A Generalized Scalar Potential Integral Equation Formulation for the DC Analysis of Conductors

TL;DR

This paper introduces a unified boundary element method framework using electric scalar potential for electrostatic and steady current modeling of conductors, overcoming limitations of existing application-specific formulations.

Contribution

A generalized BEM formulation based on scalar potential that handles various scenarios without restrictive assumptions and addresses null space issues.

Findings

Accurate modeling across diverse applications.

Handles null space in steady current problems.

Validated with numerical examples.

Abstract

The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological, microelectromechanical, and sensing systems. The boundary element method (BEM) can be an effective simulation tool for these problems because it allows modeling three-dimensional objects with only a surface mesh. However, existing BEM formulations can be restrictive because they make assumptions specific to particular applications. For example, capacitance extraction formulations usually assume a constant electric scalar potential on the surface of each conductor and cannot be used to model a flowing current, nor to extract the resistance. When modeling steady currents, many existing techniques do not address mathematical challenges such as the null space associated with the operators representing the internal region of a conductor. We propose a more general BEM framework based on the electric scalar potential for modeling conductive objects in various scenarios in a unified manner. Restrictive application-specific assumptions are not made, and the aforementioned operator null space is handled in an intuitive and rigorous manner. Numerical examples drawn from diverse applications confirm the accuracy and generality of the proposed method.