fiat team mailing list archive

["Robert Kirby" <robert.c.kirby@xxxxxxxxx>]

1.) Integration rules tend to do poorly on discontinuous functions.  I'd
recommend breaking up the domain onto regions where the integrand is
continuous.2.) The collapsed coordinates are thoroughly described in
Karniadakis & Sheriwn's "hp and spectral methods for CFD" -- it's a book (I
believe from Oxford press).  The get quadrature rules (and polynomials) on
simplices via singular mappings from rectangles.
3.) Create whatever kinds of rules you like for FIAT -- the QuadratureRule
class is pretty simple for the reference element -- just provide the points
and quadrature weights.

On Jan 8, 2008 4:22 PM, Shi Jin <jinzishuai@xxxxxxxxx> wrote:

> Hi there,
>
> I have been using FIAT as a component from PETSc and I love it. Thank you.
> Recently I have the need to integrate a discontinuous function in a
> tetrahedral finite element (integrate only inside a sphere instead of the
> whole domain) and the Gaussian quadrature rules does not work very well,
> even if I put lots of quadrature points. My naive idea is that if I use the
> trapezoidal quadrature rules, the accuracy of integration is guaranteed when
> the number of quadrature points is large enough. Therefore, I am wondering
> if it is possible to create trapezoidal quadrature rules using FIAT.
>
> Note that I am not very familiar with the mathematics of quadratures. I
> originally thought the one created by PETSc using FIAT is default to
> Gaussian quadratures. But then I read the FIAT manual and it says  "FIAT
> implements arbitrary-order collapsed quadrature, as discussed in Karniadakis
> and Sherwin [], for the simplex of dimension one, two, or three." I am not
> sure what "collapsed quadrature" is. Does it include Gaussian and
> Trapezoidal quadratures? How do I choose from them? I would greatly
> appreciate it if some guidance can be provided. Also, could more information
> be provided about the Karniadakis and Sherwin paper, such as title, journal
> and year? Maybe better quadrature rules exist for the integration of
> discontinuous functions and I would love to hear some advice.
>
> Thank you very much.
>
> Shi Jin
>
>
>
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