A Patch-Based Mesh Optimization Algorithm for Partitioned Meshes ?

The finite element method is commonly used in the numerical solution of partial differential equations (PDEs). Poor quality elements effect the convergence and stability of the method as well as the accuracy of the computed PDE solution. Thus, mesh quality improvement methods are often used as a post-processing step in automatic mesh ? The work of the first author was supported by a Lockheed Martin Graduate Fellow Award, a Harry G. Miller Graduate Fellowship, and The Pennsylvania State University. The work of the second author was funded in part by NSF grant CNS 0720749, a Grace Woodward grant from The Pennsylvania State University, and the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38. Part of the work of the second author was performed while a member of the Center for Applied Mathematics at Cornell University and an intern at Argonne National Laboratory. The work of the third and fifth authors was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38. The work of the third author was performed at Argonne National Laboratory. The work of the fourth author was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract DE-AC-94AL85000. 2 Voshell, Shontz, Diachin, Knupp, and Munson