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In particular, for sparse matrix triangular solves the traditional compressed sparse matrix format is poor, and minor adjustments to the data structure can increase the processor utilization dramatically. Such adjustments involve storing the L and U factors separately and storing the U rows \u2018backwards' so that they are accessed in a simple streaming fashion during the triangular solves. Changes to the PETSc libraries to use this modified storage format resulted in over twice the floating-point rate for some matrices. 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