Uniform accuracy of the quasicontinuum method

The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient condition for uniform first-order accuracy and, consequently, the elimination of the “ghost force” is formulated in terms of the reconstruction schemes. The quasi-nonlocal approach is discussed as a special case of this condition. Examples of reconstruction schemes that satisfy this condition are presented. Transition between atom-based and element-based summation rules are studied.

Figure 1

1D chain.

Figure 2

1D chain with cluster-based summation rule.

Figure 3

(Color online) Modified reconstruction scheme based on the CB rule.

Figure 4

(Color online) 2D triangular lattice, ${\mathit{a}}_1=(1∕2,\sqrt{3}∕2)$ and ${\mathit{a}}_2=(1,0)$.

Figure 5

(Color online) f.c.c. lattice.

Figure 6

(Color online) All atoms except atom 0 (the circle one) use atom-based summation, while atom 0 uses element-based summation.

Figure 7

(Color online) Solid atoms use atom-based summation, while circle atoms use element-based summation.

Figure 8

(Color online) Flat interface. Solid atoms use atom-based summation, while circle atoms use element-based summation.

Figure 9

(Color online) Illustration of different atoms.

Figure 10

Edge atoms.