## Some Reports on Data Parallel Domain Decomposition Algorithms

for Convection Dominated Linear and Nonlinear Problems

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Some of these algorithms have been tested at PSC,the Pittsburgh
Supercomputing Center.

PFEM: The Parallel Finite
Element Method

- W Layton and P Rabier,

Domain decomposition via operator splitting for nonsymmetric problems,

Appl math l.,5(1992)67-70.

- W Layton,

Domain decomposition for multi-dimensional, first order systems of
partial differential equations,

Applicable Analysis,47(1992)139-150.

- W Layton, J Maubach, P Rabier and A Sunmonu

Parallel finite element methods,

in: Proc 5th ISMM Conf on Parallel and Distributed Computing
Systems,(1992).

- V Ervin, W Layton and J Maubach,

Some graph coloring problems in
parallel numerical methods,

Algorithms in Algebra (A H M Levelt, ed) 39-48, 1993.

- R Jeurissen and W Layton,

Load balancing via graph coloring:an algorithm,

Computers and Math w. Applications,27(1994),27-32.

- W Layton and P Rabier,

Peaceman-Rachford procedures and domain decomposition for finite element
problems,

J Num Lin Algb and Appls, 2(1995) 363-394.

- W Layton , J Maubach and P Rabier,

Parallel algorithms for maximal monotone operators of local type,

Numer. Math.,71(1995), 29-58.

- W Layton and P Rabier,

The element separation property and parallel finite element methods for
the Navier Stokes equations,

Appl Math L,8(1995) 97-102.

- W Layton, J Maubach and P Rabier,

Robustness of an elementwise parallel finite element method for
convection-diffusion problems,

SIAM I Sci Comput, 19(1998) 1870-1891.

- W Layton, J Maubach and P Rabier,

Robust Methods for Highly Nonsymmatric Problems,

Contemporary Mathematics,180(1994)265-270.

- V Ervin and W Layton,

A robust and parallel relaxation method based on algebraic splittings,

Num Meth for PDE's, (1999)91-110.