For more information about this meeting, contact Yuxi Zheng.
| Title: | Constrained Hyperbolic Equations: Mathematical and Numerical Analysis |
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| Seminar: | CCMA PDEs and Numerical Methods Seminar Series |
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| Speaker: | Nicolae Tarfulea, Purdue |
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| Abstract: |
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| 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 |
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| Date: | 10 / 27 / 2008 |
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| Time: | 03:35pm - 04:25pm |
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