POWRE: New Numerical Algorithms for Particle Transport and Integral Equations

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This work is funded through the Professional Opportunities for Women in Research and Education (POWRE) program as a Visiting Professorship Activity. This proposal is for a visiting assistant professor position at the University of Iowa. Under this award, the PI will spend six months at the University of Iowa next Spring and Summer. The host institution will provide financial support for some of the PI's salary, and she is requesting half of her current salary from NSF POWRE funds. The invitation for this visit is important for the PI because there she can extend her current research through collaboration and discussions with well-known scientists in the areas of numerical analysis, computer science, and astronomy. The PI's areas of research are Numerical Methods for Particle Transport Problems and Numerical Methods for Large-Scale Eigenvalue Problems. Particle and radiation transport problems arise in many astronomical phenomena, such as the solar wind, radiation in the outer layers of the sun, and the behavior of dust clouds and nebulae illuminated by stars. (Dust clouds are considered to be the birth-place of stars.) Eigenvalue problems enter into particle transport problems as a way of solving criticality problems; that is, determining for what parameters there can be a self-sustaining reaction. This is of crucial importance in the areas of nuclear reactor design, and also in the initiation of nuclear activity in stars. The PI has developed new algorithms (sequential and parallel) for solving transport equations and eigenvalue problems. Transport equations are integro-differential equations, and the study of these equations can be fruitfully extended by deeper understanding of how the integral and differential terms interact. However, the new applications areas will lead to new equations, and to significantly new methods and ideas. The astronomical applications incorporate a number of new phenomena such as reaction terms, and strong interactions between the particles (or radiation) and the medium through which the particles move. The anticipated outcome from this project will be a deeper understanding of the mathematics arising in differential-integral equations which are related to transport phenoma, better sequential and parallel algorithms for equations in the related applications areas, and improvement of techniques available to astronomers for simulating and studying the activity of stars and the sun.