help-octave
[Top][All Lists]

## Re: BIM versus Finite Element

 From: c. Subject: Re: BIM versus Finite Element Date: Wed, 7 Sep 2011 18:47:57 +0200

```On 7 Sep 2011, at 17:34, J Stasko wrote:

> I have been looking at Anastasis C. Polycarpou's book, Introduction to the
> Finite Element Method in Electromagnetics, and I understand it well so far,
> I'm just starting the second half.
>
> I have also been looking at Johann Cervenka's dissertation which can be found
> here, http://www.iue.tuwien.ac.at/phd/cervenka/diss.html .
>
> He mentions that there are three different techniques, finite element, finite
> difference, and box integration.  He does mention that finite elements use
> Ansatzfunktionen,
the use of Shape/Test Functions is partially apparent in the mesh structure:

>> msh = msh2m_structured_mesh (linspace(0,1,3), linspace(0,1,3), 1, 1:4);
>> msh = bim2c_mesh_properties (msh)
msh =

scalar structure containing the fields:

p: 2x9 matrix
e: 7x8 matrix
t: 4x8 matrix
wjacdet: 3x8 matrix
area: 8x1 matrix
shg: 2x3x8 matrix

The field shg represents the gradient of the shape functions computed at each
element vertices
(as the trapezoidal rule is used for quadrature triangle vertices coincide with

> which is covered in Polycarpou's work, and I don't see much mention of it in
> the BIM software.  I'm beginning to suspect that BIM is a special case of
> FEM, where the Ansatzfunktionen chosen are the set with a polynomial of
> degree one (as Polycarpou describes in section 1.5).

Yes, BIM uses piece-wise linear continuous Finite Elements with Exponential
Fitting
stabilization for convection dominated problems and Mass-Matrix Lumping.
The resulting algebraic system is equivalent to that of the Box Integration
Method (hence the name).

> Does anyone has a reference which explicitly compares the three?

The equivalence of many methods with Exponential Fitting is shown here:
http://10.1007/s007910050012

a comparison of even more discretization methods is in my thesis:
http://mox.polimi.it/it/progetti/pubblicazioni/viewtesi.php?id=159&en=en

c.

```