  We present a new computation method for simulating reflection high-energy
electron diffraction and the total-reflection high-energy positron diffraction
experiments. The two experiments are used commonly for the structural analysis
of material surface. The present paper improves the conventional numerical
method, the multi-slice method, for faster computation, since the present
method avoids the matrix-eigenvalue solver for the computation of matrix
exponentials and can adopt higher-order ordinary differential equation solvers.
Moreover, we propose a high-performance implementation based on multi-thread
parallelization and cache-reusable subroutines. In our tests, this new method
performs up to 2,000 times faster than the conventional method.
