A New Objective Function for Mesh Untangling, Smoothing, Refinement and Coarsening

摘要

A new objective function for optimization-based mesh untangling, smoothing, refinement and coarsening is presented for quadrilateral elements. Unlike most existing method in which mesh untangling and smoothing are carried out with the help of two-stage schemes, the new objective function can be used to carry out these operations simultaneously. The corresponding optimization problem is solved with the help of the steepest decent method. The method can be used together with any type of mesh refinement approach, e.g., hanging nodes. Numerical examples using the current approach demonstrating its robustness and effectiveness will be presented and discussed.