Technical Report 2014-020

Parallel Data Structures and Algorithms for High-Dimensional Structured Adaptive Mesh Refinement

Magnus Grandin and Sverker Holmgren

October 2014

Numerical solution of high-dimensional partial differential equations often results in challenging computations. Using a uniform discretization of the spatial domain quickly becomes untractable due to the exponential increase in problem size with dimensionality. However, by employing a spatially adaptive discretization scheme the number of grid points can often be reduced significantly. In this note we describe a parallel version of an earlier presented adaptive scheme which generates the mesh by recursive bisection, allowing mesh blocks to be arbitrarily anisotropic to allow for fine structures in some directions without over-refining in other directions. We extend the serial framework by presenting parallel algorithms for organizing the mesh blocks in a distributed kd-tree and the necessary operations for implementing structured adaptive mesh refinement on a parallel computer system.

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