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Dune (mathematics Software)
DUNE (Distributed and Unified Numerics Environment) is a modular C++ library for the solution of partial differential equations using grid-based methods. The DUNE library is divided into modules. In version 2.9 are the core modules * general classes and infrastructure: ''dune-common'', * geometry classes: ''dune-geometry'', * grid interface: ''dune-grid'', * linear algebra classes: ''dune-istl'', * local ansatz functions: ''dune-localfunctions''. In addition, there are several further modules, including some which have been developed by third parties. History The development of DUNE started in 2002 on the initiative of Prof. Bastian (Heidelberg University), Dr. Ohlberger (during his habilitation at the University of Freiburg), and Prof. Rumpf (then University of Duisburg-Essen). The aim was a development model which was not attached to a single university, in order to make the project attractive for a wide audience. For the same reason a license was chosen which allows DUN ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linux
Linux ( ) is a family of open source Unix-like operating systems based on the Linux kernel, an kernel (operating system), operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically package manager, packaged as a Linux distribution (distro), which includes the kernel and supporting system software and library (computing), libraries—most of which are provided by third parties—to create a complete operating system, designed as a clone of Unix and released under the copyleft GPL license. List of Linux distributions, Thousands of Linux distributions exist, many based directly or indirectly on other distributions; popular Linux distributions include Debian, Fedora Linux, Linux Mint, Arch Linux, and Ubuntu, while commercial distributions include Red Hat Enterprise Linux, SUSE Linux Enterprise, and ChromeOS. Linux distributions are frequently used in server platforms. Many Linux distributions use the word "Linux" in their name, but the Free ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Volume
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. "Finite volume" refers to the small volume surrounding each node point on a mesh. Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a soluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C++ Libraries
C++ (, pronounced "C plus plus" and sometimes abbreviated as CPP or CXX) is a high-level programming language, high-level, general-purpose programming language created by Danish computer scientist Bjarne Stroustrup. First released in 1985 as an extension of the C (programming language), C programming language, adding object-oriented programming, object-oriented (OOP) features, it has since expanded significantly over time adding more OOP and other features; /C++98 standardization, C++ has added functional programming, functional features, in addition to facilities for low-level programming language, low-level memory (computing), memory manipulation for systems like microcomputers or to make operating systems like Linux or Microsoft Windows, Windows, and even later came features like generic programming, generic (template (C++), template) programming. C++ is usually implemented as a compiled language, and many vendors provide List of compilers#C.2B.2B compilers, C++ compilers, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Simulation Software
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which study the physical world, and the social sciences, which study individuals and societies. While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology. Meanwhile, applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine. The history of science spans the majority of the historical record, with the earliest identifiable predecessors to modern science dating to the Bronze Age in Egypt and Mesopotamia (). Their contributions to mathematics, astronomy, and medicine entered and shaped the Greek nat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Linear Algebra
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible. Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social scienc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Software
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compiler
In computing, a compiler is a computer program that Translator (computing), translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a lower level language, low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program.Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different Central processing unit, CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template Metaprogramming
Template metaprogramming (TMP) is a metaprogramming technique in which templates are used by a compiler to generate temporary source code, which is merged by the compiler with the rest of the source code and then compiled. The output of these templates can include compile-time constants, data structures, and complete functions. The use of templates can be thought of as compile-time polymorphism. The technique is used by a number of languages, the best-known being C++, but also Curl, D, Nim, and XL. Template metaprogramming was, in a sense, discovered accidentally. Some other languages support similar, if not more powerful, compile-time facilities (such as Lisp macros), but those are outside the scope of this article. Components of template metaprogramming The use of templates as a metaprogramming technique requires two distinct operations: a template must be defined, and a defined template must be instantiated. The generic form of the generated source code is describ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generic Programming
Generic programming is a style of computer programming in which algorithms are written in terms of data types ''to-be-specified-later'' that are then ''instantiated'' when needed for specific types provided as parameters. This approach, pioneered in the programming language ML in 1973, permits writing common functions or data types that differ only in the set of types on which they operate when used, thus reducing duplicate code. Generic programming was introduced to the mainstream with Ada in 1977. With templates in C++, generic programming became part of the repertoire of professional library design. The techniques were further improved and ''parameterized types'' were introduced in the influential 1994 book '' Design Patterns''. New techniques were introduced by Andrei Alexandrescu in his 2001 book '' Modern C++ Design: Generic Programming and Design Patterns Applied''. Subsequently, D implemented the same ideas. Such software entities are known as ''generics'' in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template (programming)
Templates are a feature of the C++ programming language that allows functions and classes to operate with generic types. This allows a function or class declaration to reference via a generic variable another different class (built-in or newly declared data type) without creating full declaration for each of these different classes. In plain terms, a templated class or function would be the equivalent of (before "compiling") copying and pasting the templated block of code where it is used, and then replacing the template parameter with the actual one. For this reason, classes employing templated methods place the implementation in the headers (*.h files) as no symbol could be compiled without knowing the type beforehand. The C++ Standard Library provides many useful functions within a framework of connected templates. Major inspirations for C++ templates were the parameterized modules provided by the language CLU and the generics provided by Ada. Technical overview T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Differences
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 denoted \Delta, is the operator (mathematics), operator that maps a function to the function \Delta[f] defined by \Delta[f](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. Certain Recurrence relation#Relationship to difference equations narrowly defined, recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for #Relation with derivatives, approximating derivatives, and the term "finite difference" is often used a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
