A thread-parallel algorithm for anisotropic mesh adaptation

Anisotropic mesh adaptation is a powerful way to directly minimise the computational cost of mesh based simulation. It is particularly important for multi-scale problems where the required number of floating-point operations can be reduced by orders of magnitude relative to more traditional static mesh approaches. Increasingly, finite element and finite volume codes are being optimised for modern multi-core architectures. Typically, decomposition methods implemented through the Message Passing Interface (MPI) are applied for inter-node parallelisation, while a threaded programming model, such as OpenMP, is used for intra-node parallelisation. Inter-node parallelism for mesh adaptivity has been successfully implemented by a number of groups. However, thread-level parallelism is significantly more challenging because the underlying data structures are extensively modified during mesh adaptation and a greater degree of parallelism must be realised. In this paper we describe a new thread-parallel algorithm for anisotropic mesh adaptation algorithms. For each of the mesh optimisation phases (refinement, coarsening, swapping and smoothing) we describe how independent sets of tasks are defined. We show how a deferred updates strategy can be used to update the mesh data structures in parallel and without data contention. We show that despite the complex nature of mesh adaptation and inherent load imbalances in the mesh adaptivity, a parallel efficiency of 60% is achieved on an 8 core Intel Xeon Sandybridge, and a 40% parallel efficiency is achieved using 16 cores in a 2 socket Intel Xeon Sandybridge ccNUMA system.