HPRMAT: A high-performance R-matrix solver with GPU acceleration for coupled-channel problems in nuclear physics

TL;DR

HPRMAT is a GPU-accelerated, high-performance R-matrix solver library that significantly speeds up coupled-channel calculations in nuclear physics, making large-scale computations more accessible on standard desktops.

Contribution

The paper introduces HPRMAT, a novel GPU-accelerated solver with mixed-precision strategies and multiple backends, optimized for large-scale nuclear physics calculations.

Findings

GPU solver achieves up to 18× speedup over legacy codes

Mixed-precision approach maintains accuracy while improving performance

All solvers maintain errors below 10^{-5} in cross-section calculations

Abstract

I present HPRMAT, a high-performance solver library for the linear systems arising in R-matrix coupled-channel scattering calculations in nuclear physics. Designed as a drop-in replacement for the linear algebra routines in existing R-matrix codes, HPRMAT employs direct linear equation solving with optimized libraries instead of traditional matrix inversion, achieving significant performance improvements. The package provides four solver backends: (1) double-precision LU factorization, (2) mixed-precision arithmetic with iterative refinement, (3) a Woodbury formula approach exploiting the kinetic-coupling matrix structure, and (4) GPU acceleration. Benchmark calculations demonstrate that the GPU solver achieves up to 9$\times$ speedup over optimized CPU direct solvers, and 18$\times$ over legacy inversion-based codes, for large matrices ($N=25600$). The mixed-precision strategy is particularly effective on consumer GPUs (e.g., NVIDIA RTX 3090/4090), where single-precision throughput exceeds double-precision by a factor of 64:1; by performing factorization in single precision with iterative refinement, HPRMAT overcomes the poor FP64 performance of consumer hardware while maintaining double-precision accuracy. This makes large-scale CDCC and coupled-channel calculations accessible to researchers using standard desktop workstations, without requiring expensive data-center GPUs. CPU-only solvers provide 5--7$\times$ speedup through optimized libraries and algorithmic improvements. All solvers maintain physics accuracy with relative errors below $10^{-5}$ in cross-section calculations, validated against Descouvemont's reference code (Comput.\ Phys.\ Commun.\ 200, 199--219 (2016)). HPRMAT provides interfaces for Fortran, C, Python, and Julia.