High-order geometry conforming immersed finite element particle-in-cell method for plasma–material simulations with curved interfaces and nonhomogeneous jumps

Abstract

This work develops a high-order geometry-conforming immersed finite-element particle-in-cell (GCIFE--PIC) method for electrostatic plasma simulations with charged curved interfaces on Cartesian meshes. The potential is approximated by standard Legendre basis functions on ordinary elements and specially constructed GCIFE basis functions on interface elements, confining geometry-dependent constructions to interface elements to retain efficient regular-grid operations and represent curved interfaces without a fitted mesh. A separate function satisfies the prescribed nonhomogeneous jump conditions, allowing surface charge and one-sided deposited density to be treated consistently. Smooth tensor-product particle shapes contribute directly to the Poisson load through integrals against field test functions, avoiding intermediate nodal charge interpolation and, for supports crossing the interface, using side-restricted, normalized shapes to preserve represented charge and maintain deposition-gathering consistency. Absorbed particle charge is transferred to the curved interface through an arclength-normalized surface kernel. Boris--SDC advances particles within the self-consistent field update, completing the high-order coupling of field solution, particle transfer, and time integration. Numerical results validate the proposed method and show that even the lowest-order GCIFE--PIC yields higher accuracy than the bilinear IFE--PIC with straight-segment geometry approximation, providing a foundation for accurate high-order PIC simulations of complex charged interfaces.