CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Numerical integration

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   June 23, 2001, 10:28
Default Numerical integration
Damir Galeev
Posts: n/a
Hallo, dear colleagues! I use the discontinues galerkin (DG) approach to obtain approximation for PDE in 3D case. So I need to integrate over the cells (tetrahedrons) and faces (triangles) with the given order of accuracy. I use the Gaussian points method for numerical integration, but it seems to me that it's not the optimal way (it's optimal only in 1D case). For example, to obtain numerical integral of the 1st degree of accuracy (that is integral is absolutely accurate for polynomials of degree k = 1) over the triangle it's enough to take only one point in the center of gravity of triangle with the weight equal to unit, while in the Gaussian points method it's necessary to take at least two points for the same accuracy. So I'm interested if there exist methods to get optimal points and weights for numerical integration in multidimensional (2D & 3D) case for different degrees of accuracy (for tetrahedrons & triangles). Tanks in advance.
  Reply With Quote

Old   June 23, 2001, 22:43
Default Re: Numerical integration
Posts: n/a
You may want to read 4.6(Multidimensional Integrals) at
  Reply With Quote

Old   June 24, 2001, 05:59
Default Re: Numerical integration
Damir Galeev
Posts: n/a
Unfortunately, the method described is the same as I use (gauss method or as I call it the Gaussian points method)
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
numerical integration of a set of ordinary partial differential equation wlt_1985 FLUENT 0 November 5, 2010 17:17
Numerical integration of Spalart Allmaras turbulence model RenardP Main CFD Forum 0 June 11, 2009 14:53
Numerical integration of 'T' across a 3D surface ACFD-student Main CFD Forum 5 March 23, 2006 16:51
Any numerical triple integration program is available in Fortran? Radhakrishnan Main CFD Forum 3 March 4, 1999 02:03
New Books and Numerical Software Eleuterio TORO Main CFD Forum 0 December 18, 1998 13:41

All times are GMT -4. The time now is 19:44.