REU Site: Research in Computational Mathematics

Florida State University, Tallahassee FL

Investigators

Abstract

Twelve undergraduates will be engaged in research experiences in computational mathematics for eight weeks during the summers of 2004 and 2005 at Florida State University. The basic model is for a pair of undergraduate students to work on a problem under the supervision of a post doctoral research fellow or faculty member. Short courses, workshops, and seminars will constitute important components of the experience. During the academic year following the summer experience, the students will be invited to participate in the regional SIAM -SEAS meeting. Student participants will be interviewed by a graduate student in Mathematics Education in order to determine the effectiveness of the REU approach and to provide input for improvements in the program. Some of the specific projects for Summer 2004 are indicated below. - Students will solve fluid dynamics problems using commercial codes and visualization programs under the guidance of Dr. Svetlana Poroseva. Students will learn to solve a sequence of fluid dynamics problems: mathematical formulation of the problem, choosing a method to solve it, building a mesh, solving the problem, analysis and visualization of results, presenting results to other students. - The students who work with Dr. Mohamed Jardak will solve numerically a simple stochastic ODE where either the initial condition or one of the coefficients in the equation is a random variable. Solutions to the Stochastic ODE's are obtained by making use of a random number generator or the stochastic collocation method. Consequently, the statistics of the solution, the mean, the variance and even the probability density function are determined. - Undergraduate researchers working with Dr. Shannon Grady would be responsible for making modifications to existing subroutines in order to study the optimal location of wind turbines (written in MATLAB) to make changes in wind models more seamless. After improvement of the existing code, model equations will be provided to one student to develop additional wake model subroutines and a second student would be working on converting the MATLAB codes to C in order to make use of supercomputing facilities. - A pair of students will be studying fuel cells with Dr. Jinquan Xu. After gaining perspective of the subject during the first few weeks, students will run the fuel cell modeling code, learn how to analyze and visualize the mathematical data. - Students working with Dr. Steven Blumsack will research current models of the spread of forest fires, then refine and implement models computationally over a range of parameter space. The site is supported by the Department of Defense in partnership with the NSF REU program.