Feasibility of ultraweak-DPG approach for radio-frequency wave simulation in plasmas

The high frequency (>MHz) radio-frequency (RF) wave fullwave simulation typically solves the time-harmonic second order Maxwell equation. However, the resultant discretized linear system is indefinite and the plasma dielectric response involves strong anisotropy, the resultant linear system is difficult to pre-condition. Thus, in most simulations, we rely on the distributed sparse linear solvers. A promising alternative is the ultraweak Discontinuous Petrov-Galerkin (DPG) method, in which the first order equation for E and H are solved. This approach yields a definite linear system, which could be solved iteratively with standard pre-conditioners like Conjugate Gradient (CG). Furthermore, the formulation provides an error estimator, enabling adaptive mesh refinement. We successfully implemented this method for simulation of the propagation of simplified lower hybrid (LH) waves launched from a grill-type launcher, confirming that the mesh refinement occurs selectively along the wave trajectory. Extension to induce a full cold plasma dielectric tensor model and to other wave branches such as ICRF waves is under-way. Possible enhancement to include the finite temperature effects using the spectrally-equivalent differential operators will be discussed.