Collaborative Research: Lab-Data-Enabled Modeling, Numerical Methods, and Validation for a Three-Dimensional Interface Inverse Problem for Plasma-Material Interactions

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Plasma-material interactions play a crucial role in many science and engineering applications, including nanoparticle synthesis, soot formation in combustion, and space science. This collaborative project will advance the state of the art of computational plasma science and engineering, and applications related to plasma-material interactions. It will also prepare the next generation of researchers for the era of exascale computing on modern and future supercomputing platforms. This project provides undergraduate and graduate students valuable training opportunities in data-enabled modeling, development of numerical methods and code packages, mathematical analysis, and engineering applications. They will gain a solid foundation in computational math and data science, valuable research experience, and extensive collaboration experience with mathematicians and engineers. Starting from this collaborative work, the investigators plan to disseminate the proposed model, methods, and code packages to more engineers and scientists for solving their problems, present the work in professional conferences and colloquia, and organize special sessions in conferences for related works. In the Particle-In-Cell (PIC) method for plasma simulation involving materials, the electric potential is governed by the second-order elliptic interface problem with discontinuous dielectric coefficients and non-homogeneous flux jumps. Immersed finite element (IFE) methods are a class of accurate and efficient numerical methods for solving interface problems on structured meshes, which are desirable in PIC method because of the efficient particle-mesh interactions. However, in simulations involving conductors, one usually only knows the total electric charge quantity on the conductor surface, not the surface charge density, which is necessary for solving the second-order elliptic interface equation. Therefore, this project will start from the modeling for an inverse interface problem to identify the surface charge density based on the lab experiment data. According to the lab data availability, different mathematical considerations of the data in the cost functionals will lead to various adjoint problems. Then efficient iterative algorithms based on IFEs will be developed to solve the inverse problem. The key techniques to improve the IFE solver include new trilinear IFE basis functions, a partially penalized scheme, realistic interface shapes, and adaptive mesh refinement based on a posteriori error estimates. The numerical results will be compared with the corresponding lab experiment results. Finally, the developed model and method will be incorporated into PIC simulations of the charging of lunar landers/rovers/habitats and dusts under solar wind plasma conditions for lunar exploration.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.