Compound space on different meshes

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1

Dear all,
to simulate a PDE-ODE-System, I was trying to use a compound FE-Space on two different mesh, one with only one DOF (for the ODE). However, it seems that assembling in such a space does not work properly.

Is this a bug or am I using it in an unintended way?

Minimal example:

from ngsolve.meshes import Make1DMesh
from ngsolve.meshes import Mesh as NgMesh
from netgen.meshing import *

from ngsolve import *

nx = 10
ngsmesh = Make1DMesh(nx)
ngsmesh_ODE = Make1DMesh(1) # For the ODE, thus only one DOF

fes1 = L2(ngsmesh_ODE, order=0)
fes2 = L2(ngsmesh, order=1, dgjumps=True)
fes = FESpace([fes1,fes2])
u,v = fes.TnT()

m = BilinearForm(fes)

m.components[0] += BFI("mass", coef=1) #u[0]*v[0]*dx
m.components[1] += BFI("mass", coef=1) #u[1]*v[1]*dx

m.Assemble()

print(m.mat)
2

The component-spaces of a compound space have to live on the same mesh.

You can use NumberFESpace instead. It is one constant function on the whole domain.

Joachim

3

Compound spaces expect the same mesh to be defined on. But you can use a global space with one dof by using the NumberSpace:

fes1 = NumberSpace(ngsmesh)
fes2 = L2(ngsmesh, order=1, dgjumps=True)
fes = fes1 * fes2
(uO, u), (vO, v) = fes.TnT()

m = BilinearForm(fes)
m += uO * vO * dx
m += u * v * dx
m.Assemble()
print(m.mat)
4

Many thanks!