Title: Numerical Treatment of Differential Constraints in Evolution Systems

Abstract: Applications in electromagnetism, computational fluid
dynamics and general relativity have something in common: they are
solutions to the evolution systems with differential constraints. In
general, the presence of differential constraints in the system makes
its numerical solution more challenging. Due to the sometimes
complicated dependence between the evolution equations and the
constraint equations, it is difficult to identify the properties of
the solution and thus it is difficult to construct a consistent
numerical method. A significant understanding of these relationships
have been achieved for the Maxwell equations which are often used as
the insight for general relativity. The basic techniques for the
formulations of relativity include constraint projection, constraint
damping and constraint-preserving boundary conditions. I will attempt
to summarize the procedures involved in the design of a well-posed
numerical formulation for hyperbolic evolution systems with
differential constraints based on the common techniques that were
proposed for the numerical solution of the Einstein equations.