Elimination Forest Guided D Sparse LU Factorization

Sparse LU factorization with partial pivoting is important for many scienti c applications and delivering high perfor mance for this problem is di cult on distributed memory machines Our previous work has developed an approach called S that incorporates static symbolic factorization supernode partitioning and graph scheduling This paper studies the properties of elimination forests and uses them to guide supernode partitioning amalgamation and execu tion scheduling The new design with D mapping e ec tively identi es dense structures without introducing too many zeros in the BLAS computation and exploits asyn chronous parallelism with low bu er space cost The imple mentation of this code called S uses supernodal matrix multiplication which retains the BLAS level e ciency and avoids unnecessary arithmetic operations The experiments show that S improves our previous code substantially and can achieve up to GFLOPS on Cray T E MHz nodes which is the highest performance reported in the lit erature