D. J. Diestler
Physical Review B, 66, 184104 (2002).
Several extant hybrid atomistic-continuum computational schemes designed to
handle coupled processes on vastly separated spatial scales are based on a
"dynamic" coarse graining of the continuum by means of finite elements. Such
an exact coarse-graining treatment of the one-dimensional harmonic chain of
identical atoms was carried out as a test. It is shown that the error in
thermomechanical properties (e.g., the tension) engendered by "dynamic"
finite-element coarse graining can be substantial, depending on the
thermodynamic state. An alternative "static" finite-element coarse-graining
description, which is an extension to nonzero temperature of the
"quasicontinuum" procedure of Tadmor, Ortiz, and Phillips, is proposed in an
attempt to correct this error. The extended quasicontinuum technique applied
to the pure one-dimensional harmonic chain yields the exact solution, thus
indicating its promise for more general applications. Problems anticipated
in the extension of the technique to realistic three-dimensional models of
solids are discussed.