UNIVERSITY OF COLORADO AT DENVER

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

TIME: 12:30

DATE: April 6, 2000

Andrea Toselli

FETI DOMAIN DECOMPOSITION METHODS FOR MAXWELL'S EQUATIONS AND ADVECTION-DIFFUSION PROBLEMS

In this talk, we report on some new results on iterative
substructuring methods of FETI type for some edge element 
approximations of Maxwell's equations and for some finite element 
approximations of advection-diffusion problems.

Iterative substructuring methods provide powerful
preconditioners for the solution of linear systems arising 
from the finite element approximation of partial differential 
equations.
For these methods, the computational domain is partitioned into 
a family of non-overlapping subdomains and, for FETI methods, 
the continuity of the solution across the subdomain  
boundaries is enforced by introducing a vector of Lagrange 
multipliers. The primal variables are then eliminated and, 
for the resulting linear system for the Lagrange multipliers, 
a preconditioner  is built by solving a coarse problem and 
local problems on the subdomains.

We first consider a FETI method for edge element approximations on 
matching grids. This method is quasi-optimal and scalable, and 
its condition  number is  independent of possibly large jumps of 
the  coefficients.
We then generalize this method to the case of approximations 
on non-matching grids (mortar approximations).

Finally, we consider a FETI method for finite element approximations 
of advection-diffusion problems on matching grids. Our numerical 
results show that this method performs very well for 
advection-dominated problems.