NIU Department of Mathematical SciencesTitle: Numerical Solution of Evolution Systems with Differential Constraints
Speaker: Prof. Alexander Alekseenko, California State University Northridge
Abstract: Formulations of general relativity combine partial differential equations of two kinds. The equations of the first kind, called the evolution equations, involve both time and space derivatives. The equations of the second kind, called the constraint equations, involve spatial derivatives only. For some time, the biggest challenge in the numerical simulation of the Einstein equations was to keep the constraints from growing exponentially in time. Techniques of constraint projection, constraint damping and constraint-preserving boundary conditions have been proposed to achieve stable long term evolutions. Although the implementation of the new techniques resulted in a breakthrough simulation of inspiral and collision of two black holes in 2005, no unifying theory has been developed until now for studying the numerical properties of these systems. I will summarize the procedures involved in the design of a well-posed initial-boundary value problem for an evolution system with differential constraints and discuss the design of a unified approach for the solution of such systems.
Algebra Seminar
Tuesday, Nov 17, 2:00-2:50pm, DU 418
Speaker: Harvey Blau
Topic: Classification of Various Fusion Categories (Continued)