Combined equivalent charge formulations and fast waveletGalerkin BEM for 3-D electrostatic analysis

摘要

We describe a new equivalent charge formulation (ECF), i.e. the combined ECF (CECF), for electrostaticanalysis of structures consisting of conductors and dielectrics. The CECF uses a weighted combination ofthe single- and the adjoint double-layer operators to account for the potential on the conductor-dielectricsurface and is found to have better conditioning than the standard ECF. A perturbation approach ispresented to insure that the capacitances are computed accurately even when the permittivity ratios ofthe dielectrics are vary large. Unlike the original perturbation approach, this new approach uses only onesystem matrix with different right-hand sides. A wavelet Galerkin boundary element method (WGBEM) for solving the ECF and CECF is developedbased on the new variable-order WGBEM introduced in (J. Numer. Math. 2004; 12(3):233-254). Thewavelets are directly constructed on the usual boundary element triangulation. This enables the proposedWGBEM to solve electrostatic problems in complicated geometries, unstructured meshes and comparativelycoarse discretizations. The quasi-vanishing moment wavelets introduced in (Comput. Methods Appl. Mech.Engng 2008; 197:4000-4006) are used to further reduce the memory and CPU time requirements. Several numerical examples show that the proposed CECF converges faster than the ECF, and thatthe WGBEM, using both the ECF and CECF, has almost linear complexity in solving large-scale 3-Delectrostatic problems. Moreover, since the truncated non-standard form is computed once and then stored,the WGBEM is very suitable for solving problems with multiple right-hand sides, like the perturbationapproach in this paper.