Accuracy control in ultra-large-scale electronic structure calculations

Numerical aspects are investigated in ultra-large-scale electronic structure calculations. Accuracy control methods in process (molecular-dynamics) calculations are focused upon. Flexible control methods are proposed so as to control variational freedoms, automatically at each time step, within the framework of generalized Wannier state theory. The method is demonstrated in a silicon cleavage simulation with 10(2)-10(5) atoms. The idea is of general importance among process calculations and is also used in Krylov subspace theory, which is another large-scale calculation theory.