2025/12/12 by Lei, Jin
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Nuclear Theory (nucl-th)
paper · doi:10.48550/arxiv.2512.11590
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× speedup over optimized CPU direct solvers, and 18× 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× 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.