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PETSc
The Portable, Extensible Toolkit for Scientific Computation (PETSc, pronounced PET-see; the S is silent), is a suite of data structures and routines developed by Argonne National Laboratory 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. PETSc is the world’s most widely used parallel numerical software library for partial differential equations and sparse matrix 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. Its careful design allows advanced users to have detailed control over the solution process. PETSc includes a large suite of parallel linear and nonlinear equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linux
Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which includes the kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name "GNU/Linux" to emphasize the importance of GNU software, causing some controversy. Popular Linux distributions include Debian, Fedora Linux, and Ubuntu, the latter of which itself consists of many different distributions and modifications, including Lubuntu and Xubuntu. Commercial distributions include Red Hat Enterprise Linux and SUSE Linux Enterprise. Desktop Linux distributions include a windowing system such as X11 or Wayland, and a desktop environment such as GNOME or KDE Plasma. Distributions intended for ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinearity
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 scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (computer Science)
In computer science, an object can be a variable, a data structure, a function, or a method. As regions of memory, they contain value and are referenced by identifiers. In the object-oriented programming paradigm, ''object'' can be a combination of variables, functions, and data structures; in particular in class-based variations of the paradigm it refers to a particular instance of a class. In the relational model of database management, an object can be a table or column, or an association between data and a database entity (such as relating a person's age to a specific person). Object-based languages An important distinction in programming languages is the difference between an object-oriented language and an object-based language. A language is usually considered object-based if it includes the basic capabilities for an object: identity, properties, and attributes. A language is considered object-oriented if it is object-based and also has the capability of polymorphism, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (computer Science)
In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name for the default constructor of the class (a subroutine that creates objects), and as the type of objects generated by instantiating the class; these distinct concepts are easily conflated. Although, to the point of conflation, one could argue that is a feature inherent in a language because of its polymorphic nature and why these languages are so powerful, dynamic and adaptable for use compared to languages without polymorphism present. Thus they can model dynamic systems (i.e. the real world, machine learning, AI) more easily. When an object is created by a constructor of the class, the resulting object is called an instance of the class, and the member variabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Library Structure
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 virtual space, or both. A library's collection can include printed materials and other physical resources in many formats such as DVD, CD and cassette as well as access to information, music or other content held on bibliographic databases. A library, which may vary widely in size, may be organized for use and maintained by a public body such as a government; an institution such as a school or museum; a corporation; or a private individual. In addition to providing materials, libraries also provide the services of librarians who are trained and experts at finding, selecting, circulating and organizing information and at interpreting information needs, navigating and analyzing very large amounts of information with a variety of resources. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Array Data Structure
In computer science, an array is a data structure consisting of a collection of ''elements'' (values or variables), each identified by at least one ''array index'' or ''key''. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index ''i'' has the address 2000 + (''i'' × 4). The memory address of the first element of an array is called first address, foundation address, or base address. Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 especially well-known discipline of the study of computation is computer science. Physical process of Computation Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers. This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing. An even more radical point of view, pancomputationalism (inaudible word), is the postulate of digital physics that argues that the evolution of the universe is itself ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Networking
A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are made up of telecommunication network technologies, based on physically wired, optical, and wireless radio-frequency methods that may be arranged in a variety of network topologies. The nodes of a computer network can include personal computers, servers, networking hardware, or other specialised or general-purpose hosts. They are identified by network addresses, and may have hostnames. Hostnames serve as memorable labels for the nodes, rarely changed after initial assignment. Network addresses serve for locating and identifying the nodes by communication protocols such as the Internet Protocol. Computer networks may be classified by many criteria, including the transmission medium used to carry signals, bandwidth, communications protocols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix, which allows computing in vector spaces. This provides a concise and synthetic way for manipulating and studying systems of linear eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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