James Demmel, University of California, Berkeley, and NERSC, Lawrence Berkeley National Laboratory Mark Adams, David Blackston, and Tzu-Yi Chen, University of California, Berkeley Xiaoye Li and Osni Marques, NERSC, Lawrence Berkeley National Laboratory

Research Objectives

We have several goals:
1. Produce a scalable sparse direct linear system solver.
2. Produce a scalable sparse incomplete factorization preconditioner.
3. Produce a scalable multigrid solver for partial differential equations (PDEs) on irregular meshes.
4. Produce a scalable symmetric eigensolver and singular value decomposition (SVD) for dense matrices.
5. Produce a scalable N-body code based on the fast multipole method (FMM) and the Barnes-Hut algorithm.

Computational Approach

All codes are written with performance and portability across distributed memory architectures in mind. Some codes are also portable to shared memory systems and clusters of SMPs. MPI, C, C++ and occasionally some Fortran are the programming tools. The codes use state-of-the-art algorithms, many of which we designed.

Accomplishments

	System architecture for Prometheus, a multigrid solver for finite element matrices on unstructured meshes in solid mechanics.

1. The prototype sparse direct linear system solver is being used for computational chemistry research. An early version of the code is about to be released.
2. The sparse incomplete factorization preconditioner will be used as an iterative solver for linear systems too large for direct solvers.
3. The multigrid PDE code, which has been released in beta form, is designed for very large linear systems arising in finite element modeling in solid mechanics. Earlier versions of this system, developed by Mark Adams, have won two prizes for algorithms and scalability. The code will be integrated into a large earthquake modeling code.
4. An earlier version of the eigensolver/SVD code already in ScaLAPACK has been incorporated into a quantum chemistry code called MP-Quest at Sandia National Laboratories, and was runner-up for the Gordon Bell Prize at SC98. An early version of the code is about to be released.
5. The N-body code has been incorporated into a full-scale simulation of an electron-beam lithography device for semiconductor manufacturing and has been made available to an astrophysics data analysis project.

Significance

All five projects will produce useful tools for high performance computing widely relevant to DOE research projects, with early versions already in use. In all cases, the code will be publicly available.

Publications

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