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In tree-based adaptive mesh refinement (AMR) we store refinement trees in the cells of an unstructured coarse mesh. This lets us combine the speed and simpler management of structured refinement trees with the more flexible mesh generation of the unstructured coarse mesh. But this creates a conflict between performance and geometrical accuracy. If we favor speed we reduce the cells in our coarse mesh and hence reduce the accuracy of our geometrical representation. If we want more accurate results we generate a finer coarse mesh and lose performance by managing more cells in our unstructured coarse mesh. To mitigate this conflict we present the prototype of an geometry description which we implement in an already existing library. With this description we build geometry adapted hexahedral refinement trees, which also support high-order curved boundary cells. We also present examples on how to use this description. Moreover, we test the speedup of this new algorithm compared with coarse meshes with different geometrical errors.
Modern GPUs come with dedicated hardware to perform ray/triangle intersections and bounding volume hierarchy (BVH) traversal. While the primary use case for this hardware is photorealistic 3D computer graphics, with careful algorithm design scientists can also use this special-purpose hardware to accelerate general-purpose computations such as point containment queries. This article explains the principles behind these techniques and their application to vector field visualization of large simulation data using particle tracing.