ShahuK283/trixi-gpu-amr-gsoc ? reverse-engineered prompt

Build me a Julia project that reproduces this GPU AMR profiling setup for Trixi.jl.

I want a simple script that warms up the GPU, runs the mortar related kernels, and then profiles just the real work so the results are not polluted by compilation or setup. It should use the same idea as the report, where the adaptive mesh refinement cycle stays on the GPU and the key kernels like prolonging to mortars and computing mortar fluxes can be measured cleanly.

Please make it easy to switch between CPU and GPU paths, and keep the current solver behavior unchanged on the CPU. I also want the script to print enough context to confirm the mesh and element counts match between runs, and to work with current Julia GPU tooling if anything needs checking online.

If useful, add a small example of how to run the profiler from the command line and how to compare two runs.