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This is interesting and has identical issues to those of parallelizing Gauss-Seidel Iterative solver where one preserves natural update order and does not use red-black artifice
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Note that for Elliptic solvers natural lexicographic ordering
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Index in x direction runs fastest, then that in h and then that in z
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Has similar convergence properties to red-black ordering
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As red-black has simple parallelization, one always uses this
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However according to:
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Solution of Regular Sparse Triangular Linear Systems on Vector and Distributed-Memory Processors by E. Barszcz, R. Fatoohi, V. Venkatakrishnan, S. Weeratunga, RNR-93-007 (NASA Ames Memo)
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This looks at LU NAS Benchmark for Cray YMP, CM-2, and iPSC860.
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This is NOT true for hyperbolic solvers where lexicographic ordering seems superior to red-black ordering.
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