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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


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 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 <address@hidden> wrote:

Dear Torquil,

There is an example in which allows to define a mesh_fem  with some arbitry global functions (i.e. a spectral method). Moreover, with 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.


----- Original Message -----
From: "Torquil Macdonald Sørensen" <address@hidden>
To: address@hidden
Sent: Tuesday, April 22, 2014 9:03:59 PM
Subject: [Getfem-users] Non-polynomial basis functions


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, I know how to specify polynomial basis functions.
But I have not found any examples of non-polynomial mesh_fem's other
than piecewise polynomial composite mesh_fem's.

Best regards
Torquil Sørensen

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