Parallel unstructured tetrahedral mesh adaptation: algorithms, implementation and scalability

Abstract

The use of unstructured adaptive tetrahedral meshes in the solution of transient flows poses a challenge for parallel computing due to the irregular and frequently changing nature of the data and its distribution. A parallel mesh adaptation algorithm, PTETRAD, for unstructured tetrahedral meshes (based on the serial code TETRAD) is described and analysed. The portable implementation of the parallel code in C with MPI is described and discussed. The scalability of the code is considered, analysed and illustrated by numerical experiments using a shock wave diffraction problem.

Coarse Mesh Partitioning for Tree-Based AMR

“…Most tree-based AMR codes make use of a space filling curve to order the elements within a tree [21,42,43] as well as points or other primitives [30]. Two main approaches for partitioning a forest of elements have been discussed [47], namely (a) assigning each tree and thus all of its elements to one owner process [8,34] or (b) allowing a tree to contain elements belonging to multiple processes [3,12]. The first approach offers a simpler logic, but may not provide acceptable load balance when the number of elements differs vastly between trees.…”

Flexible Distributed Mesh Data Structure for Parallel Adaptive Analysis

“…Issues associated with supporting parallel adaptive analysis on a given unstructured mesh include dynamic mesh load balancing techniques [8,11,32,34], and data structure and algorithms for parallel mesh adaptation [9,17,20,21,23,24,27]. The focus of this chapter is a parallel mesh infrastructure capable of handling general non-manifold [19,35] models and effectively supporting automated adaptive analysis.…”

Towards a Three-Dimensional Parallel, Adaptive, Multilevel Solver for the Solution of Nonlinear, Time-Dependent, Phase-Change Problems

“…There has been significant amount of research into the combination of adaptive mesh refinement (in three dimensions) and an efficient parallel implementation in recent years, see for example, [2,15,27,36,39,44]. The effect of modifying the computational mesh, via local refinement or coarsening, is to alter the load-balance across the parallel processors and so it is essential to couple such an implementation with a suitable dynamic load-balancing strategy, e.g.…”