Development of Adaptive Sparse Grid Discontinuous Galerkin Methods for Multiscale Kinetic Simulations in Plasmas

This project aims at designing efficient numerical schemes for simulating complex plasma phenomena. Plasma is a state of matter similar to gas in which a certain portion of the particles is ionized. Understanding the complex behaviors of plasmas has led to important advances in areas ranging from space physics, fusion energy, to high-power microwave generation and large scale particle accelerators. There is strong need for laying out mathematical and algorithmic foundations for the design of efficient numerical methods so that we can advance basic research in plasma simulations. The algorithms developed in this project have the potential to provide high fidelity simulations in plasma physics with manageable computational cost and will have applications and impacts in multiscale simulations in fusion devices. The principal investigator (PI) will organize special events at professional meetings and workshops to promote the participation of female researchers. This project provides research training opportunities for graduate students. The objective of the project is to make significant advances on the design and analysis of a class of numerical methods called adaptive sparse grid (aSG) discontinuous Galerkin (DG) methods. The methods incorporate high order accurate DG solver that excels at transport simulations and the dimension reduction technique by aSG approach. The aim of this proposal is to advance the algorithmic foundations of the schemes for time-dependent PDEs, and push them onto the broader arena of multiscale simulations and applications for fusion science. The PI will investigate several fundamental issues including the analysis of CFL conditions, development of multiscale time stepping, postprocessing and hybrid aSG schemes. For a class of multiscale kinetic problems bridging kinetic and fluid models, by utilizing the multiresolution offered in the aSG-DG framework, the research will take advantage of both multiscale simulation tools and multiresolution on hierarchically defined meshes to achieve acceleration in computations. The schemes will be applied to simulations of runaway electrons in tokamak devices. 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.