The Target-Matrix Optimization Paradigm for High-Order Meshes
This work provides a practical framework for mesh quality improvement in high-order finite element simulations, addressing a known bottleneck in computational science and engineering.
The paper extends the Target-Matrix Optimization Paradigm (TMOP) to high-order finite element meshes, enabling precise local quality control while improving meshes globally. The method is demonstrated on test problems and a high-order ALE application, with an open-source implementation provided.
We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of Knupp. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Eulerian-Lagrangian (ALE) application. Our implementation is freely available in an open-source library form.