Fast stencil-code computation on a wafer-scale processor

The performance of CPU-based and GPUbased systems is often low for PDE codes, where large, sparse, and often structured systems of linear equations must be solved. Iterative solvers are limited by data movement, both between caches and memory and between nodes. Here we describe the solution of such systems of equations on the Cerebras Systems CS-1, a wafer-scale processor that has the memory bandwidth and communication latency to perform well. We achieve 0.86 PFLOPS on a single wafer-scale system for the solution by BiCGStab of a linear system arising from a 7-point finite difference stencil on a 600 × 595 × 1536 mesh, achieving about one third of the machine's peak performance. We explain the system, its architecture and programming, and its performance on this problem and related problems. We discuss issues of memory capacity and floating point precision. We outline plans to extend this work towards full applications.

Index Terms-Algorithms for numerical methods and algebraic systems, Computational fluid dynamics and mechanics, Multi-processor architecture and microarchitecture

The recent introduction of wafer-scale processors promises to change this situation. The Cerebras Systems CS-1, a system whose compute and memory resources are all fabricated in a single 462 cm 2 silicon wafer, can move three bytes to and from memory for every flop. This is achieved in a highly parallel, distributed memory