We have developed an accurate atomic-scale finite element method (AFEM) that has exactly the same formal structure as continuum finite element methods, and therefore can seamlessly be combined with them in multiscale computations. The AFEM uses both first and second derivatives of system energy in the energy minimization computation. It is faster than the standard conjugate gradient method which uses only the first order derivative of system energy, and can thus significantly save computation time especially in studying large scale problems. Woven nanostructures of carbon nanotubes are proposed and studied via this new method, and strong defect insensitivity in such nanostructures is revealed. The AFEM is also readily applicable for solving many physics related optimization problems.

• Received 11 January 2005

DOI:https://doi.org/10.1103/PhysRevB.72.035435