POWRE: New Numerical Algorithms for Particle Transport and Integral Equations

这项工作是通过妇女在研究和教育中的职业机会方案作为访问教授活动资助的。 这份建议书是关于爱荷华州大学的客座助理教授职位的。根据这项奖励，PI将在明年春季和夏季在爱荷华州大学度过六个月。主办机构将为PI的部分工资提供财政支持，她要求从NSF POWRE基金中获得目前工资的一半。 这次访问的邀请对PI来说很重要，因为在那里她可以通过与数值分析，计算机科学和天文学领域的知名科学家合作和讨论来扩展她目前的研究。 PI的研究领域是粒子输运问题的数值方法和大规模特征值问题的数值方法。 粒子和辐射传输问题出现在许多天文现象中，例如太阳风，太阳外层的辐射，以及被恒星照亮的尘埃云和星云的行为。 (Dust云被认为是恒星的诞生地。 本征值问题作为解决临界问题的一种方法进入粒子输运问题;也就是说，确定什么参数可以有一个自持反应。 这在核反应堆设计以及恒星核活动的启动方面至关重要。 PI已经开发了新的算法（顺序和并行）求解输运方程和本征值问题。 输运方程是积分-微分方程，通过深入理解积分项和微分项之间的相互作用，可以有效地扩展对这些方程的研究。 然而，新的应用领域将导致新的方程，并显着新的方法和想法。 天文学的应用包括了许多新的现象，如反应项，和强相互作用之间的 粒子（或辐射）和粒子运动的介质。 该项目的预期成果将是更深入地了解与输运现象有关的微分-积分方程中的数学，在相关应用领域中更好地使用方程的顺序和并行算法，以及改进天文学家模拟和研究恒星和太阳活动的技术。

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.