Extend QN acceleration to waveform iterations

[NiklasKotarsky]

Main changes of this PR

Adds support for Quasi Newton acceleration for waveform iterations.

Motivation and additional information

Implements the algorithm described https://onlinelibrary.wiley.com/doi/10.1002/nme.6443 for fixed time grids. For moving time grids everything will be interpolated to the first time grid from the first time window inside the QNWR class instead of using the waveforms inside the QN method as done in #1834.

For IMVJ variant the same fix for all time steps as described in issue #1996 will be used.

Author's checklist

• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I added a changelog file with make changelog if there are user-observable changes since the last release.
• I added a test to cover the proposed changes in our test suite.
• For breaking changes: I documented the changes in the appropriate porting guide.
• I sticked to C++17 features.
• I sticked to CMake version 3.16.3.
• I squashed / am about to squash all commits that should be seen as one.

Reviewers' checklist

• Does the changelog entry make sense? Is it formatted correctly?
• Do you understand the code changes?

[BenjaminRodenberg]

@NiklasKotarsky currently this PR does not build on my system and also not in our CI pipeline. Does it build on your system? Did you maybe forget to push some file?

[NiklasKotarsky]

@NiklasKotarsky currently this PR does not build on my system and also not in our CI pipeline. Does it build on your system? Did you maybe forget to push some file?

Yes, it compiles on my system and some of the systems in the CI pipline. This is probably due to different versions of Eigen having different feature support.

[BenjaminRodenberg]

@NiklasKotarsky currently this PR does not build on my system and also not in our CI pipeline. Does it build on your system? Did you maybe forget to push some file?

Yes, it compiles on my system and some of the systems in the CI pipline. This is probably due to different versions of Eigen having different feature support.

If it is an issue with different eigen version: I once had a similar problem with some features not being supported by the Eigen version used by the CI pipeline and added the following code to resolve this:

precice/src/math/Bspline.cpp

Lines 18 to 22 in 0d43d14

	#if EIGEN_VERSION_AT_LEAST(3, 4, 0)
	PRECICE_ASSERT(std::is_sorted(ts.begin(), ts.end()), "Timestamps must be sorted");
	#else
	PRECICE_ASSERT(std::is_sorted(ts.data(), ts.data() + ts.size()), "Timestamps must be sorted");
	#endif

Which Eigen version are you using on your system?

[uekerman]

For moving time grids everything will be interpolated to the first time grid from the first time window inside the QNWR class instead of using the waveforms inside the QN method as done in #1834.

Couldn't we instead use a fixed time grid with equally spaced time steps? We could hard-code this number of samples to waveform-degree + 1? Or simply to 4 for the moment.

It could also be very helpful to know how many time steps to include in W (cf. #1996) during initialization already.