Barry Smith

Scalable, extensible, and portable numerical libraries

Designing a scalable and portable numerical library requires consideration of many factors, including choice of parallel communication technology, data structures, and user interfaces. The PETSc library (Portable Extensible Tools for Scientific computing) makes use of modern software technology to provide a flexible and portable implementation. This paper discusses the use of a meta-communication layer (allowing the user to choose different transport layers such as MPI, p4, pvm, or vendor-specific libraries) for portability, an aggressive data-structure-neutral implementation that minimizes dependence on particular data structures (even vectors), permitting the library to adapt to the user rather than the other way around, and the separation of implementation language from user-interface language. Examples are presented.<<ETX>>

Users Manual for KSP Data-Structure-Neutral Codes Implementing Krylov Space Methods

The combination of a Krylov space method and a pre-conditioner is at the heart of most modern numerical codes for the iterative solution of linear systems. This document contains both a users manual and a description of the implementation for the Krylov space methods package KSP included as part of the Portable, Extensible Tools for Scientific computation package (PETSc). PETSc is a large suite of data-structure-neutral libraries for the solution of large-scale problems in scientific computation, in particular on massively parallel computers. The methods in KSP are conjugate gradient method, GMRES, BiCG-Stab, two versions of transpose-free QMR, and others. All of the methods are coded using a common, data-structure-neutral framework and are compatible with the sequential, parallel, and out-of-core solution of linear systems. The codes make no assumptions about the representation of the linear operator; implicitly defined operators (say, calculated using differencing) are fully supported. In addition, unlike all other iterative packages we are aware of, the vector operations are also data-structure neutral. Once certain vector primitives are provided, the same KSP software runs unchanged using any vector storage format. It is not restricted to a few common vector representations. The codes described are actual working codes that run on a large variety of machines including the IBM SP1, Intel DELTA, workstations, networks of workstations, the TMC CM-5, and the CRAY C90. New Krylov space methods may be easily added to the package and used immediately with any application code that has been written using KSP; no changes to the application code are needed.

Simplified Linear Equation Solvers users manual

The solution of large sparse systems of linear equations is at the heart of many algorithms in scientific computing. The SLES package is a set of easy-to-use yet powerful and extensible routines for solving large sparse linear systems. The design of the package allows new techniques to be used in existing applications without any source code changes in the applications.

Using the scalable nonlinear equations solvers package

SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.