UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: April 9, 2001

Title:
Vector potentials, gauges and edge elements: matching algorithms
with the physics of eddy currents in inhomogeneous conductors

Speaker:
 Pavel Bochev,  CSRI, Sandia National Laboratories and
              University of Texas at Arlington



Abstract:
The physics of the Z-pinch is an excellent example of a
"multi-compartment" process in which electromagnetics, radiation,
hydrodynamics, and etc. interact and produce highly complex phenomena
with largely varying time and space scales.

To obtain a usable 3D fully integrated Z-pinch calculations, it is
essential to develop computational methods for each compartment that
match the algorithm to the physics. In this talk we focus on recent
developments in the numerical simulations of the MHD component, and 
more specifically - on the transient magnetics sub-component. This 
component is obtained by neglecting terms that couple magnetic effects 
with hydro effects.

Our primary objective is to obtain accurate numerical simulation of
magnetic field diffusion in highly heterogeneous conducting media.
Because material properties are not static, it is desirable to work 
with a model that uses a single set of field variables.  This rules 
out approaches which couple a vector magnetic potential with a scalar 
potential in non-conducting regions.

We first consider a vector magnetic potential approach and discuss
several gauge choices. Neither one of them leads to satisfactory numerical
results for materials with large variations in the conductivity.
Next, we consider an approach which exploits the exactness property of
tangentially continuous vector finite element bases. For brick and prism
elements these spaces coincide with the well-known Nedelec spaces while
for isoparametric bricks the first example of such spaces was given by
Van Welij in 1985. Numerical results show that these elements meet the goal
of "matching" the algorithm to physics and produce higly accurate simulations
of the magnetic diffusion in heterogeneous media.