  Performance evaluations on the deterministic algorithms for 6-D problems are
rarely found in literatures except some recent advances in the Vlasov and
Boltzmann community [Dimarco et al. (2018), Kormann et al. (2019)], due to the
extremely high complexity. Thus a detailed comparison among various techniques
shall be useful to the researchers in the related fields. We try to make a
thorough evaluation on a parallel CHAracteristic-Spectral-Mixed (CHASM) scheme
to support its usage. CHASM utilizes the cubic B-spline expansion in the
spatial space and spectral expansion in the momentum space, which many
potentially overcome the computational burden in solving classical and quantum
kinetic equations in 6-D phase space. Our purpose is three-pronged. First, we
would like show that by imposing some effective Hermite boundary conditions,
the local cubic spline can approximate to the global one as accurately as
possible. Second, we will illustrate the necessity of adopting the truncated
kernel method in calculating the pseudodifferential operator with a singular
symbol, since the widely used pseudo-spectral method [Ringhofer (1990)] might
fail to properly tackle the singularity. Finally, we make a comparison among
non-splitting Lawson schemes and Strang operator splitting. Our numerical
results demonstrate the advantage of the one-stage Lawson predictor-corrector
scheme over multi-stage ones as well as the splitting scheme in both accuracy
and stability.
