Flexible and scalable particle-in-cell methods for massively parallel computations
For computational scientists using particle-in-cell methods, this work enables efficient use of modern adaptive mesh refinement and parallel computing, but it is an incremental improvement on existing methods.
The paper addresses the need for particle-in-cell methods that work with dynamically changing, parallel meshes at scale. It presents algorithms with optimal complexity and demonstrates scalability in geodynamic simulations using ASPECT.
Particle-in-cell methods couple mesh-based methods for the solution of continuum mechanics problems, with the ability to advect and evolve particles. They have a long history and many applications in scientific computing. However, they have most often only been implemented for either sequential codes, or parallel codes with static meshes that are statically partitioned. In contrast, many mesh-based codes today use adaptively changing, dynamically partitioned meshes, and can scale to thousands or tens of thousands of processors. Consequently, there is a need to revisit the data structures and algorithms necessary to use particle methods with modern, mesh-based methods. Here we review commonly encountered requirements of particle-in-cell methods, and describe efficient ways to implement them in the context of large-scale parallel finite-element codes that use dynamically changing meshes. We also provide practical experience for how to address bottlenecks that impede the efficient implementation of these algorithms and demonstrate with numerical tests both that our algorithms can be implemented with optimal complexity and that they are suitable for very large-scale, practical applications. We provide a reference implementation in ASPECT, an open source code for geodynamic mantle-convection simulations built on the deal.II library.