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January 24 (3:45PM) in the 2nd Floor Conference Room in Dearborn Speaker: Vassilis Paschalidis (University of Chicago) “Suppressing the constraint growth in numerical relativity” The "constraint damping" strategy has proven to be a key ingredient for the successful numerical integration of the Einstein equations. The goal of many formulations in numerical relativity has been to incorporate constraint drivers in symmetric or strongly hyperbolic systems, without changing the principal part of the evolution equations. However, not all formulations with such drivers have been successful. In this talk I will introduce a new formulation which I call the PADM formulation. This system changes the principal part of the evolution equations and turns the Einstein equations into a mixed hyperbolic - second-order parabolic type. This PADM system admits a well-posed Cauchy problem and possesses the desirable property of constraint damping. In particular, it forces the constraints to evolve according to parabolic equations, thus the most hazardous short-wavelength constraint-violating modes are damped extremely efficiently. Finally, I will present a first series of numerical tests of the PADM system and I will demonstrate its potential based on a comparison with the ADM and KST formulations. |