http://www.math.psu.edu/seminars/calendar.php Seminars and special events at Penn State's mathematics department 2008-05-12 webmaster@math.psu.edu http://www.math.psu.edu/seminars/meeting.php?id=2291 Speaker(s): Konstantin Lipnikov ABSTRACT. A successful discretization method inherits or mimics fundamental properties of the underlying PDEs such as conservation laws, symmetries, solution positivity and maximum principle. Construction of such a method is made more difficult when the mesh is distorted so that it can conform and adapt to the physical domain and problem solution. The talk is about one such method - the mimetic finite difference (MFD) method. The MFD method is used to solve problems with full tensor coefficients on unstructured polygonal and polyhedral meshes. Polyhedral meshes may include arbitrary elements: tetrahedrons, pyramids, hexahedrons, degenerated and non-convex polyhedrons, generalized polyhedrons, etc. Modeling with polyhedral meshes has a number of advantages that will be addressed in the talk. The MFD method has been applied successfully to several applications including diffusion, electromagnetics, acoustics, and gasdynamics. I present a general framework for building MFD methods, give examples of discretizations of the gradient, divergence and curl operators on polygonal and polyhedral meshes, and review existing theoretical results including convergence estimates, orthogonal decomposition theorems, etc. I'll present in more details the MFD methods for solving a linear diffusion problem. I'll show how the method produces a family of schemes with equivalent properties and establish connections with the mixed finite element, finite volume and multi-point flux approximation methods. 2008-05-12EDT15:30:00 CCMA PDEs and Numerical Methods Seminar Series liu@math.psu.edu math@math.psu.edu psu@math.psu.edu http://www.math.psu.edu/seminars/meeting.php?id=2722 Speaker(s): Yunrong Zhu Adviser: Jinhcao Xu 2008-05-14EDT15:00:00 Ph.D. Thesis Defense halpenny@math.psu.edu http://www.math.psu.edu/seminars/meeting.php?id=2790 Speaker(s): A. De Simone We will discuss swimming strategies for microscopic swimmers and recipes to optimize their stroke. 2008-05-15EDT11:00:00 Applied Analysis Seminar berlyand@math.psu.edu http://www.math.psu.edu/seminars/meeting.php?id=2759 Speaker(s): Vitaliy Gyrya Adviser: Leonid Berlyand 2008-05-16EDT10:30:00 Ph.D. Oral Comprehensive Examination halpenny@math.psu.edu