LEAPS-MPS: Hybridizable discontinuous Galerkin methods for non-linear integro-differential boundary value problems in magnetic plasma confinement

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The goal of this project is to develop computational methods for the solution of a family of non-linear and integro-differential equations that arise from the study of magnetic equilibrium in axisymmetric fusion reactors. The tools and techniques developed as part of the project will contribute to the theoretical understanding of the behavior of magnetic confinement fusion. In addition, it will provide a tool to the plasma physics community for the efficient simulation of some of the processes taking place in a reactor. Thus, the project has the potential to contribute to the development of clean energy sources. As part of the broader goal of increasing the participation of ethnic minorities in Science, Technology, Engineering and Mathematics, the project will organize a colloquium addressed to undergraduate and beginning graduate students at the University of Arizona. The colloquium will feature mathematicians from underrepresented communities who are successful practitioners of mathematics in a variety of settings (academia, national laboratories, industrial research and development, and government agencies). Speakers will present a broad and accessible view of their research and will interact with the students, share advice and personal experiences related to the mathematical profession and their own educational career. This will serve the dual purpose of (1) challenging the perceived "traditional image" of a professional mathematician by showcasing the contributions of individuals with diverse cultural and ethnical backgrounds, and (2) providing students with several non-standard role models and a more diverse image of the mathematical profession. The scientific component of the project has two main goals: (1) devise and analyze hybridizable discontinuous Galerkin (HDG) discretizations for a broad class of non-linear elliptic integro-differential equations, and (2) apply the results obtained from the previous point into a freely available software implementation that can be used directly by the computational plasma physics community. The mathematical interest in the problems considered extends well beyond the field of plasma physics and will motivate the expansion of the theory of the HDG method into areas where it had not been applied before. From the point of view of applications, the project will develop a set of freely available computational tools and software that will directly influence the magnetic fusion community and can be beneficial to other areas of applied science and engineering.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.