Parallel Incomplete Factorizations based on the 
	Domain Decomposition Data Distribution


 			Gundolf Haase


 The presentation analyses various parallel incomplete factorizations 
 based on the non-overlapping domain decomposition.  
 The general framework is applied to the investigation of the preconditioning 
 step in cg-like methods. 
 Under certain conditions imposed on the finite element mesh, all 
 matrix and vector types given by the special data distribution can be 
 used in the matrix-by-vector multiplications. 
 Not only the well-known domain decomposition preconditioners fit into 
 the concept but also parallelized global incomplete factorizations  
 are feasible. 
 It will be shown that for the given data distribution the application 
 of an IUL factorisation reqiures half of the communication in comparison
 to an application of an ILU factorization. 
 If just a few level-1 fill-ins in the factorization are omitted 
 then even a factorization very close to the exact UL (LU) factorization 
 is feasible. 
 Additionally, those global incomplete factorizations can be used as 
 smoothers in global multigrid methods, especially the latter one in 
 the proper coarse grid solver. 
 Numerical results on a parallel machine with distributed 
 memory are presented.



Contact_Address: Johannes Kepler University Linz
  		 Institute of Mathematics
  		 Altenbergerstr. 69
  		 A-4040 Linz, Austria

Email: 		ghaase@numa.uni-linz.ac.at