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CHAPTER 1
Introduction to Computational Modeling
1.1 THE IMPORTANCE OF COMPUTATIONAL SCIENCE
Advances in science and engineering have come traditionally from the application of the scientific method using theory and experimentation to pose and test our ideas about the nature of our world from multiple perspectives. Through experimentation and observation, scientists develop theories that are then tested with additional experimentation. The cause and effect relationships associated with those discoveries can then be represented by mathematical expressions that approximate the behavior of the system being studied.
With the rapid development of computers, scientists and engineers translated those mathematical expressions into computer codes that allowed them to imitate the operation of the system over time. This process is called simulation. Early computers did not have the capability of solving many of the complex system simulations of interest to scientists and engineers. This led to the development of supercomputers, computers with higher level capacity for computation compared to the general-purpose computers of the time. In 1982, a panel of scientists provided a report to the U.S. Department of Defense and the National Science Foundation urging the government to aid in the development of supercomputers (Lax, 1982). They indicated that “the primacy of the U.S. in science, engineering, and computing technology could be threatened relative to that of other countries with national efforts in supercomputer access and development.” They recommended both investments in research and development and in the training of personnel in science and engineering computing.
The capability of the computer chips in your cell phone today far exceeds that of the supercomputers of the 1980s. The Cray-1 supercomputer released in 1975 had a raw computing power of 80 million floating-point operations per second (FLOPS). The iPhone 5s has a graphics processor capable of 76.8 Gigaflops, nearly one thousand times more powerful (Nick, 2014). With that growth in capability, there has been a dramatic expansion in the use of simulation for engineering design and research in science, engineering, social science, and the humanities. Over the years, that has led to many efforts to integrate computational science into the curriculum, to calls for development of a workforce prepared to apply computing to both academic and commercial pursuits, and to investments in the computer and networking infrastructure required to meet the demands of those applications. For example, in 2001 the Society for Industrial and Applied Mathematics (SIAM) provided a review of the graduate education programs in science and engineering (SIAM, 2001). They defined computational science and engineering as a multidisciplinary field requiring expertise in computer science, applied mathematics, and a subject field of science and engineering. They provided examples of emerging research, an outline of a curriculum, and curriculum examples from both North America and Europe.
Yasar and Landau (2001) provided a similar overview of the interdisciplinary nature of the field. They also describe the possible scope of programs at the both the undergraduate and graduate levels and provide a survey of existing programs and their content. More recently, Gordon et al. (2008) described the creation of a competency-based undergraduate minor program in computational science that was put into place at several institutions in Ohio. The competencies were developed by an interdisciplinary group of faculty and reviewed by an industry advisory committee from the perspective of the skills that prospective employers are looking for in students entering the job market. The competencies have guided the creation of several other undergraduate programs. They have also been updated and augmented with graduate-level computational science competencies and competencies for data-driven science. The most recent version of those competencies can be found on the HPC University website (HPC University, 2016).
More recently, there have been a number of national studies and panels emphasizing the need for the infrastructure and workforce required to undertake large-scale modeling and simulation (Council on Competitiveness, 2004; Joseph et al., 2004; Reed, 2005; SBES, 2006). This book provides an introduction to computational science relevant to students across the spectrum of science and engineering. In this chapter, we begin with a brief review of the history or computational modeling and its contributions to the advancement of science. We then provide an overview of the modeling process and the terminology associated with modeling and simulation.
As we progress through the book, we guide students through basic programming principles using two of the widely used simulation environments—MATLAB® and Python. Each chapter introduces either a new set of programming principles or applies them to the solution of one class of models. Each chapter is accompanied by exercises that help to build both basic modeling and programming skills that will provide a background for more advanced modeling courses.
1.2 HOW MODELING HAS CONTRIBUTED TO ADVANCES IN SCIENCE AND ENGINEERING
There are a myriad of examples documenting how modeling and simulation has contributed to research and to the design and manufacture of new products. Here, we trace the history of computation and modeling to illustrate how the combination of advances in computing hardware, software, and scientific knowledge has led to the integration of computational modeling techniques throughout the sciences and engineering. We then provide a few, more recent examples of advances to further illustrate the state-of-the-art. One exercise at the end of the chapter provides an opportunity for students to examine additional examples and share them with their classmates.
The first electronic programmable computer was the ENIAC built for the army toward the end of World War II as a way to quickly calculate artillery trajectories. Herman Goldstine (1990), the project leader, and two professors from the University of Pennsylvania, J. Presper Eckert, and John Mauchly sold the idea to the army in 1942 (McCartney, 1999). As the machine was being built and tested, a large team of engineers and mathematicians was assembled to learn how to use it. That included six women mathematicians who were recruited from colleges across the country. As the machine was completed in 1945, the war was near an end.
ENIAC was used extensively by the mathematician John von Neumann not only to undertake its original purposes for the army but also to create the first weather model in 1950. That machine was capable of 400 floating-point operations per second and needed 24 hours to calculate the simple daily weather model for North America. To provide a contrast to the power of current processors, Peter and Owen Lynch (2008) created a version of the model that ran on a Nokia 6300 mobile phone in less than one second!
It is impossible to document all of the changes in computational power and its relationship to the advancements in science that have occurred since this first computer. Tables 1.1 and 1.2 show a timeline of the development of selected major hardware advances, software and algorithm development, and scientific applications from a few fields. Looking at the first column in Table 1.1, one can see the tremendous growth in the power of the computers used in large-scale scientific computation. Advances in electronics and computer design have brought us from the ENIAC with 400 flops to Blue Waters with 13.34 petaflops, an increase in the maximum number of floating-point operations per second of more than 1015!
TABLE 1.1 Timeline of Advances in Computer Power and Scientific Modeling (Part 1)
Example Hardware | Max. Speed | Date | Weather and Climate Modeling |
ENIAC | 400 Flops | 1945 | |
| | 1950 | First automatic weather forecasts |
UNIVAC | | 1951 | |
IBM 704 | 12 KFLOP | 1956 | |
| | 1959 | Ed Lorenz discovers the chaotic behavior of meteorological processes |
IBM7030 Stretch; UNIVAC LARC | 500-500 KFLOP | ~1960 | |
| | 1965 | Global climate modeling underway |
CDC6600 | 1 Megaflop | 1966 | |
CDC7600 | 10 MFLOP | 1975 | |
CRAY1 | 100 MFLOP | 1976 | |
CRAY-X-MP | 400 MFLOP | | |
| | 1979 | Jule Charney report to NAS |
CRAY Y-MP | 2.67 GFLOP | | |
| | 1988 | Intergovernmental Panel on Climate Change |
| | 1992 | UNFCCC in Rio |
IBM SP2 | 10 Gigaflop | 1994 | |
ASCII Red | 2.15 TFLOP | 1995 | Coupled Model Intercomparison Project (CMIP) | ...
