Spectral/hp implementation

[JosephThomasParker]

We should implement a version of this code that is Spectral/hp in space, plus particles for velocity. I think the path-of-least-resistance way of doing this is to use Nektar++ and its solvers. From talking to @ethrelfall, my understanding is that we can keep the particles as they are, and just need to implement a new version of mesh to handle the Spectral/hp.

Here's a rough list of tasks that need to be done:

• [ ] Create a mesh interface class IMesh that has all the public methods of the current Mesh but as pure virtuals
• [ ] Inherit the current version of Mesh from IMesh, rename to MeshUniform and then fixup code to pass around pointers / refs to IMesh
• [ ] Implement a serial MeshNektar with its own: deposit function to go from particles to charge density; evaluate function to from particle to electric field; and its own solve_for_electric_field function that will call Nektar++ solvers.
• [x] Set up cmake build that can build and link nektar
• [ ] Set up file input for nektar input files

I showed Ed the serial version of the code (current main). I think it's best to implement a serial version and get it working, and then worry about a SYCL implementation later. Thoughts? @ethrelfall @jwscook

Next steps

• [ ] Work out how to configure the Nektar++ bits from the C++ rather than xml.
• [ ] Template by dimension i.e. MeshUniform<D> so that we can specialise to 1 (what we have now), 2, and 3 dims.
• [ ] SYCLify MeshNektar.

[oparry-ukaea]

This design sounds like its been superseded, at least in part, by PR #92?

[jwscook]

NESO started life as an fft based electrostatic pic code that was augmented with SYCL particles. This issue relates to the plan to remove the fft solve in favour of a nektar Poisson solve. This is not a priority for the 2d3v milestone but is required for the PIC milestone. ... Could do with new milestone labels or something..

[jwscook]

@oparry-ukaea i've added a 2D3V milestone label too. please feel free to sprinkle that around & thanks for curating the backlog - I'm pretty swamped today and tomorrow. Monday is less meeting filled.

[jwscook]

Superseded by #99