A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages

Abstract

A parallel iterative layered‐medium integral‐equation solver is presented for fast and scalable network parameter extraction of electronic packages. The solver, which relies on a 2‐D fast Fourier transform (FFT)‐based algorithm and a sparse preconditioner to reduce computational complexity, is parallelized using three workload decomposition strategies, including a pencil decomposition that increases the scalability of the computationally dominant FFT‐based multiplication stage. A set of increasingly difficult benchmark problems, which require network parameter computations for Ntrace = 1 to 257 package‐scale interconnects, are solved on a petaflop scale computer to quantify the solver's accuracy, efficiency, and scalability. The total serialized computation time is observed to scale asymptotically as Ntrace2.6logNtrace. For the largest problem, using ~1.14 million unknowns and 1536 processes, the solver requires a wall‐clock time of ~0.05 s per iteration, ~1 minute per excitation, ~9 h per frequency, and ~424 hours to extract the 514‐port network parameters at 40 sample frequencies between 1 to 40 GHz.

A Parallel Boundary Element Method for the Electromagnetic Analysis of Large Structures With Lossy Conductors

“…Furthermore, FFTs are needed in the AIM for computing far-region interactions. These operations are most efficiently parallelized by the 2-D pencil decomposition proposed in [45] for homogeneous media and in [21] for multilayered media. These 2-D pencil decompositions are adopted in the proposed method.…”

“…Parallelization methods have also been investigated for other acceleration techniques, e.g., the AIM [17], [18] and the adaptive cross approximation (ACA) algorithm [19], [20], these works were also focused on modeling PEC objects. For layered media, [21] and [22] have presented parallel AIM solvers that model lossy conductors through the surface impedance boundary condition (SIBC) [23], which is accurate only when skin effect is sufficiently developed. Parallel BEM solvers that accurately model penetrable objects are rare, yet there are examples of parallel MLFMA and ACA solvers that target dielectric objects [24]- [27].…”