Accelerating High-Order Mesh Optimization Using Finite Element Partial Assembly on GPUs

TL;DR

This paper introduces a GPU-accelerated high-order finite element mesh optimization method that leverages tensor factorization and matrix-free techniques for improved performance, enabling efficient large-scale mesh improvements.

Contribution

The paper presents a novel GPU-oriented mesh optimization approach based on finite element partial assembly, utilizing tensor factorization and matrix-free methods for high performance.

Findings

Achieves significant GPU acceleration for high-order mesh optimization.

Reduces data motion through tensor factorization and matrix-free techniques.

Provides a reproducible benchmark for mesh optimization performance.

Abstract

In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high-order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU-based HPC hardware. We describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.