SuperLU (Sparse Direct Solver)

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Symbolic Factorization• Cholesky [George/Liu `81]• Use elimination graph of L and its transitive reduction(elimination tree)• Complexity linear in output: O(nnz(L))• LU• Use elimination graphs of L and U and their transitivereductions (elimination DAGs) [Tarjan/Rose `78, Gilbert/Liu`93, Gilbert `94]• Improved by symmetric structure pruning [Eisenstat/Liu `92]• Improved by supernodes• Complexity greater than nnz(L+U), but much smaller thanflops(LU)Short Course on the DOE ACTS Collection - SIAM CSE05 ConferenceOrlando, FL - February 11, 200512
Numerical Factorization• Sequential SuperLU• Enhance data reuse in memory hierarchy by calling Level 3 BLASon the supernodes• SuperLU_MT• Exploit both coarse and fine grain parallelism• Employ dynamic scheduling to minimize parallel runtime• SuperLU_DIST• Enhance scalability by static pivoting and 2D matrix distributionShort Course on the DOE ACTS Collection - SIAM CSE05 ConferenceOrlando, FL - February 11, 200513
Page 1 and 2: SIAM Conference on Computational Sc
Page 3 and 4: What is SuperLU• Solve general sp
Page 5 and 6: Contents of the SuperLU Library•
Page 7 and 8: Supernode• Exploit dense submatri
Page 9 and 10: Numerical Pivoting• Goal of pivot
Page 11: Ordering Interface in SuperLU• Li
Page 15 and 16: 2D Block Cyclic Layout for L and U
Page 17 and 18: SuperLU_DIST Example Program (C)•
Page 19 and 20: Pddrive.c (2/2)/* Initialize ScaleP
Page 21 and 22: f_pddrive.f90 (1/2)program f_pddriv
Page 23 and 24: Applications• Used to solve open
Page 25: Summary• Efficient implementation

SuperLU (Sparse Direct Solver)

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