An atomistic capacitance is derived for a single-wall carbon nanotube in a nano-electromechanical device. Multi-scale calculation is performed using a continuum model for the geometrical capacitance, and statistical and quantum mechanical approaches for the quantum capacitance of the nanotube. The geometrical part of the capacitance is studied in detail using full three-dimensional electrostatics. Results reported in this paper are useful for compact modeling of the electronic and electromechanical nanotube devices.

SUMMARYAn accelerated boundary cloud method (BCM) for boundary-only analysis of exterior electrostatic problems is presented in this paper. The BCM uses scattered points instead of the classical boundary elements to discretize the surface of the conductors. The dense linear system of equations generated by the BCM are solved by a GMRES iterative solver combined with a singular value decomposition based rapid matrix-vector multiplication technique. The accelerated technique takes advantage of the fact that the integral equation kernel (2D Green's function in our case) is locally smooth and, therefore, can be dramatically compressed by using a singular value decomposition technique. The acceleration technique greatly speeds up the solution phase of the linear system by accelerating the computation of the dense matrix-vector product and reducing the storage required by the BCM.

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SUMMARYAn accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples.

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