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Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, May 30, 2014 - 05:00 to 06:00

Location:

GLK 115

Event Link:

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.