Subdomain sequence

  Some parallel preconditioners, e.g., Alternating Schwarz and Generalised Block SSOR, involve a certain amount of sequentiality in that the subdomains are handled in some order. The way the data flows through the processors is called `pipeline'. (This is analogous to wavefronts in sparse direct methods.)

The data pipeline can be declared by the user with the following routine or option:

Command: int PCParallelSubdomainPipelineSetType(PC pc,PipelineType pipeline_type)
		Option:T-pc_pipeline <pipeline_type      

The available choices for the pipeline_type are:

• Simultaneous processing:

  
   		Argument:TPIPELINE_NONE
  Option value: 		none      
  

  All processor act on their subdomains simultaneously. This reduces the GBSSOR method 6 to block Jacobi, and multiplicative Schwarz 5 to additive Schwarz 4.

• Sequential ordering:

  
   		Argument:TPIPELINE_SEQUENTIAL
  Option value: 		sequential      
  

  All processors are ordered sequentially according to their ranking in the MPI context. This does not necessarily mean that they will not work in parallel: eg, consider processors ordered in a grid structure.

• Red-black ordering:

  
   		Argument:TPIPELINE_REDBLACK
  Option value: 		redblack      
  

  A red-black ordering is used, with processors coloured according to whether their number is odd or even. Note that this may not reflect the processor connectivity.

• Multi-colour ordering:

  
   		Argument:TPIPELINE_MULTICOLOUR
  Option value: 		multicolour      
  

  A multi-colouring is applied to the processors such that processors of the same colour are not connected in the matrix graph.