SuperLU: Sparse Direct Solver

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Adoptions of <strong>SuperLU</strong> Industrial FEMLAB HP Mathematical Library NAG Python (NumPy, SciPy extensions) Academic/Lab: In other ACTS Tools: PETSc, Hypre NIMROD (simulate fusion reactor plasmas) Omega3P (accelerator design, SLAC) OpenSees (earthquake simluation, UCB) DSpice (parallel circuit simulation, SNL) Trilinos (object-oriented framework encompassing various solvers, SNL) NIKE (finite element code for structural mechanics, LLNL) X. Li 6
Review of Gaussian Elimination (GE) Solving a system of linear equations Ax = b First step of GE: (make sure α not too small . . . may need pivoting) A = ⎢⎣ ⎡ α v w T B ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣v 1 0⎤ ⎡ ⎥ ⋅ α / α I ⎢ ⎦ ⎣0 Repeats GE on C Results in LU factorization (A = LU) L lower triangular with unit diagonal, U upper triangular Then, x is obtained by solving two triangular systems with L and U w T C C ⎤ ⎥ ⎦ = B v ⋅ w − α T X. Li 7
Page 1 and 2: SuperLU: Sparse Direct Solver X. Sh
Page 3 and 4: What is SuperLU Solve general spars
Page 5: Content of SuperLU Library LAPACK-s
Page 9 and 10: Supernode Exploit dense submatrices
Page 11 and 12: Numerical Pivoting Goal of pivotin
Page 13 and 14: Ordering for Sparse Cholesky (2/2)
Page 15 and 16: Ordering Based on Nested Dissection
Page 17 and 18: Ordering Interface in SuperLU Libra
Page 19 and 20: Symbolic Factorization Cholesky [Ge
Page 21 and 22: How to distribute the matrices Mat
Page 23 and 24: Distributed Compressed Row Storage
Page 25 and 26: Process grid and MPI communicator E
Page 27 and 28: Scalability of SuperLU_DIST Poisso
Page 29 and 30: SuperLU_DIST Example Program Super
Page 31 and 32: EXAMPLE/pddrive.c (cont.) /* Initia
Page 33 and 34: SuperLU_DIST_2.0/FORTRAN/f_5x5.f90
Page 35 and 36: f_5x5.f90 (cont.) ! Create the dist
Page 37 and 38: Other Examples in EXAMPLE/ Pddrive1
Page 39 and 40: Accelerator (cont.) Finite element
Page 41 and 42: DDS47, Linear Elements Total eigens
Page 43: Summary Efficient implementations o

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