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**Computational science and engineering** (**CSE**) is a relatively new discipline that deals with the development and application of computational models and simulations, often coupled with high-performance computing, to solve complex physical problems arising in engineering analysis and design (computational engineering) as well as natural phenomena (computational science). CSE has been described as the "third mode of discovery" (next to theory and experimentation).^{ [1] } In many fields, computer simulation is integral and therefore essential to business and research. Computer simulation provides the capability to enter fields that are either inaccessible to traditional experimentation or where carrying out traditional empirical inquiries is prohibitively expensive. CSE should neither be confused with pure computer science, nor with computer engineering, although a wide domain in the former is used in CSE (e.g., certain algorithms, data structures, parallel programming, high performance computing) and some problems in the latter can be modeled and solved with CSE methods (as an application area).

It is typically offered as a masters or doctorate program at several institutions.

Computational Science and Engineering methods and frameworks include:

- High performance computing and techniques to gain efficiency (through change in computer architecture, parallel algorithms etc.)
- Modeling and simulation
- Algorithms for solving discrete and continuous problems
- Analysis and visualization of data
- Mathematical foundations: Numerical and applied linear algebra, initial & boundary value problems, Fourier analysis, optimization
- Data Science for developing methods and algorithms to handle and extract knowledge from large scientific data

With regard to computing, computer programming, algorithms, and parallel computing play a major role in CSE. The most widely used programming language in the scientific community is FORTRAN. Recently, C++ and C have increased in popularity over FORTRAN. Due to the wealth of legacy code in FORTRAN and its simpler syntax, the scientific computing community has been slow in completely adopting C++ as the lingua franca. Because of its very natural way of expressing mathematical computations, and its built-in visualization capacities, the proprietary language/environment MATLAB is also widely used, especially for rapid application development and model verification. Python along with external libraries (such as NumPy, SciPy, Matplotlib) has gain some popularity as a free and Copycenter alternative to MATLAB.

Computational Science and Engineering finds diverse applications, including in:

- Aerospace Engineering and Mechanical Engineering: combustion simulations, structural dynamics, computational fluid dynamics, computational thermodynamics, computational solid mechanics, vehicle crash simulation, biomechanics, trajectory calculation of satellites
- Astrophysical systems
- Battlefield simulations and military gaming, homeland security, emergency response
- Biology and Medicine: protein folding simulations (and other macromolecules), bioinformatics, genomics, computational neurological modeling, modeling of biological systems (e.g., ecological systems), 3D CT ultrasound, MRI imaging, molecular bionetworks, cancer and seizure control
- Chemistry: calculating the structures and properties of chemical compounds/molecules and solids, computational chemistry/cheminformatics, molecular mechanics simulations, computational chemical methods in solid state physics, chemical pollution transport
- Civil Engineering: finite element analysis, structures with random loads, construction engineering, water supply systems, transportation/vehicle modeling
- Computer Engineering, Electrical Engineering, and Telecommunications: VLSI, computational electromagnetics, semiconductor modeling, simulation of microelectronics, energy infrastructure, RF simulation, networks
- Epidemiology: influenza spread
- Environmental Engineering and Numerical weather prediction: climate research, Computational geophysics (seismic processing), modeling of natural disasters
- Finance: derivative pricing, risk management
- Industrial Engineering: discrete event and Monte-Carlo simulations (for logistics and manufacturing systems for example), queueing networks, mathematical optimization
- Material Science: glass manufacturing, polymers, and crystals
- Nuclear Engineering: nuclear reactor modeling, radiation shielding simulations, fusion simulations
- Petroleum engineering: petroleum reservoir modeling, oil and gas exploration
- Physics: Computational particle physics, automatic calculation of particle interaction or decay, plasma modeling, cosmological simulations
- Transportation

**Numerical analysis** is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

**Computational physics** is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science.

**Computer science** is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. One well known subject classification system for computer science is the ACM Computing Classification System devised by the Association for Computing Machinery.

**Theoretical computer science** (**TCS**) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

**Computational science**, also known as **scientific computing** or **scientific computation** (**SC**), is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core it involves the development of models and simulations to understand natural systems.

**Numerical methods for partial differential equations** is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).

**Mesh generation** is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. The goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.

In engineering, mathematics, physics, chemistry, bioinformatics, computational biology, meteorology and computer science, **multiscale modeling** or **multiscale mathematics** is the field of solving problems which have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids, solids, polymers, proteins, nucleic acids as well as various physical and chemical phenomena.

**Computational mechanics** is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.

**Numerical linear algebra** is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to mathematical questions. It is a subfield of numerical analysis, and a type of linear algebra. Because computers use floating-point arithmetic, they cannot exactly represent irrational data, and many algorithms increase that imprecision when implemented by a computer. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize computer error while retaining efficiency and precision.

*Computational mathematics* may refer to two different aspects of the relation between computing and mathematics.

The * SIAM Journal on Scientific Computing* (

The **Sidney Fernbach Award** established in 1992 by the IEEE Computer Society, in memory of Sidney Fernbach, one of the pioneers in the development and application of high performance computers for the solution of large computational problems as the Division Chief for the Computation Division at Lawrence Livermore Laboratory from the late 1950s through the 1970s. A certificate and $2,000 are awarded for outstanding contributions in the application of high performance computers using innovative approaches. The nomination deadline is 1 July each year.

The following outline is provided as an overview of and topical guide to formal science:

**FEATool Multiphysics** is a physics, finite element analysis (FEA), and PDE simulation toolbox. FEATool Multiphysics features the ability to model fully coupled heat transfer, fluid dynamics, chemical engineering, structural mechanics, fluid-structure interaction (FSI), electromagnetics, as well as user-defined and custom PDE problems in 1D, 2D (axisymmetry), or 3D, all within a simple graphical user interface (GUI) or optionally as convenient script files. Having specifically been designed to have a low learning curve and to be able to be used without requiring reading documentation, FEATool has been employed and used in academic research, teaching, and industrial engineering simulation contexts.

*Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.*

- ↑ "Computational Science and Engineering Program: Graduate Student Handbook" (PDF).
*cseprograms.gatech.edu*. September 2009. Archived from the original (PDF) on 2014-10-14. Retrieved 2012-04-08.

- Oden Institute for Computational Engineering and Sciences
- Scope of Computational engineering
- Society of Industrial and Applied Mathematics
- International Centre for Computational Engineering (IC2E)
- Georgia Institute of Technology, USA, MS/PhD Programme Computational Science & Engineering
- The graduate program for the University of Tennessee at Chattanooga
- Master and PhD Program in Computational Modeling at Rio de Janeiro State University
- Computational Science and Engineering with Scilab
- Internacional Center for Numerical Methods in Engineering (CIMNE)

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