In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP [1] and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new "precorrected-FFT" algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

The problem of automated macromodel generation is interesting from the viewpoint of system-level design because if small, accurate reduced-order models of system component blocks can be extracted, then much larger portions of a design, or more complicated systems, can be simulated or verified than if the analysis were to have to proceed at a detailed level. The prospect of generating the reduced model from a detailed analysis of component blocks is attractive because then the influence of second-order device effects or parasitic components on the overall system performance can be assessed. In this way overly conservative design specifications can be avoided. This paper reports on experiences with extending model reduction techniques to nonlinear systems of differential-algebraic equations, specifically, systems representative of RF circuit components. The discussion proceeds from linear time-varying, to weakly nonlinear, to nonlinear time-varying analysis, relying generally on perturbational techniques to handle deviations from the linear time-invariant case. The main intent is to explore which perturbational techniques work, which do not, and outline some problems that remain to be solved in developing robust, general nonlinear reduction methods.

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Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the boundary of the domain of interest. In order to solve such problems, the boundary element method (BEM) can be applied. The advantage compared to domain-discretisation-based methods such as finite element methods is that only a discretisation of the boundary is necessary, which significantly reduces the number of unknowns. Yet, BEM formulations are much more difficult to implement than finite element methods. In this article, we present BEM++, a novel open-source library for the solution of boundary integral equations for Laplace, Helmholtz and Maxwell problems in three space dimensions. BEM++ is a C++ library with Python bindings for all important features, making it possible to integrate the library into other C++ projects or to use it directly via Python scripts. The internal structure and design decisions for BEM++ are discussed. Several examples are presented to demonstrate the performance of the library for larger problems.