Authors: DUK-SOON OH


Title: AN OVERLAPPING SCHWARZ ALGORITHM FOR RAVIART-THOMAS VECTOR FIELDS WITH DISCONTINUOUS COEFFICIENTS

 Abstract: 
Overlapping Schwarz methods form one of two major families of domain decomposition
methods. We consider a two-level overlapping Schwarz method for Raviart-Thomas vector
fields. The coarse part of the preconditioner is based on the energy-minimizing extensions and the
local parts are based on traditional solvers on overlapping subdomains. We show that the condition
number grows linearly with the logarithm of the number of degrees of freedom in the individual subdomains 
and linearly with the relative overlap between the overlapping subdomains. The condition number of 
the method is also independent of the values and jumps of the coefficients. Numerical results for 2D and 3D 
problems, which support the theory, are also presented.