Today computation is considered as an equal partner with theory and experiment.

Computation provides a means of studying  complex natural phenomena that would be too expensive or dangerous to study by direct experimentation. With the advent of large-scale computers, computational methods and analysis have become indispensable for simulating physical events and engineering systems.  Computation has become integral part every sector of science and engineering, in addition to economic, social and cultural aspects of our daily life [1].

Computational engineering (CE) is a newly emerging multidisciplinary field that applies advanced computational techniques to engineering practice. It embraces engineering, science, applied mathematics, numerical analysis, and computer science. It applies techniques from these areas to solve complex scientific and engineering problems [2].

Computational engineers can build several physical prototypes and test their performance early in the design process. A computational engineer needs to have fundamental knowledge of engineering, advanced mathematics, algorithms, high-performance computing, and computer languages. He must use this knowledge to solve physics-based equations, simulate scenarios, and make predictions. FORTRAN is the most widely used programming language among scientific researchers. Although C++ and C are recently more popular, the scientific computing community has been reluctant to adopt C++ as the lingua franca. MATLAB and Python are also widely used [3].

Computational Modeling

Computational modeling usually involves the two major steps [4]:

• Modeling of a  system

• solving the resulting model equations using computational techniques

The model will normally allow us to express the behavior of the system in terms of ordinary differential equations (ODEs) or partial differential equations (PDEs). Computational modelling includes using numerical techniques to process, analyze and visualize data. There are basically three different numerical techniques available for solving engineering problems [5]:

• the finite-difference method (FDM)

• the finite-element method (FEM)

• the Monte Carlo method (MCM)

The FDM involves the simple discretization of ODEs or PDEs. The FEM  is a computational technique that divides solution region into non-overlapping meshes (or elements), typically triangles in two dimensions and tetrahedral in three dimensions. It is more powerful than FDM.  It is the most widely used method for numerical computations in all fields of engineering and can be regarded as a standard tool. The MCM is a nondeterministic numerical approach, unlike FDM and FEM. It is mostly used for solving stochastic problems.

ApplicationsComputational engineering finds diverse applications in many areas including aircraft design, electronic design automation, weather and climate prediction, predictive surgery, image analysis, trajectory calculation of satellites, battlefield simulation and military gaming, chemical pollution transport, nuclear weapons, computational electromagnetics, energy infrastructure, weather prediction and climate research, combustion, risk management and derivative pricing, oil and gas exploration, and particle physics.        For example, the automobile industry improves their products by modeling crashes by using high-performance simulation. Manufacturers of integrated circuits (ICs) models their products to minimize defects and power consumption [6].Benefits and ChallengesMany companies use CE tools to assist their engineers in analyzing, building, and testing new products because those tools help engineers to be more productive in their work. 

Computations offer a cost effective, attractive possibility for investigating and optimizing new products. They also help manufacturers reduce design costs, product cycle time, and time-to-market. Several companies have replaced the traditional process of design-build-test-and-repeat process with physics-based CE tools to design, mesh, and analyze new products with great success.  These include Goodyear, GM, Ford, 3M, Proctor and Gamble, Whirlpool, Boeing, and Pratt and Whitney [7].

Today, people regard computer-based prediction as very important in making critical decisions that impact every aspect of human existence.

However, some companies do not have the expertise to develop their own CE tools; they depend on commercially available packages such as MATLAB, MAPLE, MATHEMATICA,  and COMSOL. Today, meshes with 5 to 100 million elements are becoming feasible. The memory and processing requirements of such a huge mesh size means that producing interactive displays using a single graphics workstation is difficult if not impossible.

Computational engineering is relatively new branch of engineering that embraces engineering, applied mathematics, and computer science. Being a frontier field, practitioner comes from different walks of life [8]. 

The future holds many exciting possibilities for computational engineers.  There is a growing need for qualified computational engineers who can efficiently use CE tools to solve complex problems. To meet this need, universities across the world have started offering degrees at undergraduate and graduate levels on CE [9].

More information about CE can be found in [10,11] and in journals exclusively devoted to it: International Journal for Numerical Methods in Engineering, Journal of Computational Methods in Sciences and Engineering, IEEE Computational Science and Engineering, and Journal of Computational Engineering.

1. Mao, Z. and C. Yang. "Computational chemical engineering: Towards thorough understanding and precise application." Chinese Journal of Chemical Engineering, vol. 24, 2016, pp. 945–951.

2. SIAM Working Group on CSE Education. "Graduate education in computational science and engineering." SIAM Review, vol. 43, no. 1, 2001, pp. 163–177.

3. "Computational engineering." Wikipedia: The Free Encyclopedia, https://en.wikipedia.org/wiki/Computati onal_engineering.

4. Fangohr, H. Introduction to Python for Computational Science and Engineering: A Beginner's Guide. Sept. 2015, https://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf.

5. Sadiku, M.N.O. Computational Electromagnetics with MATLAB. 4th ed., CRC Press, 2018.

6. Post, D.E. and O. Goldfarb. "Enhancing product innovation with computational engineering." Computing in Science & Engineering, Nov.–Dec. 2017, pp. 4–5.

7. Post, D. "The promise of science-based computational engineering." Computing in Science & Engineering, May–June 2009, pp. 3–4.

8. Felippa, C.A. "Trends in computational engineering." Advances in Engineering Software, vol. 3, no. 2, 1981, pp. 50–54.

9. Peng, X. et al. "Infusing computational engineering tools in engineering design sequence curricula." Computer-Aided Design and Applications, vol. 7, no. 2, 2010, pp. 183–194.

10. Schäfer, M. Computational Engineering: Introduction to Numerical Methods. Springer-Verlag, 2006.

11. Hofstetter, G., editor. Computational Engineering. Springer-Verlag, 2014.