are the optimal sampling points (and weights) for 9
|> integration points in 2d ?
|> 
|> --------- Dr. Dan Kidger ------ Dept. of Civ Eng. Manchester, UK ---------

Most integration formulae that were known in 1971 are listed in the book
   A.H. Stroud: Approximate calculation of multiple integrals,
   Prentice Hall, Englewood Cliffs, N.J., 1971

Since then a lot of new integration formulae were constructed. The report
   R. Cools and P. Rabinowitz:
   Monomial cubature rules since 'Stroud': a compilation,
   Report TW161, Dept. of Computer Science, K.U. Leuven, 1991.
contains now 99 references.

          R o n a l d

-----------------------------------------------------------------------------
| Name   : Ronald  Cools                                                    |
| Email  : ronald@cs.kuleuven.ac.be        Katholieke Universiteit Leuven   |
|          na.cools@na-net.stanford.edu    Department of Computer Science   |
|                                          Celestijnenlaan 200 A            |
|        :                                 B-3001 Leuven (Heverlee)         |
| Phone  : +(32) 16 20 10 15 x3562         BELGIUM                          |
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