A p-adaptive hybridizable discontinuous Galerkin spectral element method for electrostatic particle-in-cell simulations

This paper extends the high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for electrostatic particle-in-cell (PIC) simulations developed by Pfeiffer et al. (2019) to support p-adaptation. This approach enables element-local refinement of the polynomial degree, concentrating computational effort specifically in regions with strong gradients. Thus, the method significantly reduces the global number of degrees of freedom compared to uniform high-order methods. The proposed method is implemented in the open-source framework PICLas and validated through a series of benchmark test cases, including a dielectric sphere and a one-dimensional plasma sheath. Finally, a two-dimensional axisymmetric simulation of an ion optic demonstrates the method’s capability to efficiently model complex plasma phenomena but also highlights limitations in the current p-adaptation procedure.