Many important scientific and engineering applications require the use of linear solvers. The Aztec iterative solver package grew out of a specific application: modeling reacting flows (MPSalsa). Our primary goal has been to provide state-of-the-art iterative methods that perform well on parallel computers (applications of over 200 Gflops have been achieved on the Sandia-Intel TFlop Computer) and at the same time are easy to use for application engineers. In addition to providing standard iterative methods to engineers, the Aztec library is also used in our research on preconditioners. At present, we are working closely with a couple of specific applications in developing some new multilevel preconditioners.
|Parallel: MPI, Intel Paragon, nCUBE.|
|Unstructured Sparse Data-Local Matrices (e.g. From Finite Elements).|
|Simple Parallelization||Efficient Machine Utilization|
|No Need To:||Fast (Grouped) Communication.|
|Define Ghost Variables.||Sparse Point & Block Matrices.|
|Map Global to Local Indices.||Advanced Parallel Preconditioning.|
|Identify Neighboring Processors.||Builds on Advanced Partitioning.|
|Determine Messages.||Computation Overlaps Communication.|
Aztec is a parallel iterative library for solving linear systems, which is both easy-to-use and efficient. Simplicity is attained using the notion of a global distributed matrix. The global distributed matrix allows a user to specify pieces (different rows for different processors) of his application matrix exactly as he would in the serial setting (i.e. using a global numbering scheme). Issues such as local numbering, ghost variables, and messages are ignored by the user and are instead computed by an automated transformation function. Efficiency is achieved using standard distributed memory techniques; locally numbered submatrices, ghost variables, and message information computed by the transformation function are maintained by each processor so that local calculations and communication of data dependencies is fast. Additionally, Aztec takes advantage of advanced partitioning techniques (Chaco) and utilizes efficient dense matrix algorithms when solving block sparse matrices.
Methods: CG, CGS, BiCGSTAB, GMRES, TFQMR
Preconditioners: Point & block Jacobi, Gauss-Seidel, least-squares polynomials, and overlapping domain decomposition using sparse LU, ILU, BILU within domains.
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Last Updated: 19 August 1997
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Michael A. Heroux (mheroux at cs.sandia.gov)