XRL: An FMM-Accelerated SIE Simulator for Resistance and Inductance Extraction of Complicated 3-D Geometries

A fast multipole method (FMM)-accelerated surface integral equation (SIE) simulator, called XRL, is proposed for broadband resistance/inductance (RL) extraction under the magneto-quasi-static (MQS) assumption. The proposed XRL has three key attributes that make it highly efficient and accurate for broadband RL extraction of complicated 3-D geometries: 1) the XRL leverages a novel centroid-midpoint (CM) basis transformation while discretizing surface currents, which allows converting edge-based vector potential computations to panel-based scalar potential computations. Such conversion makes the implementation of FMM straightforward and allows for drastically reducing the memory and computational time requirements of the simulator; 2) the XRL employs a highly accurate equivalent surface impedance (ESI) model that allows extracting RL parameters at low frequencies very accurately; and 3) the XRL makes use of a novel preconditioner, effectively including both diagonal entries and some near-field entries of the system matrix; such preconditioner significantly accelerates the iterative solution of SIE. The proposed XRL can accurately compute broadband RL parameters of arbitrarily shaped and large-scale structures on a desktop computer. It has been applied to RL parameter extraction of various practical structures, including two parallel square coils, a ball grid array (BGA) package, and a high brand package on package (HBPOP). Its application to the parameter extraction of the BGA shows that the XRL requires <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$93.2\times $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$14.2\times $ </tex-math></inline-formula> less computational time and memory resources compared to the commercial simulator Ansys Q3D for the same level of accuracy, respectively.