A sixth-order finite volume method is proposed to solve the Poisson equation for two-and three-dimensional geometries involving curved boundaries. A specific polynomial reconstruction is used to provide accurate fluxes for diffusive operators even with discontinuous coefficients while we introduce a new technique to preserve the sixth-order approximation for non-polygonal domains. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.
Articles you may be interested inNumerical simulations of electrostatic interactions between an atomic force microscopy tip and a dielectric sample in presence of buried nano-particles Electric Force-Distance Curves (EFDC) is one of the ways whereby electrical charges trapped at the surface of dielectric materials can be probed. To reach a quantitative analysis of stored charge quantities, measurements using an Atomic Force Microscope (AFM) must go with an appropriate simulation of electrostatic forces at play in the method. This is the objective of this work, where simulation results for the electrostatic force between an AFM sensor and the dielectric surface are presented for different bias voltages on the tip. The aim is to analyse force-distance curves modification induced by electrostatic charges. The sensor is composed by a cantilever supporting a pyramidal tip terminated by a spherical apex. The contribution to force from cantilever is neglected here. A model of force curve has been developed using the Finite Volume Method. The scheme is based on the Polynomial Reconstruction Operator-PRO-scheme. First results of the computation of electrostatic force for different tip-sample distances (from 0 to 600 nm) and for different DC voltages applied to the tip (6 to 20 V) are shown and compared with experimental data in order to validate our approach. V C 2014 AIP Publishing LLC. [http://dx.
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