Improvement of unstructured quadrilateral mesh quality for multigrid analysis

Due to more complex and severe design restrictions, more effective and faster finite element analyses are demanded. There are several ways to compute FE analysis efficiently: parallel computing, fast iterative or direct solvers, adaptive analysis and so on. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with difference resolutions and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to be applied to an initial mesh, and better convergence is achieved by the improved initial mesh.