  Criteria of selecting strain and fitting schemes are proposed for the
calculation of higher-order elastic constants more efficiently, robustly and
accurately. As demonstrated by the third-order elastic constants (TOECs) of
diamond, the proposed method is 3-5 times faster than existing methods, and the
range of strain for getting correct TOECs is expanded. In addition, our result
provides an evidence for the inaccuracy of some previous experiments caused by
higher-order effect, and the difference among experiments and several different
theoretical methods is resolved. Finally, we give the recommend TOECs values
for diamond.
