The Portable, Extensible Toolkit for Scientific Computation (PETSc, pronounced PET-see; the S is silent), is a suite of

data structures In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, a ...

and routines developed by

Argonne National Laboratory Argonne National Laboratory is a science and engineering research United States Department of Energy National Labs, national laboratory operated by University of Chicago, UChicago Argonne LLC for the United States Department of Energy. The facil ...

for the

scalable Scalability is the property of a system to handle a growing amount of work by adding resources to the system. In an economic context, a scalable business model implies that a company can increase sales given increased resources. For example, a ...

(

parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of IBM ...

) solution of scientific applications modeled by

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

. It employs the Message Passing Interface (MPI) standard for all message-passing communication. PETSc is the world’s most widely used parallel numerical software library for

and

sparse matrix In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...

computations. PETSc received an R&D 100 Award in 2009. The PETSc Core Development Group won the SIAM/ACM Prize in Computational Science and Engineering for 2015. PETSc is intended for use in large-scale application projects, many ongoing computational science projects are built around the PETSc

libraries A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

. Its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel

linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...

and

nonlinear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...

equation solvers that are easily used in application codes written in C,

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

, Fortran and now

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

. PETSc provides many of the mechanisms needed within parallel application code, such as simple parallel

matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

and

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

assembly routines that allow the overlap of

communication Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...

and

computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An es ...

. In addition, PETSc includes support for parallel distributed

arrays An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...

useful for

finite difference A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for t ...

methods.

Components

PETSc consists of a variety of components consisting of major classes and supporting infrastructure. Users typically interact with

objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...

of the highest level classes relevant to their application, essential lower level objects such as vectors, and may customize or extend any others. All major components of PETSc have an extensible plugin architecture.

Features and modules

PETSc provides many features for parallel computation, broken into several modules: * Index sets, including

permutations In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

, for

index Index (or its plural form indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on a Halo megastru ...

ing into vectors, renumbering, etc. * Parallel vectors; and

matrices Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

(generally sparse) * Scatters (handles communicating ghost point information) and

gathers Gathers is a surname. Notable people with the surname include: * Hank Gathers (1967–1990), American basketball player * James Gathers (1930–2002), American sprinter * Rico Gathers (born 1994), American basketball player See also * Mathers Ma ...

(the opposite of scatters) * Data management for parallel

structured Structuring, also known as smurfing in banking jargon, is the practice of executing financial transactions such as making bank deposits in a specific pattern, calculated to avoid triggering financial institutions to file reports required by law ...

and unstructured meshes * Several sparse

storage Storage may refer to: Goods Containers * Dry cask storage, for storing high-level radioactive waste * Food storage * Intermodal container, cargo shipping * Storage tank Facilities * Garage (residential), a storage space normally used to store car ...

formats * Scalable parallel

preconditioners In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing ...

, including

multigrid In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhi ...

and sparse direct solvers *

Krylov subspace In 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'' (starting from A^0=I), ...

methods * Parallel nonlinear solvers, such as

Newton's method In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...

and nonlinear GMRES * Parallel time-stepping (

ODE An ode (from grc, ᾠδή, ōdḗ) is a type of lyric poetry. Odes are elaborately structured poems praising or glorifying an event or individual, describing nature intellectually as well as emotionally. A classic ode is structured in three majo ...

and

DAE DAE or Dae may refer to: As an acronym * DAE (chemotherapy), a chemotherapy regimen consisting of Daunorubicin, Ara-C (cytarabine) and Etoposide * Daporijo Airport, the IATA code for an airport in India * Daxing Airport Express, the airport trans ...

) solvers * Parallel

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

solvers, such as BFGS * Automatic profiling of

floating point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

and

memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, ...

usage * Consistent

interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * ''Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Inte ...

* Intensive error checking * Portable to

UNIX Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, and ot ...

Mac OS X macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac (computer), Mac computers. Within the market of ...

, and

Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...

Notes

Bibliography

''PETSc Users Manual''
Satish Balay, Shrirang Abhyankar, Mark F. Adams, Jed Brown, Peter Brune, Kris Buschelman, Victor Eijkhout, William D. Gropp, Dinesh Kaushik, Matthew G. Knepley,

Lois Curfman McInnes Lois Virginia Curfman McInnes is an American applied mathematician who works as a senior computational scientist at Argonne National Laboratory, where she works on the numerical solution of nonlinear partial differential equations for scientific ap ...

, Karl Rupp, Barry F. Smith, and Hong Zhang, ANL-95/11 Revision 3.5, Argonne National Laboratory, June, 2014. * ''Efficient Management of Parallelism in Object Oriented Numerical Software Libraries'', Satish Balay, William D. Gropp, Lois Curfman McInnes, Barry F. Smith, Modern Software Tools in Scientific Computing, ed. Bruaset et al., pp. 163–202, 1997.
''Numerical simulation of geodynamic processes with the Portable Extensible Toolkit for Scientific Computation'', R.F. Katz, M.G. Knepley, B. Smith, M. Spiegelman, and E.T. Coon, Physics of The Earth and Planetary Interiors, 163, pp. 52-68, 2007.
* Ed Bueler: "PETSc for Partial Differential Equations: Numerical Solutions in C and Python", SIAM, {{ISBN, 978-1-611976-30-4 (2020).

External links

The Official PETSc web site
Numerical libraries Numerical linear algebra Scientific simulation software C++ numerical libraries