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Re: [Getfem-users] Quadrature question.

From: Renard Yves
Subject: Re: [Getfem-users] Quadrature question.
Date: Wed, 24 Mar 2010 20:29:29 +0100
User-agent: Dynamic Internet Messaging Program (DIMP) H3 (1.1.2)

Ronan Perrussel <address@hidden> a écrit :

Dear getfem users,

I am using getfem for solving an axisymmetric problem and I have to integrate a term of the following form :
\int_\Omega 1/r u v dr dz
where u and v are respectively solution and test function, r is the radial distance and z is the height. Of course u and v are enforced to be zero on the axis. Consequently the integrand should be regular even for the elements touching the axis. I wonder how to perform an accurate quadrature of this term particularly for the elements touching the axis because I do not know how to describe the function 1/r properly by a mesh_fem object (only in the area close to the axis). I could do something by hand for the elements touching the axis but it would be helpful if someone had a better proposition.

Thanks in advance for your proposition(s).
Best regards,


Dear Ronan,

If the integral is not singular, you can use a standard integration method (there is also some adpated integration methods for some singular terms in the Xfem implementation). You can represent the 1/r term with a mesh_fem_global_function object.

I hope this can help you.


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