Design And Study Of High-presciesion Numerical Dielectric Model Of Composite Materials

For high-precisely simulating the effective dielectric constants of compositematerials, a new model, the finite element method based on the Laguerre-Voronoidiagram (LVFEM), is designed, implemented and evaluated. The model LVFEM isbuilt through two steps: the first step constructs the Laguerre-Voronoi diagram whichis used to optimally simulate the microstructure of polycrystalline material; thesecond step applies the finite element method with adaptive mesh refinement toaccurately calculate the electrostatic field of the complex construct. So, in this paper, firstly, the Laguerre-Voronoi diagram (the L_V diagram) issurveyed in details. Some related geometrical structures have also been discussed ,which include the convex hull, the lower face, the lower hull of convex hull, theLaugerre_Delaunay diagram (the L_D diagram), the Laguerre-Voronoi region(theL_V region). Based on these structures relationships and a powerful software packageqhull for constructing the convex hull, we design and implement a fast algorithm forgenerating the L_V diagram in 2 or 3 dimension. Through the algorithm, we can , ona 2.0GHz single-Pentium 4 computer running Windows, construct theLaguerre-Voronoi diagram which consists of 1×105 L_V regions in 500 seconds. In addition, a posteriori error estimator and the formulations for the special modelin 2 or 3 dimension space are presented in details. Based on two software packages,taucs and triangle, the effective dielectric constants of the 2 dimension LVFEM canbe fast and precisely calculated. At last, depending on the model, we evaluate several numerical dielectric modelsof mixtures and the corresponding fitted parameters have been obtained.