Computational science (transferred from wiki)

Computational Science , also known as Scientific Computing , is a research field related to mathematical modelling, quantitative analysis and the use of computers to analyze and solve scientific problems. In practical application, computational science is mainly applied to: the problems in each science subject, computer simulation and other forms of calculation.

This field differs from computer science (research on Computing, computer, and information processing), but also differs from traditional forms of science and engineering-theory and experimentation. In order to get an understanding of scientific computing technology, it is necessary to analyze it by the mathematical model which is realized on computer.

Scientists and engineers have developed computer programs and application software to create models for the systems under study and to run them with multiple input parameters. In general, these models require a large number of computations (usually floating-point computations) that are often performed on supercomputers or distributed computing platforms.

Numerical analysis is an important basis for the techniques used in computational science.

Directory[Hide]

• 1 Applications
  • 1.1 Numerical simulation
  • 1.2 model Fitting and data analysis
  • 1.3 Calculation Optimization
• 2 methods and algorithms
• 3 Education
• 4 related fields
• 5 See also
• 6 References
• 7 External Links

Application

The problem domains of computational science include:

Numerical Simulation

Numerical simulations have various purposes, depending on the characteristics of the task being simulated:

• Reconstruct and understand known events (such as earthquakes, tsunamis, and other natural disasters).
• Predict future or unobserved conditions (such as weather, subatomic particle behavior).

model fit and data analysis

• Proper adjustment of the model or the use of observation to solve the equation, but also to obey the constraints of the model (such as oil exploration geophysics, computational linguistics).

• Use graph theory to create models of networks, especially those that are connected to individuals, organizations, and websites.

Calculation OptimizationMain article: Math optimization

• Optimized known solutions (e.g. process and manufacturing processes, front-end engineering).

methods and Algorithms

Algorithms and mathematical methods in computational science are diverse and commonly used methods include:

• Numerical analysis
• The application of Taylor series as Convergence and asymptotic series
• Differential calculation using automatic differential calculus
• Differential calculation using finite difference
• Graph theory Set
• Higher order differential approximation by Taylor series and Richardson extrapolation
• Integral method on homogeneous grids: Rectangle method, Trapezoid method, midpoint method and Simpson integral method
• Runge-Kutta method solutions to ordinary differential equations
• Monte Carlo method
• Molecular dynamics
• Numerical linear algebra
• Calculation of LU factor by Gaussian elimination method
• Cholesky decomposition
• Discrete Fourier transform and its application
• Newton's Method
• The time footwork of the dynamical system

Programming language is widely used in scientific computing applications, including R language, MATLAB, Mathematica^{[1], Scilab, GNU Octave, COMSOL multiphysics, scipy python language and so on. Scientific calculations biased towards intensive computing often take advantage of some variants of C or Fortran and the most optimized algebraic libraries such as Blas or Lapack.}

Computational science applications often create models of real-world changes, including weather, airflow around airplanes, deformation of car bodies in accidents, movement of stars in galaxies, and explosive devices. Such programs create a "logical grid" in computer memory, where each item in the grid corresponds to a region and contains information about the space associated with the model. For example, in a weather model, each item can be a square kilometer and contains the ground elevation, current wind direction, temperature, pressure, and so on. The program calculates the possible next state based on the current state in the simulation time step, solving the equation describing how the system works, and then repeating the process to calculate the next state.

The term "computational scientist" is often used to describe a skilled person in the field of scientific computing. They are usually scientists, engineers, or applied mathematicians who use high-performance computers in different ways to improve the most advanced theories and techniques in their respective disciplines of applied science, such as physics, chemistry, or engineering. Scientific computing also has an increasing influence on economics, biology and medicine.

Computational science is often regarded as the third method of science, which complements and expands the two methods of experiment/observation and theory. ^{[2] The essence of computational science is the numerical algorithm [3] as well as computational mathematics [4]. In the development of scientific computing algorithms, the effective realization of programming language and the confirmation of calculation results, people have made a substantial effort. A series of problems and solutions in computational science can be found in the relevant literature. [5]}

Education

In the syllabus of applied mathematics or computer science, or in the standard mathematical, scientific or engineering syllabus, there are often related courses in computational science. In some research universities, scientific computing can be used as a secondary major in another level or at different levels. In recent years, however, the number of bachelor's and master's degrees in computing science in Europe and the United States has been increasing, and some schools have PhD points in computational science, computational Engineering, Computational science and engineering, and scientific computing, and many schools in greater China have also offered undergraduate majors in information and computational science.

There are some schools in the fields of computational physics and computational chemistry.

related fields

Bio-Informatics Chemical Informatics Chemical Metrology Computational biology Computational chemistry Computational economics

Computational electromagnetics Computational Engineering Computational Finance Computational fluid dynamics Computational forensics Computational geophysics

Computational linguistics Computational mathematics Computational mechanics Computational neuroscience Computational particle physics Computational physics

Computational statistics Computer algebra Environmental simulation Financial modelling Geographic Information System (GIS) High Performance Computing

Machine learning Network analysis Numerical weather forecast Pattern recognition

See

• List of numerical analysis software
• Comparison of computer algebra systems
• List of statistical software
• List of modeling software for molecular mechanics
• (English) Computational Science Strategy Report

Reference Documents

1. ^  mathematica 6  scientific Computing World, May
2. ^   Association of Industrial and Applied Mathematics (SIAM)
3. ^   nonweiler T. R., 1986. Computational Mathematics:an Introduction to numerical approximation, John Wiley and Sons
4. ^  yang X. S., 2008. Introduction to computational mathematics, World Scientific publishing
5. ^  steeb w.-h., Hardy Y., Hardy A. and Stoop R., 2004. Problems and Solutions in scientific Computing with C + + and Java simulations, world scientific PUBLISHING. ISBN 981-2 56-112-9

External links

• Links to downloadable computational Tools
• Journal of advanced, in scientific Computing
• SIAM Journal on scientific Computing
• Computing in Science & Engineering Magazine
• Scientific Computing Magazine
• Educational materials for undergraduate computational studies
• Brockport State College Computational and science B.S, with reports
• The Institute for Computational Science & Engineering | icse| At the University of Michigan

Hidden Search--on--compiling computer science Fundamentals of Mathematics Mathematical logic set theory · Number Theory · graph theory · type theory · category theory · Numerical Analysis · information theory Computational theory Self-Motive · computable Theory · Computational complexity theory · Quantum Computing · Numerical calculation method Algorithms and data structures Algorithm Analysis · Algorithmic Design · Calculate Geometry Programming languages and compilers Grammar Analyzer · Interpreter · Programming paradigm (Procedural programming · Object-oriented program programming · Functional Programming · logic Programming, etc.) Concurrent, parallel, and distributed systems Multi-processor · Grid Computing · concurrency control Software Demand Analysis · Software Design · Programming · Formal Methods · Software Testing · Software development process System architecture Computer system Architecture · microprocessor Architecture · Operating System Telecommunications and networking Routing Network topology · Cryptographic Science Database Database management System · relational Database · Structured Query Language · NoSQL Transaction Processing · Database Index · Data Mining Artificial intelligence Automatic reasoning · Computational Linguistics · Computer Vision · Evolutionary Computing · Expert System · Machine Learning · Natural Language Processing · Robot Science Computer graphics Visualization · Computer Animation · image processing Interactive Computer-assisted features · User Interface · Wearable Computer · Pervasive Computing · Virtual Reality · chat robot Scientific calculations Artificial Life · Bioinformatics · Cognitive Science · Computational Chemistry · Computational Neuroscience · Computational Physics · numerical Algorithms · Symbolic calculation Note: Computer science can also be categorized according to the ACM-2012 classification system.

Classification:

• Computational Science

Computational science (transferred from wiki)