A fast boundary cloud method for 3D exterior electrostatic analysis

Abstract

SUMMARYAn accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples.

The meshless Galerkin boundary node method for Stokes problems in three dimensions

“…This makes the GBNM and other MLS‐based meshless methods too expensive for problems requiring a dense distribution of points. Some strategies have been developed for the alleviation of this problem, such as fast algorithm 10, 24, 25, coupling algorithm 12, 13, 27, and parallel computing 23. Since the system matrix in the GBNM is not only symmetric but also positive definite, this method is an ideal choice for coupling the FEM or other established domain type meshless methods such as the EFG.…”

“…Since the system matrix in the GBNM is not only symmetric but also positive definite, this method is an ideal choice for coupling the FEM or other established domain type meshless methods such as the EFG. Besides, fast algorithms based on multipole expansions 10, 25, fast Fourier transform or singular value decomposition 24 can also be used for acceleration of the GBNM.…”

“…Especially for exterior problems, the use of domain type methods requires discretization of the entire exterior, whereas with BIEs only the surface needs to be discretized. Boundary type meshless methods are developed by the combination of the meshless idea with BIEs, such as the boundary node method (BNM) 22, 23, the boundary cloud method (BCM) 24, the hybrid boundary node method (HBNM) 25, and the boundary face method (BFM) 26. In the four methods, the moving least‐squares (MLS) approximations are used to generate the shape functions on the boundary of a domain.…”

A 2-D model that accounts for 3-D fringing in MEMS devices

“…(16), (17) and (18) Observe that the variational equation described in Eq. (21) when translated to a strong formulation [19] is of the simple form:…”

“…However, underlying all of these challenges is the basic 3-D electrostatic simulation problem that needs to be solved as efficiently as possible. Thus, despite the availability of commercial packages that address electrostatic simulation, for example, see [11][12][13], 3-D electrostatic simulation continues to generate interest among researchers, and new techniques are constantly being developed [14][15][16].…”