GPU Acceleration of A High-precision Stochastic Solver for Steady-state Thermal Analysis with Robin Boundary Conditions

Thermal analysis is crucial for modern chip design. The Path Integral Random Walk (PIRW) solver is a high-precision and highly parallel stochastic method-based solver, which is accurate for steady-state thermal analysis with mixed boundary conditions. However, it requires a large number of paths to ensure a result with small variance, as well as massive jump steps to ensure the convergence of the accumulated temperature. This results in limited performance when executed on CPUs. To address these limitations, we have developed a GPU-accelerated implementation of PIRW that capitalizes on the massive parallelism and advanced scheduling capabilities of modern GPUs. Our implementation enables large-scale parallel computation of random walk paths, significantly enhancing computational efficiency. Furthermore, by leveraging the algorithm’s inherent characteristics, we have developed a fitting algorithm that substantially reduces the number of path steps required for convergence. The experiment shows that, compared to multithreaded version on CPU with 80 threads, the PIRW on NVIDIA A800 GPU with step-reducing fitting technology achieves a speed up of 64.1x.