Add Build with Explicit Multi-Level Geometry for EB

[jmsexton03]

Summary

This PR adds a new EB2::Build variant that accepts a Vector<Geometry> to explicitly specify the geometry at each AMR level. Unlike the existing Build function that generates coarse levels through automatic coarsening, this version constructs EB data directly from the provided geometries at each level. This is useful for applications that need precise control over domain specification at each AMR level or when coarse levels are not simple coarsenings of the finest level.

Additional background

Checklist

The proposed changes:

• fix a bug or incorrect behavior in AMReX
• add new capabilities to AMReX
• changes answers in the test suite to more than roundoff level
• are likely to significantly affect the results of downstream AMReX users
• include documentation in the code and/or rst files, if appropriate

[WeiqunZhang]

Does the order matter?

[jmsexton03]

I don't think it matters in terms of 0 being finest, would it be better to not mention order here? The other Build only has the finest Geometry and then builds coarser, I think, but for this it's just using the order that comes in.

[WeiqunZhang]

The thing is AmrMesh stores Geometry in the opposite order. We should try to accept unordered Geometry objects. Internally, we could make a copy and then sort it.

[jmsexton03]

I see, that sounds like a better approach then assuming a certain order. Would you sort on CellSize or something else? Is there an example of sorting somewhere else (I only saw << >> and = as overloaded operators)

    [[nodiscard]] AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    Real CellSize (int dir) const noexcept { return dx[dir]; }

[WeiqunZhang]

Make the function take Vector<Geometry> geom instead of Vector<Geometry> const& geom. Then

std::sort(geom.begin(), geom.end(), [] (Geometry const& a, Geometry const& b) { return a.Domain().numPts() > b.Domain().numPts(); });

[jmsexton03]

Thanks for the code and for finding that lack of generality. I've pushed what I think fixes it.