Hi,

it seems like there is an inconsistency between the two methods of a BilinearForm in a skeleton boundary integral:

[ul]

[li]Apply(): all occurences of proxy.Other() are set to the same values as the proxy itself[/li]

[li]Assemble(): all occurences of proxy.Other() are set to zero[/li]

[/ul]

Here is an example:

```
from ngsolve import *
from netgen.geom2d import unit_square
mesh = Mesh(unit_square.GenerateMesh())
Draw(mesh)
fes = L2(mesh, flags={'dgjumps': True})
v = fes.TrialFunction()
w = fes.TestFunction()
a = BilinearForm(fes)
a += SymbolicBFI(v.Other()*w, BND, skeleton=True)
g = GridFunction(fes)
g.Set(CoefficientFunction(1))
app = GridFunction(fes)
ass = GridFunction(fes)
a.Apply(g.vec, app.vec)
print(app.vec)
a.Assemble()
ass.vec.data = a.mat*g.vec
print(ass.vec)
print(Integrate((app-ass)*(app-ass), mesh))
```

Output:

```
2
2
0
0
3.999999999999984
```

I believe the relevant lines in symbolicintegrator.cpp are here for Apply() and here for Assemble().

Is this a bug?

Alex

Hi Alex,

you can get indeed different results from Apply and Assemble + matrix times vector:

The Appyl computes the nonlinear operator (which includes also an affine linear operator from inhomogeneous Dirichlet data). Here the class-name BilinearForm might be misleading, since it can be non-linear in the trial-argument.

The Assemble can only compute a matrix, and assumes you are really providing a bilinear-form (linear in both arguments). AssembleLinearized computes the linearization at a given point.

What is the u.Other() doing for skeleton-BND integrals ?

It uses boundary values only if you give a bnd=… parameter, otherwise it’s using the value from inside (and thus you got the non-zero result).

This modification gave me identical results (i.e. 0):

`a += SymbolicBFI(v.Other(bnd=0)*w, BND, skeleton=True)`

Joachim

Hi Joachim,

Isn’t the expression v.Other()*w bilinear anyway, regardless of whether the inner value or 0 is used for v.Other()? So I would have expected Assemble() and Apply() to do the same thing.

[quote]What is the u.Other() doing for skeleton-BND integrals ?

It uses boundary values only if you give a bnd=… parameter, otherwise it’s using the value from inside (and thus you got the non-zero result).[/quote]

Apply() uses the inside value, Assemble() always uses zero.

Using bnd=0 gives identical results, but does that mean Other() without argument is allowed to be inconsistent? Another example would be

```
a += SymbolicBFI(v*v.Other(2)*w, BND, skeleton=True)
```

which is also bilinear (on the boundary), uses the bnd argument, but gives different results.

That said, nobody would actually write v.Other(2) instead of 2, and I don’t have a real-world example right now, so maybe this issue is not all that important

Alex

you are right, it’s a bilinear-expression, but both cases are artificial: why should one use Other() to get the internal value, or to get the 0-function ? and you are right, Assemble and Apply should be consistent in this artificial case, I think setting it to 0 is the better choice (i.e. change the behaviour of Apply).

Currently, there is indeed a real application for the last example you gave. There is an intended difference between a1 and a2:

```
vals = CoefficientFunction( [3,7,15] )
a1 += SymbolicBFI(v*v.Other(bnd=vals)*w, BND, skeleton=True)
a2 += SymbolicBFI(v*vals*w, BND, skeleton=True)
```

a1 uses the MappedIntegrationRule (mir) on the boundary, while a2 uses the mir of the volume. The mir contains also the region index, either material index or boundary condition index. So different elements of the vals - CF are chosen.

As soon as we have the .Other() also for ordinary CoefficientFunctions, we don’t need this tricky construct via the proxy anymore.