The Synergy of Scientific Computing and Computer Science

1
The Synergy of Scientific Computing and Computer
Science

• Sanjukta Bhowmick
  
• Columbia University and Argonne National
  Laboratory

2
What is Scientific Computing ?
Application Code (physics, chemistry,
biology,)
Computer Science
Applied Mathematics (numerical analysis,
modeling)
Scientific Computing

• Scientific computing is the field of study
  concerned with constructing mathematical models
  and numerical solution techniques and using
  computers to analyze and solve scientific and
  engineering problems.
• Numerical Analysis is the study of algorithms for
  the problems of continuous mathematics--Trefethen
  1992
• Computer Science involves discrete problems

3
Scientific Computing and Computer Science

• The field is distinct from computer science
  Wikipedia
• Computer science began as an interdisciplinary
  subject once synonymous with scientific
  computing. Today, the two have little in common
  besides the transposed names. - NA-Digest Survey
  1999
• Scientific Computing as a discipline is more
  often offered by computer science departments

4
Some Topics in Computer Science

• Computer Architecture Operation Systems
• Algorithms
• Visualization
• Database Management
• Programming Languages
• Compiler Design
• Software Engineering
• Machine Learning

5
Scientific Computing and Computer Development

• Computer architecture and hardware provide
  platforms for simulating scientific computing
  applications
• Scientific computing problems are the motivation
  for development of supercomputers
• 2005 Blue Gene IBM,MHD, ITER(Nuclear Fusion)
• 2002 Earth Simulator NASDA, JAERI, and JAMSTEC ,
  Computational Earth Science Research Program
• 1972 Cray1 Seymour Cray Los Alamos National
  Laboratory
• .. as well as the first models
• 1944 Harvard Mark 1Howard Aiken and Grace
  Hopper used by the US Navy for gunnery and
  ballistic calculations
• 1946 ENIAC I John Mauchly and J Presper Eckert
  used as a calculating device for writing
  artillery-firing tables
• 1936 Z1 Konrad Zuse used for lengthy
  engineering calculations for Henschel Aircraft
  Company

1943 Church-Turing Thesis (Introducing Turing
Machines)
6
Algorithms are Important

• Moore's Law(1965)--- the number of transistors
  on an integrated circuit (computing power)
  doubles every 24 months.
• Over 36 years, processor architecture goes
  through 18 doubling periods
• Algorithms produce an equal factor of speedup on
  a small problem much more on a larger problem

Speedup on a 3D Poisson problem
Slide from David Keyes Lectures
Many branches of computer science are being
tapped to create better algorithms
7
Algorithms are Important

• Moore's Law(1965)--- the number of transistors
  on an integrated circuit (computing power)
  doubles every 24 months.
• Over 36 years, processor architecture goes
  through 18 doubling periods
• Algorithms produce an equal factor of speedup on
  a small problem much more on a larger problem

Speedup on a 3D Poisson problem
Many branches of computer science are being
tapped to create better algorithms
8
Combinatorial Scientific Computing

• When the arithmetic is easy and the challenge
  lies in efficient reordering a sequence of
  operations computational science turns to graph
  theory---L.N. Trefethen
• Many algorithms from graph theory are used in
  scientific computing
• Graph and Hyper-graph partitioning, coloring,
  matching, reordering
• Graph algorithms are applied to many areas in
  scientific computing
• Load balancing
• Sparse Direct Solvers
• Preconditioners
• Performance Improvement (Automatic
  Differentiation)
• Simulations for applications from physics,
  biology, etc.

See Poster 15 (CSCAPES Poster)
9
Numerical Algorithms in Computer Science

• Computer applications also benefit from numerical
  algorithms
• Singular Value Decomposition are used in image
  compression
• Fast Fourier Transform used in multiplying long
  integers (Schönhage-Strassen algorithm)
• Eigen Values in Principal Component Analysis

10
Visualization Tools

• Visualization tools are important in advancing
  scientific computing
• understanding of the solution schemes
• understanding the underlying physics and
  mechanics of the application
• performance analysis
• Goals for Visualization tools (excerpt from Top
  Scientific Visualization ResearchC. R. Johnson)
• Understanding science
• Quantify effectiveness
• Human computer interaction
• Integrated problem solving environment

11
Some Topics in Computer Science

• Computer Architecture Operation Systems
• Algorithms
• Visualization
• Database Management
• Programming Languages
• Compiler Design
• Software Engineering
• Machine Learning

12
Maxims about Numerical Mathematics, Computer
Science and LifeL.N. Trefethen

• There are three great branches of sciencetheory,
  experiment and computation
• A computational study is unlikely to lead to real
  scientific progress unless the software
  environment can encourage one to vary
  parameters, and modify the problem

Computer science disciplines contribute to the
multidisciplinary nature of scientific computing