"We believe that run-time performance can be improved significantly" is an understatement. Jacobi and Gauss Seidel have very poor convergence property on Poisson-like problem [0]. A state-of-the-art Poisson solver is likely to use a Krylov-space method [1], preconditioned with a multi-grid [2] or some sort of coarse preconditioner. This of course does not make such proof of principle less valuable.

[0] https://doi.ieeecomputersociety.org/cms/Computer.org/dl/mags... (On this graph, MG means MultiGrid)

[1] https://en.wikipedia.org/wiki/Krylov_subspace#Existing_metho...

[2] https://en.wikipedia.org/wiki/Multigrid_method