Discrete differential operators for scalable finite element plasma simulations

Finite element methods (FEMs) are capable of describing complex geometries, detailed boundary conditions, and variable material properties. As a result, they are especially well-suited to plasma simulations geared toward the design and prototype of fusion devices. Their rigorous mathematical structure furthermore ensures FEMs' fidelity to their underlying physical models. Nevertheless, the inefficient scaling of many FEMs can be prohibitive in time-dynamical simulations. In this work, we explore novel methods to overcome this limitation; we investigate various sparse approximations of finite element differential operators, offering scalable modifications to FEMs that preserve much of their appeal. We examine the utility of these approximation methods in simulations of plasma waves that span a wide spectrum of frequencies and applications. We further demonstrate that these approximations preserve the order of accuracy and mathematical structure of exact FEM methods. Our study provides a foundation for efficient, large-scale finite element plasma simulations in flexible and complex geometrical settings.