The short courses will be held on September 19th. Courses offered will be taught by internationally known experts in the field of Mesh Generation. The courses will run an hour and a half in length and include course notes, coffee breaks and a lunch. Instructors will be addressing practical issues in the design and implementation of both structured and unstructured mesh generation codes.

The courses are ideal for students just entering the field needing a foundation for research, or for seasoned professionals who would like to expand their current skill-set in the development of mesh and grid generation algorithms. to register for the short courses, mark the appropriate boxes on the registration form. The price is $125 per attendee which includes course material and a lunch.

Mesh Quality and Optimization
Lori Freitag Diachin, LLNL
Patrick Knupp, SNL

In this short course we present a number of mesh quality analysis and improvement techniques. The primary focus of the course is a priori unstructured mesh quality improvement as measured by element shape. We discuss ways in which one can measure the quality of a given mesh. For each element in the mesh, a number of element quality metrics have been developed that focus on geometric qualities such as shape, aspect ratio, skew, and orientation. We present a number of these metrics, including recently developed algebraic mesh quality metrics which are flexible enough to measure several aspects of element quality at once and to define quality in terms of an ideal, reference element. We show how to use these algebraic metrics to define meaningful element measures for both tetrahedral and hexahedral elements. Once the quality of individual elements has been defined, they must be combined in some manner that gives an overall measure of mesh quality. We use mathematical norms to derive several different measures of mesh quality, and use these to define objective functions that can be used to optimize the quality of the mesh.

Given several different mesh quality objective functions, we examine the techniques that are best suited for solving the resulting optimization problems. The solution techniques can be loosely categorized into single-vertex techniques and all-vertex techniques. Single vertex methods optimize the position of each vertex of the mesh individually and make several sweeps over the mesh to improve the overall quality. All-vertex methods use sophisticated optimization solvers to simultaneously reposition all the vertices. In each case, we discuss different optimization methods that can be used to maximize the objective function. We discuss the tradeoffs associated with using these two different approaches and discuss preliminary results that highlight the advantages and disadvantages of each.

Many of these methods have been implemented in the Mesquite mesh quality improvement toolkit, and we conclude the short course by describing this software. We describe the design goals of the software and its current status. We show how to use the software to quickly and easily optimize application meshes and also to develop custom mesh quality improvement schemes.

Lori Freitag Diachin is a research program manager in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. She has worked in the area of optimization-based mesh quality improvement for 10 years and has many conference and journal publications in this area. She is the co-PI on the Mesquite mesh quality improvement toolkit. She received her PhD in applied mathematics from the University of Virginia in 1992.