  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.
