On 7/13/21 10:36 AM, Lucas Myers wrote:
1. For the projection operation that you describe, are you specifically
talking about this implementation
<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2FnamespaceVectorTools.html%23a51a13e948e1296dbfdfc297167e4fd5a&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Ccbbf3fb8d8c64abda0af08d9461c682f%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637617910090413636%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=dqvRQzIeA4Q4JYMXQfwRjnbxzSVwpjvVJ6O79t3Txfg%3D&reserved=0>
of
the projection() function (the [5/7] implementation)? I ask because it
seems like the others require a Function object for which we need the
FEFieldFunction class, rather than just something that eats a quadrature &
cell index and gives back the value at the given quadrature point. If so,
am I reading it correctly that this is only for a scalar-valued finite
element function? How would we do this with vector-valued functions?
If you want to use VectorTools::project(), you will have to wrap your function
into an FEFieldFunction object in the same way as I described for the
interpolation. But it's easy enough to implement a projection yourself. You
just need to build a mass matrix and solve with it.
2. With respect to accuracy (that is, neglecting speed of computation or ease
of implementation) are either of these methods better? My guess would be
that projection is more (the most?) accurate in an L2 sense, while
interpolation is more accurate in some other sense.
We know that the L2 projection and interpolation converge at the same rate
with the mesh size h. In practice, the difference in accuracy is probably
unimportant for almost any application.
3. Is this kind of operation described in any of the tutorial steps, do you
know?
I don't think so.
4. Is this how folks typically do post-processing? Really what I would like
to do is extract eigenvectors corresponding to the largest eigenvalues
from my 3x3 tensor solution data and plot those as a vector field. Would
this be something that is typically done with scripts in a visualization
software (e.g. Paraview, Visit), or is that done in the C++ source? Just
trying to get a sense for best practices...
No, if all you care about is visualization, then it is not necessary to
project f(u) into a finite element space. What you are looking for is the
DataPostprocessor class that can be used to compute derived quantities. These
will then be output as point values that visualization programs then interpret
via bilinear/trilinear interpolation. There are numerous tutorial programs
that use DataPostprocessor. A particularly simple example is step-29.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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