We can work out the notations details and make sure it agrees with other SfePy docs for consistency.

matrices denoted by [], vectors by {}

Yes.

But I think a matrix is a second order tensor and a vector is a first order tensor so that the first equation should be:

1/2 \int E_{ij} \varepsilon_{i} \varepsilon_{j}

or something like that - at least for the 1D problem.

Am I thinking correctly?

Ryan

On Fri, Aug 1, 2008 at 4:33 AM, Robert Cimrman <cimr...@ntc.zcu.cz> wrote:

Hi Ryan,

Ondrej Certik wrote:

On Thu, Jul 31, 2008 at 10:29 PM, Ryan Krauss <ryan...@gmail.com> wrote:

And we can modify the symbols and terms to be whatever we want. I was mainly trying to follow the conventions of the book by Cook et.al. that I am using.

robert should say what he likes. My background is in theoretical physics, so I am used to using different kind of symbols.

I will print it and go through it during this weekend, ok?

On the first glance it looks ok. It uses one of the engineering notations (matrices denoted by [], vectors by {}, right?).

I would prefer the notation used in doc/sfepy_manual.pdf, both indicial and tensor are ok.

For example, the first term in your (1) would look like:

continous:

1/2 \int E_{ijkl} \varepsilon_{ij} \varepsilon_{kl} or 1/2 \int E_(4) : \ull{\varepsilon} \ull{\varepsilon} here \ull is a shortcut for double underline (denoting a second-order tensor) and (4) denotes a fourth-order tensor (4 underlines are ugly)

discretized: 1/2 \bm{u}^T \bm{K} \bm{u} (u = displacements)

\bm{K} is global stiffness matrix, \bm{K}|_e contribution of element e

(4) would be: \ul{u} \approx \bm{\varphi} \bm{u} \nabla \ul{u} \approx \bm{G} \bm{u}, i.e. G denotes \nabla \varphi (gradients of the FE base funtions)

Anyway, it looks fine as it is, I have proposed the above just in case you have enough time...

Some figure would be nice, though.

cheers, r.

ps: an interesting link I have just found: http://www.sv.vt.edu/classes/ESM4714/methods/EEG.html