Posted March 13, 2015
Last modified March 19, 2015
Peter Kuchment, Texas A&M
The Nodal Count Mystery
The beautiful nodal patterns of oscillating membranes, usually called by the (incorrect) name Chladny patterns, have been known for several centuries (Galileo, Leonardo, Hooke) and studied in the last hundred years by many leading mathematicians. In spite of that, many properties of these patterns remain a mystery. We will present the history and a recent advance in the area of counting the nodal domains. No prior knowledge of the subject is assumed. Refreshment will be served in the Keisler lounge at 2:00 pm.
Posted February 3, 20153:30 am - 4:30 pm 233 Lockett Hall
Yuri Antipov, Mathematics Department, LSU
Singular integral equations in a segment with two fixed singularities and applications
Posted March 22, 20153:30 pm - 4:30 pm 1034 Digital Media Center
Bin Zheng, Pacific Northwest National Laboratory
Fast Multilevel Solvers for Discrete Fourth Order Parabolic Problems
Abstract: In this work, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element method. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show these preconditioners only need to be solved inexactly by optimal multigrid algorithms. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems. Our numerical examples indicate the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients.
Posted December 11, 2014
Last modified January 27, 2015
Math faculty meeting with Dean Peterson