Laboratory for Computational Science & Engineering: High School Outreach Program Program Goals:

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. Computational Mathematics: • This program represents the 2-D Laplacian operator in the wave equation2a/t2 = c2 2aby 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.

14. 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.

27. 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

28. 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.

29. 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.

30. Computational Mathematics: • This program represents the 2-D Laplacian operator in the heat equationT/t =  2Tby 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.

31. 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.

50. 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.