We present extensive testing in order to find the optimum balance among errors associated
with time integration, spatial discretization, and splitting for a fully spectral semi implicit
scheme of the phase field crystal model. The scheme solves numerically the equations of
dissipative dynamics of the binary phase field crystal model proposed by Elder et al.[Elder et
al, 2007]. The fully spectral semi implicit scheme uses the operator splitting method in order
to decompose the complex equations in the phase field crystal model into sub-problems that …

We present an efficient method to solve numerically the equations of dissipative dynamics of
the binary phase-field crystal model proposed by Elder et al.[KR Elder, M. Katakowski, M.
Haataja, M. Grant, Phys. Rev. B 75 (2007) 064107] characterized by variable coefficients.
Using the operator splitting method, the problem has been decomposed into sub-problems
that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-
implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive …