Assembly of FETI dual operator using CUDA

TL;DR

This paper presents a GPU-accelerated method for assembling and applying the FETI dual operator, significantly reducing preprocessing time and achieving up to 25x speedup over CPU methods.

Contribution

The paper introduces GPU-based assembly of the FETI dual operator, enabling efficient explicit application with fewer iterations and substantial speedups.

Findings

Up to 10x faster preprocessing on GPU

Up to 25x faster dual operator application

Reduced number of iterations needed for speedup

Abstract

FETI is a numerical method used to solve engineering problems. It builds on the ideas of domain decomposition, which makes it highly scalable and capable of efficiently utilizing whole supercomputers. One of the most time-consuming parts of the FETI solver is the application of the dual operator F in every iteration of the solver. It is traditionally performed on the CPU using an implicit approach of applying the individual sparse matrices that form F right-to-left. Another approach is to apply the dual operator explicitly, which primarily involves a simple dense matrix-vector multiplication and can be efficiently performed on the GPU. However, this requires additional preprocessing on the CPU where the dense matrix is assembled, which makes the explicit approach beneficial only after hundreds of iterations are performed. In this paper, we use the GPU to accelerate the assembly process as well. This significantly shortens the preprocessing time, thus decreasing the number of solver iterations needed to make the explicit approach beneficial. With a proper configuration, we only need a few tens of iterations to achieve speedup relative to the implicit CPU approach. Compared to the CPU-only explicit approach, we achieved up to 10x speedup for the preprocessing and 25x for the application.