Model of a truncated cone, a mesh of linear hexahedral elements with 21,600 degrees of freedom, fixed at the base and loaded at the end with a twisting load. This model was used in an evaluation of unstructured multigrid methods for 3D finite element problems in solid mechanics.

James Demmel, University of California, Berkeley, and NERSC, Lawrence Berkeley National Laboratory
Mark Adams, Sandia National Laboratories
Xiaoye Sherry Li and David Blackston, NERSC, Lawrence Berkeley National Laboratory

Research Objectives
We provide highly optimized parallel computational kernels for DOE and other scientists. Our projects include a scalable sparse direct linear system solver (SuperLU), a scalable sparse incomplete factorization preconditioner (ILU), a scalable multigrid solver for partial differential equations on irregular meshes (Prometheus), a scalable symmetric eigensolver and singular value decomposition solver (xSTEVR), a scalable N-body code based on the fast multipole method and the Barnes-Hut algorithm (PBody), and a scalable structured matrix solver for matrices arising in astrophysical calculations.

Computational Approach
All codes are written with performance and portability in mind. Our codes are written in C or Fortran and use standard libraries such as BLAS, MPI, BSP communications, (Par)Metis, PETSc, etc. Since our goal is high parallel efficiency, the codes use state-of-the-art algorithms, many of which we designed.

Accomplishments
SuperLU was used by Rescigno et al. (see Publications below) in a breakthrough quantum mechanical computation done on the NERSC Cray T3E and featured on the cover of the December 24, 1999 issue of Science.

Prometheus had a second release, incorporating both aggregation and smoothed aggregation methods in its collection of restriction operators. It was used to solve a 78 million degree of freedom problem on about 1,000 processors. PBody was completed, and David Blackston began working for NERSC to incorporate PBody into the ACTS Toolkit. xSTEVR was included as part of the LAPACK 3.0 release, and is significantly faster than the previous symmetric eigensolver.

Significance
We are developing computational tools for linear algebra and N-body problems that are ubiquitous in computational science and engineering. All codes will be publicly available.

Publications
T. N. Rescigno, M. Baertschy, W. A. Isaacs, and C. W. McCurdy, "Collisional breakup in a quantum system of three charged particles," Science 286, 2474 (1999).

M. Adams, "Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics," Computing Sciences Division Technical Report CSD-00-1103, University of California, Berkeley (1999).

E. Anderson et al., LAPACK Users' Guide, 3rd edition (Society for Industrial and Applied Mathematics, Philadelphia, 1999).

http://www.cs.berkeley.edu/~{demmel,xiaoye,madams}