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*Not to be confused with computer engineering.*

**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).

**Computational science** 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.

**Computer science** is the study of processes that interact with data and that can be represented as data in the form of programs. It enables the use of algorithms to manipulate, store, and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems.

**Computer engineering** is a branch of engineering that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers usually have training in electronic engineering, software design, and hardware–software integration instead of only software engineering or electronic engineering. Computer engineers are involved in many hardware and software aspects of computing, from the design of individual microcontrollers, microprocessors, personal computers, and supercomputers, to circuit design. This field of engineering not only focuses on *how* computer systems themselves work, but also how they integrate into the larger picture.

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

A **Master of Science** is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine and is usually for programs that are more focused on scientific and mathematical subjects; however, different universities have different conventions and may also offer the degree for fields typically considered within the humanities and social sciences. While it ultimately depends upon the specific program, earning a Master of Science degree typically includes writing a thesis.

A **Doctor of Philosophy** is the highest university degree that is conferred after a course of study by universities in most English-speaking countries. PhDs are awarded for programs across the whole breadth of academic fields. As an earned research degree, those studying for a PhD are usually required to produce original research that expands the boundaries of knowledge, normally in the form of a thesis or dissertation, and defend their work against experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title *Doctor* or, in non-English-speaking countries, variants such as "Dr. phil." with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, educational, or research fields are usually addressed by this title "professionally and socially in a salutation or conversation." Alternatively, holders may use post-nominal letters such as "Ph.D.", "PhD", or "DPhil". It is, however, considered incorrect to use both the title and post-nominals at the same time.

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

A **simulation** is an approximate imitation of the operation of a process or system; the act of simulating first requires a model is developed. This model is a well-defined description of the simulated subject, and represents its key characteristics, such as its behaviour, functions and abstract or physical properties. The model represents the system itself, whereas the simulation represents its operation over time.

**Data science** is a multi-disciplinary field that uses scientific methods, processes, algorithms and systems to extract knowledge and insights from data in various forms, both structured and unstructured, and largely synonymous to data mining and big 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.

**C++** is a general-purpose programming language that was developed by Bjarne Stroustrup as an extension of the C language, or "C with Classes". It has imperative, object-oriented and generic programming features, while also providing facilities for low-level memory manipulation. It is almost always implemented as a compiled language, and many vendors provide C++ compilers, including the Free Software Foundation, Microsoft, Intel, and IBM, so it is available on many platforms.

**MATLAB** is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python.

**Python** is an interpreted, high-level, general-purpose programming language. Created by Guido van Rossum and first released in 1991, Python has a design philosophy that emphasizes code readability, notably using significant whitespace. It provides constructs that enable clear programming on both small and large scales. Van Rossum led the language community until stepping down as leader in July 2018.

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

**Combustion models for CFD** refers to combustion models for computational fluid dynamics. Combustion is defined as a chemical reaction in which a hydrocarbon fuel reacts with an oxidant to form products, accompanied with the release of energy in the form of heat. Being the integral part of various engineering applications like: internal combustion engines, aircraft engines, rocket engines, furnaces, and power station combustors, combustion manifests itself as a wide domain during the design, analysis and performance characteristics stages of the above-mentioned applications. With the added complexity of chemical kinetics and achieving reacting flow mixture environment, proper modeling physics has to be incorporated during computational fluid dynamic (CFD) simulations of combustion. Hence the following discussion presents a general outline of the various adequate models incorporated with the Computational fluid dynamic code to model the process of combustion.

Structural analysis is mainly concerned with finding out the behavior of a physical structure when subjected to force. This action can be in the form of load due to the weight of things such as people, furniture, wind, snow, etc. or some other kind of excitation such as an earthquake, shaking of the ground due to a blast nearby, etc. In essence all these loads are dynamic, including the self-weight of the structure because at some point in time these loads were not there. The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration in comparison to the structure's natural frequency. If a load is applied sufficiently slowly, the inertia forces can be ignored and the analysis can be simplified as static analysis. **Structural dynamics**, therefore, is a type of structural analysis which covers the behavior of structures subjected to dynamic loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subjected to dynamic loading. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis.

**Computational fluid dynamics** (**CFD**) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

- Applied mathematics
- Computational science
- Computational mathematics
- Computational fluid dynamics
- High-performance computing
- Engineering mathematics
- Grand Challenges
- Numerical analysis
- Multiphysics

**Applied mathematics** is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

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

**Engineering mathematics** is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an interdisciplinary subject motivated by engineers' needs both for practical, theoretical and other considerations outwith their specialization, and to deal with constraints to be effective in their work.

**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. As an aspect of mathematics and computer science that generates, analyzes, and implements algorithms, the growth in power and the revolution in computing has raised the use of realistic mathematical models in science and engineering, and complex numerical analysis is required to provide solutions to these more involved models of the world. 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.

**Monte Carlo methods** are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

A **discrete element method** (**DEM**), also called a **distinct element method**, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries. With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics. Recently, the method was expanded into the Extended Discrete Element Method taking thermodynamics and coupling to CFD and FEM into account.

**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.

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

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.

The following outline is provided as a topical overview of science:

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.

**FEATool Multiphysics** is a physics, finite element analysis (FEA), and PDE simulation toolbox for MATLAB and the cloud with rollApp. FEATool Multiphysics features the ability to model fully coupled heat transfer, fluid dynamics, chemical engineering, structural mechanics, 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 as convenient MATLAB m-code 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.

- ↑ "Computational Science and Engineering Program: Graduate Student Handbook" (PDF).
*cseprograms.gatech.edu*. September 2009.

- 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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