PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Abstract:
Title:	Derivative-Free Optimization Algorithms for Mesh Quality Improvement
Seminar:	SIAM Student Chapter Seminar
Speaker:	Suzanne M. Shontz, Penn State University (CSE)
Meshes are generated for use in the numerical solution of partial differential equations (PDEs), which arise in numerous science and engineering applications. It is essential that the meshes be of high quality in that the quality of the mesh affects the PDE solution accuracy as well as the execution time and conditioning of the relevant linear solver. Mesh quality improvement is necessary when the mesh is of less than desirable quality (either from mesh generation or deformation). In the first part of my talk, I will give an introduction to mesh quality improvement. In the second part of my talk, I will describe two derivative-free methods for mesh optimization, namely the pattern search (PS) and multidirectional search (MDS) mesh quality improvement methods, to be used with nondifferential objective functions representing the overall mesh quality. Such objective functions arise when the goal of the mesh optimization problem is to improve the worst quality element in the mesh. I will present numerical results demonstrating the effectiveness of these techniques in improving the worst quality elements of several finite element meshes.