Laboratory for Computational Science &
Engineering: High School Outreach Program
Program Goals:
• Introduce exposure to computational science
in the high school curriculum.
• Target talented high school students with an
interest in science and/or computing.
• Construct instructional materials that couple
computationally intensive applications to
graphical output through a point-and-click
user interface accessible to students.
Program Leverage:
• Build on course materials developed for
Woodward’s undergraduate-level course in
computational methods for the physical
sciences.
• Leverage computing and visualization
expertise at the LCSE.
• Leverage LCSE’s close connection with SGI.
• Leverage location of LCSE in the midst of
Minnesota’s major metro area.
The High School Teachers:
• Identify talented and motivated teachers.
• Bring teachers into the LCSE for 5 weeks each
summer to introduce them to real scientific
research environment and to cement personal
relationships they can draw upon during the
academic year.
• Involve the teachers in the choice of
instructional software and the design of the
user interfaces.
• Teachers test materials in their classes.
The High School Students:
• The high school teachers identify
outstanding, talented, and motivated
students to bring with them into the LCSE for
10 weeks during the summer.
• The students are involved in the design of the
user interfaces to the instructional software.
• The students learn C programming so that
they can modify/improve the user interfaces.
• The students help the teachers set up,
maintain, and operate instructional labs.
The High Schools:
• The high schools are large, public high
schools with diverse student bodies.
• The high schools are committed to the
program, and therefore support the teachers
with lab space and equipment.
• The high schools support the teachers by
allowing them to develop new courses that
grow out of their LCSE program experience.
• The high schools participate in other
advanced math and science programs.
Program Components:
• Development of computer programs for
instructional use.
Leveraged from Woodward’s undergraduate
course development work.
• Development of user interfaces to these
programs.
Performed by undergraduate student
employees.
• Development of written instructional
materials. LCSE postdoc part-time.
More Program Components:
• Guiding of work of teachers and high school
students in the LCSE in the summer.
LCSE postdocs, students, and staff.
• Assistance in high school lab set up and
maintenance.
LCSE system manager.
• LCSE lab tours for high school student groups.
LCSE staff.
• Overall program management.
Ms. Julia Sytine, LCSE Administrator.
Potential New Program Components:
• Summer programming course at LCSE for
group of 20 high school students.
Could potentially be taught by LCSE postdoc.
• Teacher training course at LCSE given for use
of LCSE instructional materials.
Could potentially be team taught by LCSE
postdoc and high school teachers who
helped develop these materials.
• A technology fair during the academic year
for computer-related projects.
Could be hosted at Arlington HS.
The Wave Table Program:
• Designed to duplicate a physically
realizable experiment — a square table
of shallow water with waves generated by
moving one side back and forth.
• Objects of different shapes which change
the water depth by different amounts
may be introduced.
• A graph of the wave amplitude along a
chosen horizontal line may be displayed
dynamically.
The Science:
• Wave propagation in 2-D observed.
• Wave reflection.
• Wave diffraction.
• Wave refraction.
• Focusing of wave energy by lenses.
• Focusing of wave energy by curved
mirrors.
• All can be directly observed; you can
actually see the waves.
Student Actively Involved:
• This application is interactive. The
student does not passively observe it; he
or she designs the experiment, runs it,
refines it, runs it again, . . .
• The result of the experiment can be
saved and shown as a movie to another
student, or to the instructor.
• The selected graphical output is
quantitative, while the wave displays are
more qualitative.
Computational Mathematics:
• This program represents the 2-D
Laplacian operator in the wave equation
2a/t2 = c2 2a
by an extremely simple 5-point difference
formula. The designated objects alter
the value of the local wave speed c and
each of 2562 uniform grid points is
updated on each time step by about 5
lines of Fortran code. The program runs
in real time and gives graphic output as
it executes.
Specific Example:
• Screen dumps saved from a run with a
high frequency wave input, two
completely reflecting rectangular
objects, and a refracting, lens-shaped
object are shown on the following slides.
• The first slide shows the problem set up.
• The dialog box at the upper left is shown
defining the lens-shaped object.
• The graphical data will correspond to
the horizontal dashed line.
The Heat Transfer Program:
• Designed to simulate a problem of real
concern for Minnesotans — heat
transfer in a house.
• A 2-D house floor plan is constructed by
placing rectangular objects of selected
materials onto a square region.
• An outside temperature on each side of
the house is specified.
• Regions of constant temperature (heat
registers, air conditioners) are specified
The Science:
• Heat transfer in 2-D is observed.
• Conduction front propagation and
spreading.
• Approach to asymptotic steady
temperature distribution.
• Behavior of materials with different
thermal conductivities.
• Variation of thermal insulation with
material layer thickness. Windows
versus walls. Brick versus wood.
Student Actively Involved:
• This application is interactive. The
student does not passively observe it; he
or she designs the experiment, runs it,
refines it, runs it again, . . .
• The result of the experiment can be
saved and shown as a movie to another
student, or to the instructor.
• This application is computationally
intensive. Runs are expensive and are
therefore must be planned thoughtfully.
Computational Mathematics:
• This program represents the 2-D
Laplacian operator in the heat equation
T/t =  2T
by an extremely simple 5-point difference
formula. The designated objects alter
the value of the local conductivity , and
each of 5122 uniform grid points is
updated on each time step by about 5
lines of Fortran code. The program runs
in the background, generating image
files for subsequent movie animation.
Specific Example:
• Images saved from a run for a fairly
elaborate 2-D house are shown on the
following slides.
• The first slide shows the material dialog
box used for problem set up.
• The second slide shows the blank house
layout area with outside temperature
selectors.
• The fifth slide shows the finished house,
then the heat transfer movie follows.
The Vibrating String Program:
• Designed to simulate a physical system
that can be realized in the lab — a
vibrating string (a slinky will also do).
• A set of points along the string are
selected with mouse clicks and dragged
up or down to pluck the string.
• Sliders allow the string tension, mass
per unit length, and transverse velocity
to be specified at each selected point.
• Intermediate values are interpolated.
The Science:
• Wave propagation in 1-D is observed.
• Initial velocities allow modes travelling
purely in one direction to be set up.
• String tension and density determine
local wave propagation speed.
• Wave transmission and reflection at
changes in string density and tension.
• Impedance matching to minimize wave
reflection, via gradual changes rather
than sudden ones in density or tension.
Student Actively Involved:
• This application is interactive. The
student does not passively observe it; he
or she designs the experiment, runs it,
refines it, runs it again, . . .
• The result of the experiment can be
saved and shown as a movie to another
student, or to the instructor.
• The default number of 2000 mass
points connected by 1999 springs can be
reduced, and convergence to continuous
string behavior can be observed.
Computational Mathematics:
• This program represents the string by a
discrete mechanical model consisting of
N mass points interconnected by N-1
springs. No calculus is needed, and the
equations of motion are trivial (but
many). Only Hooke’s law relating the
force linearly to spring extension is
needed, and of course F=ma. A trivial
leap-frog numerical scheme is implemented, with numerical noise damping.
The Fortran code is very simple, but
time steps cannot exceed Courant limit.
Specific Example:
• Images saved from a run for plucking the
string at 9 points are shown on the
following slides.
• The initial transverse velocities are 0, so
each triangular disturbance launches 2
identical half-amplitude signals traveling
in opposite directions.
• These waves all pass through each other,
since the equations are linear because
the transverse displacements are assumed small (and exaggerated in plots).
The Planetary System Program:
• Designed to simulate a physical system
that cannot be realized in the lab — a
solar system with 3 planets, named
Venus, Earth, and Mars.
• The default is the actual 3 planets,
begun at points on their actual orbits.
• The mass of each planet can be modified
by any positive factor.
• Either the planetary positions or the
orbit traces are displayed dynamically.
The Science:
• The actual orbits of these 3 planets may
be observed, but this is boring.
• One planet, say Earth, can be made
more massive, in which case it will
disrupt the other orbits, temporarily
capturing other planets as satellites
and/or ejecting them from the system.
• The sensitivity of this dynamical system,
when one planet is massive, to the initial
conditions (the big planet’s mass) has to
be seen to be believed.
Student Actively Involved:
• This application is interactive. The
student does not passively observe it; he
or she designs the experiment, runs it,
refines it, runs it again, . . .
• The result of the experiment can be
saved and shown as a movie to another
student, or to the instructor.
• The program can be instructed to use
different numerical integration
techniques, and their relative (and very
different) effectiveness can be studied.
Computational Mathematics:
• The program uses predictor-corrector
methods to advance the planets’
positions. The forces come from
Newton’s law of gravitation and F=ma.
The new position is first guessed using
the present position, velocity, and
acceleration only. This “prediction” is
then “corrected” by incorporating the
knowledge of the force at the newly
guessed position. Without this
correction step, the numerical scheme is
unstable. This scheme is really simple.
Specific Example:
• Planet positions for the default orbits
appear in the first set of slides.
• Planetary orbits are traced in the second
set of slides for a more interesting case.