A high-order log barrier-based mesh generation and warping method

The ability to generate high-order meshes that conform to the boundary of curved geometries is a hurdle in the adoption of high-order computational methods for the numerical solution of partial differential equations. In this paper, we propose a method for generating and warping second-order Lagrange triangular and tetrahedral meshes based on a log barrier method. In the case of generation, the approach consists of modifying an initial linear mesh by first, adding nodes at the midpoint of each edge; second, displacing the newly added boundary midpoints to the curved boundary, and third, solving for the final positions of the interior nodes based on the boundary deformation. By allowing all of the boundary nodes to move, the approach can also be used to warp second-order triangular and tetrahedral meshes. We present several numerical examples in both two and three dimensions which demonstrate the capabilities of our method in generating and warping second-order curvilinear meshes.