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

We describe a new equivalent charge formulation (ECF), i.e. the combined ECF (CECF), for electrostatic analysis of structures consisting of conductors and dielectrics. The CECF uses a weighted combination of the single- and the adjoint double-layer operators to account for the potential on the conductor–dielectric surface and is found to have better conditioning than the standard ECF. A perturbation approach is presented to insure that the capacitances are computed accurately even when the permittivity ratios of the dielectrics are vary large. Unlike the original perturbation approach, this new approach uses only one system matrix with different right-hand sides. A wavelet Galerkin boundary element method (WGBEM) for solving the ECF and CECF is developed based on the new variable-order WGBEM introduced in (J. Numer. Math. 2004; 12(3):233–254). The wavelets are directly constructed on the usual boundary element triangulation. This enables the proposed WGBEM to solve electrostatic problems in complicated geometries, unstructured meshes and comparatively coarse 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 that the WGBEM, using both the ECF and CECF, has almost linear complexity in solving large-scale 3-D electrostatic 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 perturbation approach in this paper. Copyright © 2009 John Wiley & Sons, Ltd.