Parallel Sparse Gaussian Elimination

1
Parallel Sparse Gaussian Elimination

• Jim Demmel (UCB) and Xiaoye Li (NERSC)
• Prior work on sparse GE
• Sequential and Multithreaded
• High performance, Widely used
• Details at www.nersc.gov/xiaoye
• Current work targets scalability
• Conventional partial pivoting (PP) too expensive
• Cant precompute data structure, layout,
  communication schedule as in Cholesky
• Solution GE with Static Pivoting (GESP)
• Do not do partial pivoting
• Statically pivot to put large entries on diagonal
• Other protections against pivot growth
• As accurate as PP in practice
• Very scalable Speedup up to 100 on 512 PE T3E
• Details at www.nersc.gov/xiaoye/SuperLU
• Will release soon
• Proposed Future Work
• Tune GESP for applications arising in
  astrophysics
• Produce Incomplete LU version for preconditioner

2
Parallel Multigrid on Irregular Meshes

• Jim Demmel (UCB) and Mark Adams (UCB)
• Prior work on Multigrid
• Solver designed for FE problems on irregular
  meshes
• Take matrix and fine mesh as input, and
  automatically
• Generate coarse meshes
• Generate restriction, interpolation, coarse grid
  operators
• Load balance, solve using Multigrid
• Embedded in fully nonlinear FE modeling system
• Benchmarks
• 39M dof problem with discontinuous coefficients,
  near incompressibility (from solid mechanics)
• Solved on 960 processor ASCI IBM PowerPC Cluster
  with over 50 parallel efficiency
• Similar efficiency on 640 processor Cray T3E
• Details at www.cs.berkeley.edu/madams/prometheus
• Current work expands functionality
• New applications, element types, coarsening
  schemes
• Hardening of software
• Proposed Future Work
• Tune multgrid coarsening, smoother for
  astrophysics