Parallel line identification for line-implicit-solvers

Abstract

Line-implicit preconditioners are well known in computational fluid dynamics (CFD) solvers and are an essential component to handle meshes with cells of very high aspect ratio (> 1000:1). Such anisotropic cells are commonly used to resolve steep gradients in the boundary layer of a turbulent flow with high Reynolds number. To date, this technique has rarely been used to solve other partial differential equations. We show that the advantages of such preconditioners do not depend on the partial differential equation or discretization used, but also apply to other problems like a node-based mesh deformation with linear elasticity on such meshes. We show the influence of the selection of these lines, and present a new algorithm for identifying lines for line-implicit preconditioners. This new algorithm makes better use of parallel processors and leads to more homogeneous lines. Finally, we see that using the same line-implicit preconditioner, but the new line identification algorithm, even leads to faster convergence for the mesh deformation problem based on linear elasticity.