Absolutely stable IPDG and LDG methods for high frequency wave equations

Tuesday, November 2, 2010 - 5:00pm - 5:45pm
Keller 3-180
Xiaobing Feng (University of Tennessee)
In this talk I shall discuss some recent progresses in developing interior
penalty discontinuous Galerkin (IPDG) methods and local discontinuous
Galerkin (LDG) methods for high frequency scalar wave equation.
The focus of the talk is to present some non-standard (h- and hp-)
IPDG and LDG methods which are proved to be absolutely stable
(with respect to the wave number and the mesh size) and optimally
convergent (with respect to the mesh size). The proposed IPDG
and LDG methods are shown to be superior over standard finite element
and finite difference methods, which are known only to be stable under
some stringent mesh constraints. In particular, it is observed that
these non-standard IPDG and LDG methods are capable to correctly track
the phases of the highly oscillatory waves even when the mesh violates
the rule-of-thumb condition. Numerical experiments will be presented
to show the efficiency of the non-standard IPDG and LDG methods. If time
permits, latest generalizations of these DG methods to the high frequency
Maxwell equations will also be discussed. This is a joint work with Haijun Wu
of Nanjing University (China) and Yulong Xing of the University of Tennessee
and Oak Ridge National Laboratory.
MSC Code: