[Dune] Available quadrature orders?

[Jö Fahlke]

Am Fri,  6. Mar 2015, 12:28:27 +0100 schrieb Aleksejs Fomins:
> Date: Fri, 06 Mar 2015 12:28:27 +0100
> From: Aleksejs Fomins <aleksejs.fomins at lspr.ch>
> To: dune at dune-project.org
> Subject: Re: [Dune] Available quadrature orders?
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> Dear all,
> 
> I think I get it now. I can use 2D and 3D simplex rules up to order 61, they will be optimal up to orders (12, 5), and for all higher orders the quadrature points are transformed from cuboid to simplex via duffy transform, so the integration will work the same way, but there will be more points than there could have been if the optimal quadrature was known.
> 

The available order depends on the type of quadrature rule (gauss-legendre,
gauss-lobatto, etc.).  I think gauss-lobatto is only available up to order
~32.  You can request the maximum available quadrature order for a given
quadrature type and geometry type using QuadratureRules::maxOrder()[1].  This
was introduced recently in FS#1544 when I implemented the thread-safe
quadrature rule cache.

The specialized quadrature rules for simplices are only available for
gauss-legendre (see FS#1542).  They silently don't support high-precision
types (see FS#1543).

If you need a higher order then the ones that are shipped with the current
dune you can adjust the oder in
dune/geometry/quadraturerules/{gausslobatto,jacobian}.mac and regenerate the
headers that contain the 1D-Quadraturerules.  You need maxima to do that,
which is available e.g. in Debian.

Regards,
Jö.

[1] http://www.dune-project.org/doc/doxygen/html/classDune_1_1QuadratureRules.html#a55d090c68f5bff19964b3f79af52f68d

-- 
Jorrit (Jö) Fahlke, Institute for Computational und Applied Mathematics,
University of Münster, Orleans-Ring 10, D-48149 Münster
Tel: +49 251 83 35146 Fax: +49 251 83 32729

Der Horizont vieler Menschen ist ein Kreis mit Radius Null - und das
nennen sie ihren Standpunkt.
-- A. Einstein
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