Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations

Abstract

Particle-in-cell (PIC) methods couple mesh-based methods for the solution of continuum mechanics problems with the ability to advect and evolve properties on particles. PIC methods have a long history and numerous applications in geodynamic modeling. However, they are historically either implemented in sequential codes or in parallel codes with structured, statically partitioned meshes. Yet today's codes increasingly use adaptive mesh refinement (AMR) of unstructured coarse meshes, dynamic repartitioning, and scale to thousands of processors. Optimally balancing the work per processor for a PIC method in these environments is a difficult problem, and many existing implementations are not sufficient for this task. Thus, there is a need to revisit these algorithms for future applications. Here we describe challenges and solutions to implement PIC methods in the context of large-scale parallel geodynamic modeling codes that use dynamically changing meshes. We also provide guidance for how to address bottlenecks that impede the efficient implementation of these algorithms and demonstrate with numerical tests that our algorithms can be implemented with optimal complexity and that they are suitable for large-scale, practical applications. We provide a reference implementation in the Advanced Solver for Problems in Earth's ConvecTion (ASPECT), an open source code for geodynamic modeling built on the DEAL.II finite element library.