Allocation-Free GPU Adaptive Mesh Refinement for P4estMesh in Trixi.jl.

My main goal this summer is to make Adaptive Mesh Refinement (AMR) fast and efficient for P4estMesh on GPUs within Trixi.jl. Right now, whenever the mesh adapts dynamically, it triggers repeated memory allocations on the device. This creates a severe host-device synchronization bottleneck that kills performance, despite the excellent hardware support we have via KernelAbstractions.jl. To solve this, I will build an allocation-free memory manager. By implementing a multi-pool arena specifically designed to match Trixi's Struct-of-Arrays (SoA) layout, I aim to eliminate these driver-level stalls. My final deliverables include a fully functional, type-stable GPU AMR pipeline and comprehensive performance benchmarks across both NVIDIA and AMD hardware