Computational science (or scientific computing) is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyse and solve scientific, social scientific and engineering problems. In practical use, it is typically the application of computer simulation and other forms of computation to problems in various scientific disciplines.
The field is distinct from computer science (the study of computation, computers and information processing). It is also different from theory and experiment which are the traditional forms of science and engineering. The scientific computing approach is to gain understanding, mainly through the analysis of mathematical models implemented on computers.
Scientists and engineers develop computer programs, application software, that model systems being studied and run these programs with various sets of input parameters. Typically, these models require massive amounts of calculations (usually floatingpoint) and are often executed on supercomputers or distributed computing platforms.
Numerical analysis is an important underpinning for techniques used in computational science.
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Problem domains for computational science/scientific computing include:
Numerical simulations have different objectives depending on the nature of the task being simulated:
Algorithms and mathematical methods used in computational science are varied. Commonly applied methods include:
Programming languages commonly used for the more mathematical aspects of scientific computing applications include R (programming language), MATLAB, Mathematica^{[1]}, SciLab, GNU Octave, COMSOL Multiphysics, Python (programming language) with SciPy, and PDL^{[citation needed]}. The more computationallyintensive aspects of scientific computing will often utilize some variation of C or Fortran and optimized algebra libraries such as BLAS or LAPACK.
Computational science application programs often model realworld changing conditions, such as weather, air flow around a plane, automobile body distortions in a crash, the motion of stars in a galaxy, an explosive device, etc. Such programs might create a 'logical mesh' in computer memory where each item corresponds to an area in space and contains information about that space relevant to the model. For example in weather models, each item might be a square kilometer; with land elevation, current wind direction, humidity, temperature, pressure, etc. The program would calculate the likely next state based on the current state, in simulated time steps, solving equations that describe how the system operates; and then repeat the process to calculate the next state.
The term computational scientist is used to describe someone skilled in scientific computing. This person is usually a scientist, an engineer or an applied mathematician who applies highperformance computers in different ways to advance the stateoftheart in their respective applied disciplines in physics, chemistry or engineering. Scientific computing has increasingly also impacted on other areas including economics, biology and medicine.
Computational science is now commonly considered a third mode of science, complementing and adding to experimentation/observation and theory. [1]. The essence of computational science is numerical algorithm^{[2]} and/or computational mathematics^{[3]}. In fact, substantial effort in computational sciences has been devoted to the development of algorithms, the efficient implementation in programming languages, and validation of computational results. A collection of problems and solutions in computational science can be found in ^{[4]}.
Scientific computation is most often studied through an applied mathematics or computer science program, or within a standard mathematics, sciences, or engineering program. At some institutions a specialization in scientific computation can be earned as a "minor" within another program (which may be at varying levels). However, there are increasingly many bachelor's and master's programs in computational science. Some schools also offer the Ph.D. in computational science, computational engineering, computational science and engineering, or scientific computation.
There are also programs in areas such as computational physics, computational chemistry, etc.
