Home   Learning Computing History

Computational Science








A Brief History of Computational Science and Numerical Methods


Computational Science is an emerging field that using computers to analyze scientific problems, to gain understanding of science principally through the analysis of mathematical models on high performance computers. Numerical Methods utilized in computational science, which solve problems by approximation via numeric integrate or differentiate, it is as important to determine a safety factor for the approximation as to obtain the approximation. 

Computational Science is at the intersection of applied disciplines, mathematics and computer science. It is the de facto that computer revolutionized the way scientists do their work.  It is a new paradigm that has two essential uses: resolving outstanding issues and investigating new questions, both would not be possible without computational science.  The architectures in HPC more often involve pipelining, Flynn’s Taxonomy, Parallel computing and etc. 

It has made a new way -- numerical simulation, as a third methodology, to do science in addition to the traditional theory and physical experimentation. Using computational science, mathematical tools and theory have also being developed or improved on its own rights.   


A Brief History of Computational Science and High Performance Computing:

1940s, The Beginning of Computational Science with the working on ballistics and nuclear weapons design problems during the World War II, computer had showed its power and potential as to use older mathematical methods and develop new ones, especially on problems that require vast computations.

  • 1943: J. Presper Eckert, John V. Mauchly -- ENIAC founded by the army ordnance, a first programmable computer with electronic switches, which used to compute ballistics and late, the calculations of the hydrogen bomb, the research on the design of wind tunnels, random number generator, and weather prediction.
  • 1950: National Science Foundation (NSF) funding for scientific discovery which enabled many advances in computational science.
  • 1950s, IBM 7030 first parallel computers which overlap memory operations with processor, pipelining
  • 1964 Seymour Cray CDC6600 first used functional parallelism


1970s-1980s the adolescence of Computational Science supercomputing revolution, it began to make an industrial impact such as commercial aircraft design.

  • 1982: US DoD -- LAX Report sponsored project with large scale computing in science and engineering
  • 1984: NSF established five supercomputing centers in San Diego, Illinois, Pittsburgh, Cornell, and Princeton, which played important role for high-performance computing, visualization, and more.
  • 1986: K. Wilson defined computational science as: a precise mathematical statement, being tractable by traditional methods with a significant scope and require in depth knowledge of science, engineering and the arts.
  • 1985: Two Supercomputers
    • Sequent Balance 8000, which connected 20 processors
    • Intel iPSC1 hypercube <= 128 processors
  • 1985: NSF funded research on measuring stratospheric ozone loss at the South Pole.
  • 1987: K. Wilson article of “Grand Challenges to Computational Science” defined the grand challenge: “fundamental problems in science and engineering with potentially broad social, political and scientific impact, which could be advanced by applying high performance computing.”  Grand challenges are as such:
    • Simulation of X-Ray clusters
    • Genome sequencing and structural biology
    • Global climate modeling
    • Speech and language studies
    • Pharmaceutical design
    • Pollution and dispersion 

1990s-present the prime of life of Computational Science, the explosion of parallel computing as computers increasing in its problem-solving power, it has grown in breadth and importance and stands as an intellectual discipline, a powerful and indispensable method of analyzing.   

  • 1991: HPC Act of 1991/Public Law 102-194 congress passed the law and authorized the federal High Performance Computing and Communications Program.
  • 1992: Act of 1992 makes it accessible for k-graduate school.
  • 1993: Beijing 2nd International Conference on Computational Physics
  • 1998: DoD HPC Modernization Program, which designed allocate approximately 20% of total computational resource for high priority service/agency.
  • 1997: NSF’s PACI (Partnerships for Advanced Computational Infrastructure) program, it not only replace the old NSF supercomputer centers program, also formed new alliance partnerships in more than 50 academic facilities.  The goal is to building a prototype of next-generation information and computational infrastructure.
  • In 2000, NSF grant PSC (Pittsburgh Supercomputing Center) for TCS (Terascale Computing System), which geared at exceed six trillion operations per second.



Numerical Methods Analysis and advances has made computational science feasible, selected topics includes:

  • Floating-point arithmetic
  • Error, stability, convergence
  • Taylor’s series
  • Iterative solutions for finding roots/Newton’s Methods
  • Curve fitting, function approximation
  • Numerical differentiation and integration/Simpson’s Rule
  • Explicit and implicit methods
  • Differential equations/Euler’s Methods
  • Linear algebra
  • Finite differences

The purpose of numerical techniques is to solve non-algebraic equation to numerically integrate or numerically differentiate when there are difficult or analytically non-solvable.  The three main methods are finite differences, finite elements and spectral.  


There are wide ranges of computational applications established, such as: Computational Fluid Dynamics in Biology, Atmospheric Science in Economics, Seismology in Materials research, Structural Analysis in Medical Imaging, Chemistry in Animal Science, Magneto-hydrodynamics,  Reservoir Modeling, Global Ocean Modeling, Environmental Studies, and Nuclear Engineering. Computational science is at the leading edge of science and engineering and will have a fundamental impact on all disciplines ultimately.

Last modified: 2004 December 5