Mass matrix assembly on tensor cores for implicit particle-in-cell methods
Year: 2026
Type: article
Abstract: Matrix-multiply-accumulate (MMA) units, or tensor cores , are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a reduction-dominated kernel in which weighted outer products of interpolation weights are accumulated over particle support. We show that this operation can be reformulated exactly, cell by cell, as a sequence of matrix products matched to hardware MMA tiles. The formulation is general with respect to interpolation order and hardware platform, and applies to both scalar mass matrices and the tensorial block mass matrix arising in the Energy-Conserving Semi-Implicit Method (ECSIM) for Particle-in-Cell simulations. We introduce particle batching and a support-group decomposition for higher-order shape functions whose stencil extends beyond a single cell, specialize the method to first- and second-order B-spline interpolation, and implement it on NVIDIA tensor cores. The resulting kernels achieve up to 3 × over optimized conventional implementations and reduce end-to-end ECSIM runtime by ∼ 15%.
Source: Journal of Computational Physics
Authors: Luca Pennati, Stefano Markidis
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Hardware and Architecture
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,980
OpenAlex ID: W7155222014