Portable, Extensible Toolkit for Scientific Computation
Encyclopedia
The Portable, Extensible Toolkit for Scientific Computation (PETSc, pronounced PET-see; the S is silent), is a suite of data structures and routines for the scalable
(parallel
) solution of scientific applications modeled by partial differential equations. It employs the Message Passing Interface
(MPI) standard for all message-passing communication. The current version of PETSc is 3.2; released September 8, 2011.
PETSc is intended for use in large-scale application projects, many ongoing computational science projects are built around the PETSc libraries
. Its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel linear
and nonlinear
equation solvers that are easily used in application codes written in C
, C++
, Fortran
and now Python
. PETSc provides many of the mechanisms needed within parallel application code, such as simple parallel matrix
and vector
assembly routines that allow the overlap of communication and computation
. In addition, PETSc includes support for parallel distributed arrays useful for finite difference
methods.
PETSc consists of a variety of libraries (similar to classes
in C++
). Each library manipulates a particular family of objects
(for instance, vectors) and the operations one would like to perform on the objects.
Scalability
In electronics scalability is the ability of a system, network, or process, to handle growing amount of work in a graceful manner or its ability to be enlarged to accommodate that growth...
(parallel
Parallel computing
Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...
) solution of scientific applications modeled by partial differential equations. It employs the Message Passing Interface
Message Passing Interface
Message Passing Interface is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers...
(MPI) standard for all message-passing communication. The current version of PETSc is 3.2; released September 8, 2011.
PETSc is intended for use in large-scale application projects, many ongoing computational science projects are built around the PETSc libraries
Library (computer science)
In computer science, a library is a collection of resources used to develop software. These may include pre-written code and subroutines, classes, values or type specifications....
. Its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel linear
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
and nonlinear
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...
equation solvers that are easily used in application codes written in C
C (programming language)
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
, C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
, Fortran
Fortran
Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...
and now Python
Python (programming language)
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
. PETSc provides many of the mechanisms needed within parallel application code, such as simple parallel matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
and vector
Vector space
A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
assembly routines that allow the overlap of communication and computation
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
. In addition, PETSc includes support for parallel distributed arrays useful for finite difference
Finite difference
A finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...
methods.
Components
Class (computer science)
In object-oriented programming, a class is a construct that is used as a blueprint to create instances of itself – referred to as class instances, class objects, instance objects or simply objects. A class defines constituent members which enable these class instances to have state and behavior...
in C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
). Each library manipulates a particular family of objects
Object (computer science)
In computer science, an object is any entity that can be manipulated by the commands of a programming language, such as a value, variable, function, or data structure...
(for instance, vectors) and the operations one would like to perform on the objects.
Features
PETSc provides the following features:- Parallel vectors and matrices
- ScattersParallel computingParallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...
(handles communicating ghost point information) - Gathers (the opposite of scatters)
- Several sparseSparse matrixIn the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
storageComputer storageComputer data storage, often called storage or memory, refers to computer components and recording media that retain digital data. Data storage is one of the core functions and fundamental components of computers....
formatsFile formatA file format is a particular way that information is encoded for storage in a computer file.Since a disk drive, or indeed any computer storage, can store only bits, the computer must have some way of converting information to 0s and 1s and vice-versa. There are different kinds of formats for... - Scalable parallel preconditioners
- Krylov subspaceKrylov subspaceIn linear algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under the first r powers of A , that is,...
methods - Parallel Newton-basedNewton's methodIn numerical analysis, Newton's method , named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots of a real-valued function. The algorithm is first in the class of Householder's methods, succeeded by Halley's method...
nonlinear solvers - Parallel time-steppingNumerical ordinary differential equationsNumerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations...
(ODEOrdinary differential equationIn mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
) solvers - Automatic profiling of floating pointFloating pointIn computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
and memory usage - Consistent interfaceInterface (computer science)In the field of computer science, an interface is a tool and concept that refers to a point of interaction between components, and is applicable at the level of both hardware and software...
- Intensive error checking
- Portable to UNIXUnixUnix is a multitasking, multi-user computer operating system originally developed in 1969 by a group of AT&T employees at Bell Labs, including Ken Thompson, Dennis Ritchie, Brian Kernighan, Douglas McIlroy, and Joe Ossanna...
, Mac OS XMac OS XMac OS X is a series of Unix-based operating systems and graphical user interfaces developed, marketed, and sold by Apple Inc. Since 2002, has been included with all new Macintosh computer systems...
, and WindowsMicrosoft WindowsMicrosoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...
Modules
Some of the PETSc modules deal with- Index sets, including permutations, for indexingIndex (information technology)In computer science, an index can be:# an integer that identifies an array element# a data structure that enables sublinear-time lookup -Array element identifier:...
into vectors, renumbering, etc; - Vectors;
- MatricesMatrix (mathematics)In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
(generally sparseSparse matrixIn the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
); - Distributed arrays (useful for parallelizing regular grid-based problems);
- Krylov subspace methods;
- Preconditioners, including multigrid and sparse direct solvers;
- Nonlinear solvers; and
- Time-steppers for solving time-dependent (nonlinear) PDEs.