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Communication is needed when one sweeps in a given index, say i, and that index location changes
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Note Algorithms for sequential tridiagonal solvers are given in the appendix of volume 1 of Hirsch
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For a scalar tridiagonal matrix with N rows, the solution takes time 5N
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For a block tridiagonal matrix, one increases this by a factor between 25 and 125 for 5 by 5 blocks.
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Note communication proportional to "5" i.e. size of vector being calculated as one changes block size
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However calculation proportional to 52 to 53 as one changes block size i.e. it increases faster with block size than communication
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This illustrates that extra CFD components (1 goes to 5) increases efficiency of parallel CFD codes compared to comparable scalar equations
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