GPU accelerated spectral finite elements on all-hex meshes

TL;DR

This paper introduces a GPU-accelerated spectral finite element method for efficiently solving large-scale elliptic problems on unstructured hexahedral meshes, leveraging a matrix-free approach and multi-threading APIs.

Contribution

It presents a novel GPU-accelerated spectral element scheme with a flexible multi-threading API and an additive Schwartz preconditioner that achieves h-independent convergence.

Findings

Solves problems with over 50 million degrees of freedom in seconds on a standard GPU.

Uses a matrix-free conjugate gradient algorithm with an additive Schwartz preconditioner.

Demonstrates high efficiency and scalability on unstructured hexahedral meshes.

Abstract

This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An additive Schwartz two-scale preconditioner is employed that allows h-independence convergence. An extensible multi-threading programming API is used as a common kernel language that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.