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A generic strategy to obtain semi‐analytical mesh sensitivities/velocities for tetrahedral mesh generators

This article proposes a generic approach to obtain semi‐analytical mesh sensitivities and shows how to compute mesh updates for any tetrahedral mesher. The proposed strategy allows sensitivities to be computed for a given mesh or first improve an initial mesh and then compute sensitivities. The strategy is based on a modification of Persson and Strang's mesher, Distmesh, analogizing the mesh to a simple truss structure. The boundary of the mesh is maintained using Lagrangian multipoint constraints. An analytical relationship between the mesh and the boundary permits the nodes to move freely along the boundary. This links the mesh directly to the parameterized geometry. We demonstrate the approach's ability to produce accurate, smooth and continuous mesh sensitivities and update the mesh. We use the resulting sensitivities to predict mesh updates corresponding to geometry updates. Four examples are given that show the method can accurately describe linear and nonlinear convex and concave domains. An example is given that also demonstrates the ability to generate accurate mesh sensitivities for a mesh created using the third party mesher GMSH.