This work presents an adaptive strategy in order to visualize volumetric data generated from numerical simulations of partial differential equations. The mesh is represented by a graph data structure. Moreover, the Autonomous Leaves Graph is extended to the three-dimensional case. This scheme intends to achieve better transversal cost than a tree-like (e.g., bintree, quadtree and octree) space arrangement approach. Furthermore, this strategy intends to reduce the computational cost of constructing the discretization and the visualization of data. The total-ordering of the mesh volumes used in the discretization and the visualization processes is by the 3D Modified Hilbert space-filling Curve. To evaluate the performance, the strategy is applied on a Heat Conduction simulation problem using finite difference discretizations and the experimental results are discussed. Comparisons are made between numerical results obtained when using the Hilbert Curve and its modified version. In addition, experiments are shown when visualization is made from inside and outside the volume. The results expose the efficiency of using this strategy.
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