XDC: A Mesh-Friendly VIE Simulator for Efficient DC Resistance and Inductance Extraction of Complicated 3-D Structures

A mesh-friendly volume integral equation (VIE)-based simulator, named XDC, is proposed for efficient dc resistance/inductance (DCRL) extraction of complicated 3-D geometries. This study demonstrates three key innovations that make it highly efficient and accurate: 1) a novel centroid–centroid (CC) basis transformation technique is introduced while discretizing volume currents, effectively extracting the directionality of volumetric currents from the system matrix. This transformation not only simplifies the implementation of the fast multipole method (FMM) but also enhances the system matrix compressibility, thereby achieving significant reductions in memory consumption and computation time compared with conventional approaches; 2) a loop current formulation incorporating analytical DCRL values of bonding wires is developed, eliminating the need for volumetric meshing of thin and long bonding wires while maintaining high accuracy; and 3) a compact mapping matrix formalism is proposed to reflect the directionality of all currents. This accelerates the setup of sparse mapping matrices and their multiplication with vectors during iterative solution. The proposed XDC can accurately and efficiently compute DCRL parameters of arbitrarily shaped and large-scale structures on a desktop computer. It has been applied to DCRL parameter extraction of various practical structures, including a ball grid array (BGA) package and a wire bond BGA (WBBGA) package, to present its applicability and efficiency.