HASH TABLE-BASED ADAPTIVE CARTESIAN GRIDS FOR THE POISSON EQUATION

This work presents a second-order finite difference discretization for the Poisson equation on Adaptive Cartesian Grids using a matrix-based formulation. Adaptive Mesh Refinement is employed to efficiently resolve localized features while preserving accuracy. Efficient hash table–based data structures with linked lists are developed for cell management and neighbor identification. Communication and interpolation across refinement levels are performed using the Moving Least Squares method. The proposed approach is validated through the generation of static and dynamic adaptive meshes, and the resulting sparse matrix pattern is analyzed.