Matrix Norms and the Condition Number: A General Framework to Improve Mesh211 Quality vai Node-Movement

摘要

Objective functions for unstructured hexahedral and tetrahedral mesh optimization211u001eare analyzed using matrices and matrix norms. Mesh untangling objective functions 211u001ethat create valid meshes are used to initialize the optimization process. Several 211u001enew objective functions to achieve element invertibility and quality are 211u001einvestigated, the most promising being the 'condition number'. The condition 211u001enumber of the Jacobian matrix of an element forms the basis of a barrier-based 211u001eobjective function that measures the distance to the set of singular matrices and 211u001ehas the ideal matrix as a stationary point. The method was implemented in the 211u001eCubit code, with promising results.