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 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, and the functi ...

and routines developed by

Argonne National Laboratory Argonne National Laboratory is a Federally funded research and development centers, federally funded research and development center in Lemont, Illinois, Lemont, Illinois, United States. Founded in 1946, the laboratory is owned by the United Sta ...

for the

scalable Scalability is the property of a system to handle a growing amount of work. One definition for software systems specifies that this may be done by adding resources to the system. In an economic context, a scalable business model implies that ...

(

parallel Parallel may refer to: Mathematics * Parallel (geometry), two lines in the Euclidean plane which never intersect * Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Science a ...

) solution of scientific applications modeled by

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...

. It employs the

Message Passing Interface The Message Passing Interface (MPI) is a portable message-passing standard designed to function on parallel computing architectures. The MPI standard defines the syntax and semantics of library routines that are useful to a wide range of use ...

(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 ...

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 Book, books, and possibly other Document, materials and Media (communication), media, that is accessible for use by its members and members of allied institutions. Libraries provide physical (hard copies) or electron ...

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

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

and

nonlinear In mathematics and science, a nonlinear system (or a non-linear 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, mathe ...

equation solvers that are easily used in application codes written in C, C++, 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 (prog ...

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

matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ...

and

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

assembly routines that allow the overlap of

communication Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether Intention, unintentional or failed transmissions are included and whether communication not onl ...

and

computation A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, hist ...

. 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 . Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly d ...

methods.

Components

PETSc consists of a variety of components consisting of major classes and supporting infrastructure. Users typically interact with objects 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 (mathematics), set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example ...

, for

index Index (: indexes or 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 the Halo Array in the ...

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

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

(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 ...

(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 formats * Scalable parallel preconditioners, 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 e ...

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, the Newton–Raphson method, also known simply as Newton's 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 ...

and nonlinear GMRES * Parallel time-stepping (

ODE An ode (from ) is a type of lyric poetry, with its origins in Ancient Greece. Odes are elaborately structured poems praising or glorifying an event or individual, describing nature intellectually as well as emotionally. A classic ode is structu ...

and DAE) solvers * Parallel

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

solvers, such as BFGS * Automatic profiling of

floating point In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. Numbers of this form ...

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 remembe ...

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'' * '' Inter ...

* Intensive error checking * Portable to

UNIX Unix (, ; trademarked as UNIX) is a family of multitasking, multi-user 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, a ...

Mac OS X macOS, previously OS X and originally Mac OS X, is a Unix, Unix-based operating system developed and marketed by Apple Inc., Apple since 2001. It is the current operating system for Apple's Mac (computer), Mac computers. With ...

, and

Windows Windows is a Product lining, product line of Proprietary software, proprietary graphical user interface, graphical operating systems developed and marketed by Microsoft. It is grouped into families and subfamilies that cater to particular sec ...

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, 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