A Multiregion DG-SIE Method for Efficient Full-Wave Cosimulation of MultiscaleChip–Package Modules

This article presents a multiregion discontinuous Galerkin surface integral equation (DG-SIE) method for full-wave cosimulation of multiscale chip–package systems. Conventional volumetric methods, such as finite element or finite difference approaches, face challenges in modeling complex layered substrates and multiscale geometries due to meshing inefficiencies. The proposed framework addresses these limitations by integrating an SIE formulation with layered medium Green’s functions (LMGFs), inherently resolving wave interactions with stratified backgrounds without volumetric discretization. To handle the multiscale nature of advanced packaging architectures, the DG-SIE enables nonconformal meshing across partitioned subdomains, allowing independent discretization of chip, package, and printed circuit board (PCB) components. More importantly, this approach supports localized mesh updates during design iterations: modifying a subdomain (e.g., chip layout) regenerates only the affected regions, reducing matrix recomputation significantly compared with global remeshing and resimulation. Numerical validation against HFSS and ADS demonstrates excellent agreement for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>-parameters while achieving faster computation and less memory usage for radio frequency (RF) packages. We believe this method offers a practical tool for signal integrity (SI), electromagnetic interference (EMI), and parasitic analysis in high-density packaging design and optimization cycles.