(372m) Use of Numerical Software in Education and Research

Until the early 1980’s, main frame computer use in Engineering Education and Research involved mainly FORTRAN programming and less frequently CSMP programming coding. With the introduction of personal computers in the early 1990's, several types of interactive programs for numerical solution of engineering problems developed. The intention was to replace the old time consuming and often inaccurate solution techniques (such as 1. Analytical solutions that may include model simplification by neglecting less important terms and model manipulation to bring it into a solvable form. 2. Short-cut solution techniques where the problem is replaced by a simpler one that can be solved, 3. Trial and error solution techniques and 4. Graphical solutions) with numerical solution techniques. Over the years, several types of numerical solution packages have been developed and utilized: 1. Multi-purpose general mathematical packages such as POLYMATH[1], MAPLE[2], MATLAB[3], and Mathematica[4], 2. Spreadsheet programs, such as Excel[5], 3. Process Simulators, such as Aspen and HYSIS, 4. Computational Fluid Dynamics Packages and 5. Molecular Modeling.

About 15 years after the introduction of numerical software packages, surveys regarding the extent of their use in engineering education were conducted. One such survey was carried out by Jones (1998). His conclusion was that: “Across the country, computers are usually not used effectively in undergraduate engineering science courses. Often they are not used at all. Problem solving approaches and calculation methods are little influenced by the availability of computers.” Dahm et al (2002) reached the following conclusions regarding the use of process simulators at that time: “Chemical process simulation is currently underused in the chemical engineering curriculum at many schools . . . many respondents acknowledge that the role of simulators could be beneficially expanded in their curriculum.”

Our objective in this paper is to investigate the penetration of numerical software into engineering education and research in the last 20 years and summarize the current status. Our investigation at this time is limited to the utilization of the POLYMATH package.

The roles of the various numerical software packages in CHEG education, research and practice have been discussed, for example, by Shacham et al. 2009 and Shacham and Cutlip 2004. In this presentation, the extent of the use of the POLYMATH package (that was developed by the authors of this paper) over the last 20 years is reviewed. The educational part of the review is based mainly on textbooks where POLYMATH is utilized extensively for problem solving (Fogler, 2006, Cutlip and Shacham, 2008, Hagen, 2015 and Razdolsky, 2017). The “research” related part of the review utilizes the “Google Scholar” search for “POLYMATH Software” in the scientific literature.

The first version of POLYMATH was developed for the PLATO educational computer system (Shacham and Cutlip, 1982). The first commercially available version for the IBM PC was published in 1993. Versions of this program have been continuously updated and are now available now for the current Microsoft Windows and the Android operating systems.

The most widely used capabilities within the POLYMATH package include: 1. Single and several simultaneous nonlinear algebraic equations (NLE’s) solver, 2. Simultaneous ordinary differential equations (ODE’s) solver, and 3. Linear, polynomial multiple linear and general nonlinear regression.

POLYMATH was initially intended for educational use, and as such it has several user friendly features. These features include 1. Menu based (instead of command based) program control. 2. Notation and format of the equation entry are very similar to the notation and format of the mathematical model. 3. The program reorders the equations according to the computational sequence and detects implicit relationships among variables. 4. Several debugging aids identify possible programming errors. This last user friendly feature requires keeping the problems to be solved below a certain complexity level (Single-Model Single-Algorithm problems) that are adequate for undergraduate education. Further discussion of more complex problem types (such as Multiple-Model Multiple–Algorithm) and the way of POLYMATH utilization to help solve such problem is discussed for example by Cutlip et al. (2009).

The first textbooks that included POLYMATH numerical solutions to most of the examples presented started to appear toward the end of the nineteen nineties starting with Fogler’s “Elements of Chemical Reaction Engineering” (first in 1998 in the 3rd edition and now in the 2016 in the 5th Edition) and Cutlip and Shacham’s book “Problem Solving in Chemical and Biochemical Engineering with POLYMATH, Excel, and MATLAB” (first in 1999 and now in 2007 in the 2nd Edition). Articles mentioning the use of POLYMATH in research (non-educational) oriented journals started to appear in 2000.

In the paper by Lueking et. al (2000), the authors (from the department of Civil and Environmental engineering) used the nonlinear regression program of Polymath to determine the optimal parameter values of a Michaelis-Menten equation using experimental rate data. In the paper by Satrio et al. (2000), the authors (from the ChE department) used POLYMATH to determine reaction rate data from measured slopes of octyl acetate concentration vs. time plots.

Beginning with year 2000, the number of publications in which use of POLYMATH is reported have kept increasing continuously reaching about 50 publications per year in 2017. In 2018 there were (as of the end of March) 17 such publications. Details of these publications are provided in Table A-1 which is available in the full version of this Abstract which can be found at: ftp://ftp.bgu.ac.il/shacham/AIChEMeet18/Abstract18.docx .

Among the publications listed in Table A-1, there are educational and research articles, conference papers and one US Patent application. The authors are from 13 different countries, and they also belong to different academic departments: Chemical, Biological, Pharmaceutical, Environmental, Petroleum, Electrical and Computer Engineering, Chemistry and Agriculture. There is also a wide range of subjects investigated. In educational application, POLYMATH is most widely used for solving systems of ODEs obtained from material and energy balance on chemical reactors or similar equipment. In research, the nonlinear regression tool of POLYMATH is used most often, typically for determining optimal parameter values for rate expressions.

This historical study demonstrates that the use of numerical software for engineering and scientific problem solving is continuing to increase. Solving numerical problems should be finding many applications in STEM areas of study.

In the presentation, some examples will be shown in more detail. The selection of the numerical software package most appropriate for a particular problem, based on the complexity of the problem, will also be discussed.

References

1. Cutlip, M. B. and M. Shacham, "Problem Solving In Chemical Engineering with Numerical Methods." Prentice-Hall, Upper Saddle River, New-Jersey, 1999
2. Cutlip, M. B. and M. Shacham, "Problem Solving In Chemical and Biochemical Engineering with Polymath, Excel and MATLAB." Prentice-Hall, Upper Saddle River, New-Jersey, 2008
3. Cutlip, M. B., N. Brauner. and M. Shacham, "Biokinetic Modeling of Imperfect Mixing in a Chemostat – an Example of Multiscale Modeling", Chemical Engineering Education, 43, 243-248, 2009
4. Dahm, K. D. Hesketh, R. P. and M. J. Savelski, “Is Process Simulation Used Effectively In Che Courses?”, Chemical Engineering Education, 2002
5. Fogler, H.S., Elements of Chemical Reaction Engineering, 3^rd Edition, Prentice-Hall, New York, 1998
6. Hagen, J., "Industrial Catalysis: A Practical Approach," 3^rd edition, Wiley-VCH; 2015
7. Jones, J. B. “The Non-Use of Computers in Undergraduate Engineering Science Courses”, J. Engr. Ed., 87(1), 11, (1998).
8. Kyle, B. G., "Chemical and Process Thermodynamics," 3rd Edition, Prentice Hall, 1999
9. Lueking, A. D., Huang, W., Soderstrom-Schwarz, S., Kim, M. and W. J. Weber, Jr., “Relationship of soil organic matter characteristics to organic contaminant sequestration and bioavailability”, Journal of Environmental Quality; Madison, 29(1), 317(2000).
10. Razdolsky, L., Probability Based High Temperature Engineering: Creep and Structural Fire Resistance, Springer; 2017
11. Shacham, M. and M. B. Cutlip, "A Simulation Package for the PLATO System," Computers Chem. Engng., 6(3), 209-218 (1982).
12. Shacham, M. and M. B. Cutlip, "Enhancing Computer-Based Problem Solving Skills by Combination of Software Packages", Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition, Salt Lake City, Utah, June 20-23, 2004
13. Shacham, M., M. B. Cutlip and N. Brauner, "From Numerical Problem Solving to Model Based Experimentation – Incorporating Computer Based Tools of Various Scales into the ChE Curriculum", Chemical Engineering Education, Vol. 43. No. 4, 315- 321 (2009)
14. Tharakan, J., "Developing Creative and Critical Thinking Skills Through Open Ended Design Projects at the Freshman and Senior Level", Journal of Engineering Education Transformations , 31(3), 2018, ISSN 2349-2473, EISSN 2394-1707

[1] POLYMATH is copyrighted by M. Shacham, M. B. Cutlip and M. Elly (http://www.polymath-software.com)

[2] Maple is trademark of Waterloo Maple, Inc. (http:// www.maplesoft.com)

[3] MATLAB is trademark of Math Works, Inc.(http://www.mathworks.com)

[4] Mathematica is trademark of Wolfram Research, Inc. (http://www.wolfram.com)

[5] Excel is trademark of Microsoft Corporation (http://www.micro- soft.com)