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For the stationary Wigner equation with inflow boundary conditions, itsnumerical convergence with respect to the velocity mesh size are deteriorateddue to the singularity at velocity zero. In this paper, using the fact that thesolution of the stationary Wigner equation is subject to an algebraicconstraint, we prove that the Wigner equation can be written into a form with abounded operator $\mathcal{B}[V]$, which is equivalent to the operator$\mathcal{A}[V]=\Theta[V]/v$ in the original Wigner equation under someconditions. Then the discrete operators discretizing $\mathcal{B}[V]$ areproved to be uniformly bounded with respect to the mesh size. Based on thetherectical findings, a signularity-free numerical method is proposed.Numerical reuslts are proivded to show our improved numerical scheme performsmuch better in numerical convergence than the original scheme based ondiscretizing $\mathcal{A}[V]$.

Singularity-free Numerical Scheme for the Stationary Wigner Equation