Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Date/Time: 
Friday, May 30, 2014 - 05:00 to 06:00
Location: 
GLK 115

Speaker Info

Local Speaker: 
Abstract: 

In time domain wave propagation problems, a dominant contribution to long
time integration error are numerical artifacts such phase error. Phase error
is a mismatch between physical speed of �propagation and the speed of the
discrete approximation. This error is hard to compensate for in an efficient
way as it is dependent upon the frequency content of the solution and the
computational mesh.

Mimetic Finite Differences provide a unified framework for the creation of
problem specific, non-polynomial Galerkin methods. These methods are finite
differences as only the degrees of freedom of the basis functions are
enforced. Thus the internal shape functions need not be explicitly known. In
this approach, a family of methods is described with identical formal
accuracy properties. Inside this family, a member can be selected which is
optimal for a particular property. In the literature, methods have been
optimized to enforce discrete maximum principles, handle arbitrary hanging
nodes in mesh refinement, and reduce numerical dispersion.

We construct Mimetic Finite Difference methods for the electric vector wave
equation, a second order formulation of Maxwell?s Equations. This lowest-order
family is parameterized by four variables and formally second order
accurate. From this family we select the member which exhibits fourth order
phase error. We present the construction of the method, dispersion analysis,
and simulations demonstrating our theoretical estimates.