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

Abstract

SUMMARYWe 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. 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.

Application of Wavelet Methods in Computational Physics

“…[93] Levin et al further employed high-order biorthogonal wavelets to construct the WBEM, producing even sparser matrices and boosting the algorithm's computational efficiency. [94] Other types of wavelets, including non-orthogonal spline wavelets, [95] Daubechies wavelets, [96] and variable order wavelets, [97] have also been used to create corresponding WBEMs. Presently, the WBEMs are widely used in resolving practical problems, such as solving the 2D Poisson equations, [99] analyzing 3D electric fields, [98] addressing fluid dynamics problems, [99][100][101] , and studying band structures of solid-solid and fluid-fluid phononic crystals, [187] among others.…”

Development and implementation of some BEM variants—A critical review

“…At the same time, a fully discrete wavelet Galerkin scheme for the 2D Laplacian was presented by Harbrecht and Scheider [88] and later extended to three dimensional [85]. From their work, a new approach which known as wavelet Galerkin boundary element method (WGBEM) was created and then utilized by researchers in engineering fields with successful implementation in electromagnetic shaping [66,67], acoustics scattering wave [86], elasticity [64] and electrostatic analysis [268]. To understand more on WGBEM, the Fredholm's integral equation of the first kind from Eq.…”

A New Strategy for Automatic Coupling Between the Inductive PEEC Method and an Integral Electrostatic Formulation

“…The problem of extracting parasitic capacitances has a long history, in which the BEM approach is a widely used method and has proven to be very efficient because of its ability to handle complex geometries and infinite domains. There are two alternatives to this method : the direct formulation based on the integral boundary equation derived directly from Laplace equation [24] and the indirect formulation based on singlelayer and adjoint of double-layer potential equations (with dielectric regions) [25], [26], [27], [28], [29]. Several other developments have also been introduced such as BIM dual or pure second-kind BIM [30], [31], [32].…”