Sampling point selection for energy estimation in the quasicontinuum method

The quasicontinuum (QC) method reduces computational costs of atomistic calculations by using interpolation between a small number of so-called repatoms to represent the displacements of the complete lattice and by selecting a small number of sampling atoms to estimate the total potential energy of the interpolated problem. In this contribution two new sampling point selections are introduced for the QC method. The first selection determines the total potential energy of the lattice exactly in correspondence with the interpolation. Since no error due to summation occurs, the fully resolved regions around lattice defects can remain small. However, in this case many sampling atoms must be used. Therefore a second sampling point selection is derived from the first selection that uses only one sampling atom to represent all atoms within interpolation together with the repatoms. This ensures that the exact lattice model is recovered in the fully resolved regions while a smooth transition is achieved towards coarse regions in which the method becomes very close to the local QC method