Accelerating High-Order Mesh Optimization Using Finite Element Partial Assembly on GPUs
arXiv:2205.12721 · doi:10.1016/j.jcp.2022.111808
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.
arXiv comment28 pages, 10 figures, 3 tables
References in corpus (7)
- MFEM: a modular finite element methods library
- Fast matrix-free evaluation of discontinuous Galerkin finite element operators
- Efficient Exascale Discretizations: High-Order Finite Element Methods
- Nonconforming Schwarz-Spectral Element Methods For Incompressible Flow
- Simulation-Driven Optimization of High-Order Meshes in ALE Hydrodynamics
- High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners
- Automatic penalty and degree continuation for parallel pre-conditioned mesh curving on virtual geometry