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In this work we explore acceleration of computations in AMR for astrophysical simulations. Modern scientific codes widely use Adaptive Mesh Refinement, and they need to leverage GPU supercomputing power. Specifically, this thesis demonstrates a hashtable implementation on GPU to store the grid structure. On a toy problem, we compare the performance of a typical matrix implementation against a hashtable implementation in a worst-case scenario — when all grid cells are uniformly refined. Acceleration of such large-scale astrophysical hydrodynamics simulations is critically important, making optimization techniques such as GPU-based hashtable storage essential. Our result is that there is no disadvantage in the hashtable implementation versus the matrix implementation. This result is crucial for future implementation of a hashtable-based AMR with dynamic refinement and complete hydrodynamics simulation. We also explore the application of the Grace Hopper superchip to AMR code and observe a significant speedup of ~2.3 in gradient calculation, and ~14.7 speedup in hashtable creation. Additionally, we design a linter program to streamline CUDA C++ debugging process, in particular for our AMR implementation. These approaches together aim to speed up scientific code; they combine large-scale scientific computing with cutting-edge tools in computer science.