Efficient Strict-Binning Particle-in-Cell Algorithm for Multi-core SIMD Processors

Abstract

Particle-in-Cell (PIC) codes are widely used for plasma simulations. On recent multi-core hardware, performance of these codes is often limited by memory bandwidth. We describe a multi-core PIC algorithm that achieves close-to-minimal number of memory transfers with the main memory, while at the same time exploiting SIMD instructions for numerical computations and exhibiting a high degree of OpenMPlevel parallelism. Our algorithm keeps particles sorted by cell at every time step, and represents particles from a same cell using a linked list of fixed-capacity arrays, called chunks. Chunks support either sequential or atomic insertions, the latter being used to handle fast-moving particles. To validate our code, called Pic-Vert, we consider a 3d electrostatic Landau-damping simulation as well as a 2d3v transverse instability of magnetized electron holes. Performance results on a 24-core Intel Skylake hardware confirm the effectiveness of our algorithm, in particular its high throughput and its ability to cope with fast moving particles.1 Let t denote the single-core execution time. Assume 0.5% of sequential execution, and 99.5% using 64 cores. The parallel execution time is: 0.005t + 0.995t/64 = 1.32t/64.

Efficient parallelization for 3d-3v sparse grid Particle-In-Cell: Shared memory architectures

“…Thus the multiplication of the cores without any significant increase of the memory bandwidth brings a poor speed-up. This issue is analysed in [43] and received a lot of attention for years [4,5,7]. Different workarounds are proposed to favor the locality of the data, increasing the cache reuse, therefore mitigating the number of requests to the main memory.…”

“…A non exhaustive overview of optimizations and parallelizations of PIC methods on shared memory architectures. In PIC simulations, the implementations are usually memory-bounded rather than compute-bounded [4,43].…”

“…This is thus a trade-off between the cost of re-sorting the particle population and increasing the cache-miss rate during iterations. Different elaborated data structures are proposed to alleviate the cost of the periodic particle sorting (see [4,44] and [5,6]). Another approach to mitigate the randomness of the memory accesses is to consider domain decomposition [19,42,45] with subdomains so small that they can fit in the cache system.…”

Adaptive SIMD optimizations in particle-in-cell codes with fine-grain particle sorting

“…This approach improves SIMD efficiency on many-core architectures such as the Intel Xeon Phi provided that the particles arrays have enough elements. A similar approach has been extended in [16] where the authors use additional strategies such as the division of a cell's particle set into chunks to improve cache coherence and reduce memory transfers. They report acceleration when using a few hundreds particles per cell.…”