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.
翻译:电导体的电动建模是各种应用中的一项根本挑战,包括预测电导体相互连接中的寄生效应,设计偏差网络,以及生物、微电机械和遥感系统的建模。边界元件方法(BEM)可以作为这些问题的有效模拟工具,因为它只允许用表面网格模拟三维物体的模型。然而,现有的BEM配方可能具有限制性,因为它们作出特定应用的假设。例如,电动提取配方通常在导体的表面都具有恒定的电弧波潜力,不能用来模拟流流流或提取阻力。在模拟稳定电流时,许多现有技术并不解决数学挑战,例如与代表导体内部区域的操作者有关的空格。我们提议一个更为笼统的BEM框架,其基础是电弧度潜力,以便以统一的方式模拟导电动物体。没有作出限制性的应用性假设,而且上述操作员的空空域是以一种直截面和严格的方式处理的。从拟议的一般精确度和精确性方法中得出了各种确认性的例子。