  Modeling via fractional partial differential equations or a L\'evy process
has been an active area of research and has many applications. However, the
lack of efficient numerical computation methods for general nonlocal operators
impedes people from adopting such modeling tools. We proposed an efficient
solver for the convection-diffusion equation whose operator is the
infinitesimal generator of a L\'evy process based on $\mathcal{H}$-matrix
technique. The proposed Crank Nicolson scheme is unconditionally stable and has
a theoretical $\mathcal{O}(h^2+\Delta t^2)$ convergence rate. The
$\mathcal{H}$-matrix technique has theoretical $\mathcal{O}(N)$ space and
computational complexity compared to $\mathcal{O}(N^2)$ and $\mathcal{O}(N^3)$
respectively for the direct method. Numerical experiments demonstrate the
efficiency of the new algorithm.
