Cache-Oblivious Spacetree Traversals

Bader, Michael; Weinzierl, Tobias

Abstract

In scientific computing and related fields, mathematical functions are often approximated on meshes where each mesh cell contains a local approximation (e.g., using polynomials) of the represented quantity (density functions, physical quantities such as temperature or pressure, etc.). The grid cells may adaptively refine within areas of high interest or where the applied numerical algorithms demand improved resolution. The resolution even may dynamically change throughout the computation. In this context, we consider tree-structured adaptive meshes, i.e., meshes that result from a recursive subdivision of grid cells. They can be represented via trees – quadtrees or octrees being the most prominent examples. In typical problem settings, quantities are stored on entities (vertices, edges, faces, cells) of the grid. The computation of these variables is usually characterized by local interaction rules and involves variables of adjacent grid cells only.

Citation

Bader, M., & Weinzierl, T. (2015). Cache-Oblivious Spacetree Traversals. In M. Kao (Ed.), Encyclopedia of algorithms (1-6). Springer Verlag. https://doi.org/10.1007/978-3-642-27848-8_583-1

• Online Publication Date: Jun 22, 2015
• Publication Date: Jun 22, 2015
• Deposit Date: Aug 19, 2015
• Publisher: Springer Verlag
• Pages: 1-6
• Book Title: Encyclopedia of algorithms.
• DOI: https://doi.org/10.1007/978-3-642-27848-8_583-1
• Keywords: Space-filling curves, Tree-structured grids, Octree, Quadtree, Spacetree, Grid traversals, Cache-oblivious algorithms.
• Public URL: https://durham-repository.worktribe.com/output/1669648