SuperLU (Sparse Direct Solver)

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How to distribute the matrices?• Matrices involved:• A, B (turned into X) – input, users manipulate them• L, U – output, users do not need to see them• A (sparse) and B (dense) are distributed by block rowsP0P1x x x xx x xAx x xBLocal A stored inCompressed Row FormatP2x x x• Natural for users, and consistent with other popular packages: PETSc,Aztec, etc.Short Course on the DOE ACTS Collection - SIAM CSE05 ConferenceOrlando, FL - February 11, 200514
2D Block Cyclic Layout for L and U• Better for GE scalability, load balance• Library has a “re-distribution” phase to distribute the initial values ofA to the 2D block-cyclic data structure of L and U.• All-to-all communication, entirely parallel• < 10% of total time for most matricesShort Course on the DOE ACTS Collection - SIAM CSE05 ConferenceOrlando, FL - February 11, 200515
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 and 12: Ordering Interface in SuperLU• Li
Page 13: Numerical Factorization• Sequenti
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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