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## Re: [Getfem-users] Non-polynomial basis functions

 From: Torquil Macdonald Sørensen Subject: Re: [Getfem-users] Non-polynomial basis functions Date: Sat, 26 Apr 2014 16:22:40 +0200

Hi!

Thanks, I have created a FUNC class with methods eval() and derivative(), and used getfem_fem<FUNC> to create a new mesh_fem. This worked great. I verified that I could solve a PDE using this mesh_fem together with an approximate integration method.

Now I would like to create an integration method that is exact for products between polynomials and my new non-polynomial functions. I've looked at the examples in the source code, e.g. exact_simplex() in getfem_integration.cc. It uses a class "simplex_poly_integration_" that inherits from "poly_integration", and passes it to the constructor of "integration_method".

Looking at "integration_method" in getfem_integration.h, it seems to me that in order to have "im_type = IM_EXACT", my mesh_fem must be polynomial? That is my impression, since the only constructor of "integration_method" that gives im_type = IM_EXACT is the one that takes an argument of type ppoly_integration.

Does this mean that I cannot create an exact integration method for non-polynomial functions?

Best regards
Torquil Sørensen

On 22 April 2014 21:19, Yves Renard wrote:

Dear Torquil,

There is an example in getfem_mesh_fem_global_function.cc which allows to define a mesh_fem  with some arbitry global functions (i.e. a spectral method). Moreover, with getfem_mesh_fem_product.cc it is possible to obtain the mulitplication of standard polynomial shape functions with these global functions. It is in fact possible to define some elements with non-polynomial shape functions by derivating the class getfem::fem<FUNC> (see getfem_fem.h) where FUNC should be a class provinding a certain number of operations such as derivative and eval.

Yves.

----- Original Message -----
Sent: Tuesday, April 22, 2014 9:03:59 PM
Subject: [Getfem-users] Non-polynomial basis functions

Hi!

On the Getfem web page it says "Extensions are provided to describe
Hermite elements, piecewise polynomial or non-polynomial elements,
vector elements and XFEM.":

How would I go about constructing a mesh_fem that uses e.g. the
exponential function in the definition of a basis function? After
reading mesh_fem.cc, I know how to specify polynomial basis functions.
than piecewise polynomial composite mesh_fem's.

Best regards
Torquil Sørensen

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