Hi all,

I experiencing some difficulties while learning the finite element

method and its implementation: how to deal with the case where the

topological dimension of the reference element (e.g. 1 for segment, 2

for triangle and 3 for tetrahedron) is different from the embedding

space dimension?

(i) Let us consider a phi function to be integrated over triangles lying

in 2D space. x and y are embedding coordinates. xi and eta are reference

element coordinates.

dphi/dx = dphi/dxi * dxi/dx + dphi/deta * deta/dx

dphi/dy = dphi/dxi * dxi/dy + dphi/deta * deta/dy

J is the jacobian matrix (J^-1 --> dxi/d[x,y] and deta/d[x,y])

dxdy = dej(J) * dxideta

(ii) Let us consider a phi function to be integrated over triangles

lying in 3D space. x, y and z are embedding coordinates. xi and eta are

reference element coordinates.

dphi/dx = dphi/dxi * dxi/dx + dphi/deta * deta/dx

dphi/dy = dphi/dxi * dxi/dy + dphi/deta * deta/dy

dphi/dz = dphi/dxi * dxi/dz + dphi/deta * deta/dz

dxdydz = ?

So main problem is to obtain dxi/d[x,y,z] and deta/d[x,y,z]. From an

implementation point of view the case (i) is just a matter of inverting

a matrix. What about this case ?

I am a little bit lost and I would like some pointers (www, books or

inline explanation).

Thanks all & sincerely.

PM

P.S. : I have a rather weak physics and mathematics background so feel

free to start from basics again.

P.S. : Also posted on sci.math.num-analysis & sci.engr.mech

- posted 17 years ago