L2 space with number of components different than mesh dim

NGSolve
1

Hello,

I have a VectorL2 and MatrixValued FE space defined on a 3D mesh. I need the trial and test functions to have only 2 components and not 3, which is the default for a 3D mesh. A straightforward way of doing this would be to have two scalar L2 spaces defined on a 3D mesh, but this would make the rest of the code quite tedious (even more so for the matrix space). Is there an easier way of doing this?

Thank you!

Best,
Giselle

2

HI Giselle,

with

fes = L2(mesh, order=2)**3
gfu = GridFunction(fes)

gfu.Set ( (x, y, x*y))

print (gfu.dims)
print (Grad(gfu).dims)

you can create vectorial spaces of arbitrary dimension. You can also iterate:

fes = (L2(mesh, order=2)**4) ** 5
gfu = GridFunction(fes)
print (gfu.dims)
print (Grad(gfu).dims)

Better to double-check how the ordering of higher-order tensors come out, you may need some reshape.

Joachim

3

Thank you so much, Joachim!