Mesh Deformation Strategy Optimized by the Adjoint Method on Unstructured Meshes

摘要

An adjoint-based optimization procedure is proposed for improving the robustness and extending the range of linear-elasticity-based mesh deformation techniques. Using the values of the modulus of elasticity E defined in each mesh cell as the design variables, the procedure seeks to determine an optimum distribution of E throughout the mesh, to minimize a global objective function that reflects the skew ness or lack of quality of the deformed mesh. The technique is applied to highly stretched mixed element meshes in two and three dimensions on complex geometries and is shown to be capable of recovering a valid mesh in a small number of optimization cycles for cases in which the nonoptimized linear-elasticity approach fails. However, the solution of the optimization problem remains relatively costly in terms of CPU time, compared with a nonoptimized mesh deformation calculation, making this technique best suited for precomputing improved E distributions before the simulation or for use as a plug-in module to be invoked in cases in which the nonoptimized procedure fails.