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Parallel Blocked-Diagonal-Bordered Gauss-Seidel

Implementations for the parallel block-diagonal-bordered sparse Gauss-Seidel method have been developed during this research. Pseudo-code representations of each parallel algorithm section are presented separately in figures gif through gif. In particular, each of these figures correspond to the following figure numbers:

  1. monitor convergence for the parallel Gauss-Seidel method --- figure gif,
  2. solve for in the diagonal blocks and upper border --- figure gif,
  3. update for the last diagonal block ---
  4. solve for in the last diagonal block ---
  5. perform the convergence check ---
Figure gif provides the framework for the parallel block-diagonal-bordered sparse Gauss-Seidel implementation. In this implementation, multiple iterations are performed before a check is made on convergence.

 
Figure: The Iterative Framework for the Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm  

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Diagonal Blocks 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Update --- Low-Latency Communications Paradigm 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Update --- Buffered Communications Paradigm 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Last Diagonal Block --- Low-Latency Communications Paradigm 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Last Diagonal Block --- Buffered Communications Paradigm 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Convergence Check --- Low-Latency Communications Paradigm 

 
Figure: Parallel Block-Diagonal-Bordered Sparse Gauss-Seidel Algorithm --- Convergence Check --- Buffered Communications Paradigm 



David P. Koester
Sun Oct 22 17:27:14 EDT 1995