<p>Topology optimization (TO) is a computational method utilized across diverse domains to address structural optimization challenges by optimizing the distribution of materials within a specified design domain. Its primary aim is to determine the optimal allocation of materials while satisfying predefined constraints to achieve objectives such as minimizing weight, volume, stresses, or dissipated energy or maximizing heat transfer. This iterative process involves solving partial differential equations via finite element analysis and updating design variables until convergence is achieved. However, TO often necessitates significant computational resources and time, particularly in scenarios involving complex structures or multiple objectives and constraints. Consequently, efforts have been directed towards improving algorithmic methods and computational efficiency to mitigate these challenges. This study presents novel techniques for generating high-resolution structures at reduced computational costs, which can be integrated into mesh refinement-based topology optimization strategies. These techniques involve efficiently determining the sequence of mesh levels for mapping density fields and employing various schemes for distributing the density field across meshes of varying sizes. Specifically, this research introduces a hierarchical mesh mapping approach and two density field distribution schemes aimed at accelerating TO processes. Through extensive experimentation, these techniques demonstrate substantial reductions in computational expenses while maintaining solution accuracy across a range of optimization scenarios.</p>