PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng.

Title:Constrained Hyperbolic Equations: Mathematical and Numerical Analysis
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Nicolae Tarfulea, Purdue
Abstract:
In this talk we will be mainly concerned with first order symmetric hyperbolic (FOSH) systems of differential equations, for many problems can be reduced to this form in combination with a system of constraint equations. In general, for the pure Cauchy problem, the constraints are preserved by the evolution (see Maxwell equations or Einstein's field equations in various FOSH formulations), but for an initial-boundary value problem, this will not be the case. It has become increasingly clear that in order for constraints to be preserved during evolution, the boundary conditions have to be chosen in an appropriate way. However, although from the purely theoretical point of view this might be enough, for numerical solutions to such problems the use of constraint-preserving boundary conditions might represent only a step in the right direction. In particular, this is a challenging situation for the numerical community; even if the exact solution is theoretically proved to satisfy the constraints for all time, from the numerical point of view there are always instabilities triggered in numerical simulations by round-off errors that lead to constraint violating numerical solutions. In this talk we present a technique of reducing certain constrained FOSH problems to unconstrained ones. In essence, we associate to a system with constraints an equivalent, unconstrained one by making the constrains part of the dynamical variables of the new system. Such a construction could be useful in order to control the constraint violations since the constraints are incorporated as main variables, and so kept under control for all time.

Room Reservation Information

Room Number:MB216
Date:10 / 27 / 2008
Time:03:35pm - 04:25pm