Accelerating Numerical Relativity with Code Generation: CUDA-enabled Hyperbolic Relaxation

TL;DR

This paper introduces NRPyEllipticGPU, a CUDA-optimized elliptic solver for numerical relativity, achieving significant speedups over CPU implementations and enabling more efficient gravitational wave catalog generation.

Contribution

It presents the first GPU-enabled elliptic solver in the numerical relativity community, extending NRPy to leverage CUDA for improved performance.

Findings

Up to 16x speedup in single precision on high-end GPUs

Double-precision performance increased by 2-4 times

Supports various coordinate systems for elliptic problems

Abstract

Next-generation gravitational wave detectors such as Cosmic Explorer, the Einstein Telescope, and LISA, demand highly accurate and extensive gravitational wave (GW) catalogs to faithfully extract physical parameters from observed signals. However, numerical relativity (NR) faces significant challenges in generating these catalogs at the required scale and accuracy on modern computers, as NR codes do not fully exploit modern GPU capabilities. In response, we extend NRPy, a Python-based NR code-generation framework, to develop NRPyEllipticGPU -- a CUDA-optimized elliptic solver tailored for the binary black hole (BBH) initial data problem. NRPyEllipticGPU is the first GPU-enabled elliptic solver in the NR community, supporting a variety of coordinate systems and demonstrating substantial performance improvements on both consumer-grade and HPC-grade GPUs. We show that, when compared to a high-end CPU, NRPyEllipticGPU achieves on a high-end GPU up to a sixteenfold speedup in single precision while increasing double-precision performance by a factor of 2--4. This performance boost leverages the GPU's superior parallelism and memory bandwidth to achieve a compute-bound application and enhancing the overall simulation efficiency. As NRPyEllipticGPU shares the core infrastructure common to NR codes, this work serves as a practical guide for developing full, CUDA-optimized NR codes.