Computational science (or scientific computing) is the subfield of computer science^{[citation needed]} concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems.^[1] In practical use, it is typically the application of computer simulation and other forms of computation from theoretical computer science to problems in various scientific disciplines.

The field is a branch^{[citation needed]} of computer science (the study of computation, computersand information processing) but is 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.Computational science (or scientific computing) is the subfield of computer science^{[citation needed]} concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems.^[1] In practical use, it is typically the application of computer simulation and other forms of computation from theoretical computer science to problems in various scientific disciplines.

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 floating-point) and are often executed on supercomputers or distributed computing platforms.

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

[edit]Applications of computational science

Problem domains for computational science/scientific computing include:

[edit]Numerical simulations

Numerical simulations have different objectives depending on the nature of the task being simulated:

• Reconstruct and understand known events (e.g., earthquake, tsunamis and other natural disasters).
• Predict future or unobserved situations (e.g., weather, sub-atomic particle behaviour).

[edit]Model fitting and data analysis

• Appropriately tune models or solve equations to reflect observations, subject to model constraints (e.g. oil exploration geophysics, computational linguistics).

• Use graph theory to model networks, such as those connecting individuals, organizations, websites, and biological systems.

[edit]Computational optimization

• Optimize known scenarios (e.g., technical and manufacturing processes, front-end engineering).

[edit]Methods and algorithms

Algorithms and mathematical methods used in computational science are varied. Commonly applied methods include:

• Numerical analysis
• Application of Taylor series as convergent and asymptotic series
• Computing derivatives by Automatic differentiation (AD)
• Computing derivatives by finite differences
• Graph theoretic suites
• High order difference approximations via Taylor series and Richardson extrapolation
• Methods of integration on a uniform mesh: rectangle rule (also called midpoint rule), trapezoid rule, Simpson’s rule
• Runge Kutta method for solving ordinary differential equations
• Monte Carlo methods
• Molecular dynamics
• Linear programming
• Branch and cut
• Branch and Bound
• Numerical linear algebra
• Computing the LU factors by Gaussian elimination
• Cholesky factorizations
• Discrete Fourier transform and applications.
• Newton’s method
• Time stepping methods for dynamical systems

Programming languages and computer algebra systems commonly used for the more mathematical aspects of scientific computing applications include R (programming language), MATLAB, Mathematica,^[2] SciLab, GNU Octave, Python (programming language) withSciPy, and PDL.^{[citation needed]} The more computationally intensive aspects of scientific computing will often utilize some variation of C orFortran and optimized algebra libraries such as BLAS or LAPACK.

Computational science application programs often model real-world 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 high-performance computers in different ways to advance the state-of-the-art 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/observationand theory.^[3] The essence of computational science is numerical algorithm^[4] and/or computational mathematics.^[5] 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 Steeb, Hardy, Hardy and Stoop, 2004.^[6]

[edit]Education

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.

[edit]Related fields

[edit]See also

• Comparison of computer algebra systems
• List of molecular modeling software
• List of numerical analysis software
• List of statistical packages
• Simulated reality

[edit]References

[edit]Other references

• G. Hager and G. Wellein, Introduction to High Performance Computing for Scientists and Engineers, Chapman and Hall (2010)
• A.K. Hartmann, Practical Guide to Computer Simulations, World Scientific (2009)
• Journal Computational Methods in Science and Technology] (open access), Polish Academy of Sciences
• Journal Computational Science and Discovery, Institute of Physics
• R.H. Landau, C.C. Bordeianu, and M. Jose Paez, A Survey of Computational Physics: Introductory Computational Science, Princeton University Press (2008)

[edit]External links

• John von Neumann-Institut for Computing (NIC) at Juelich (Germany)
• The National Center for Computational Science at Oak Ridge National Laboratory
• Policy Reports on Computational Science
• Educational Materials for Undergraduate Computational Studies
• Computational Science at the National Laboratories