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A parallel FFT‐accelerated layered‐medium integral‐equation solver for electronic packages
Author(s) -
Liu Chang,
Aygün Kemal,
Yılmaz Ali E.
Publication year - 2019
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2684
Subject(s) - solver , fast fourier transform , computer science , parallel computing , scalability , computation , computational science , preconditioner , multiplication (music) , multigrid method , algorithm , iterative method , mathematics , partial differential equation , mathematical analysis , combinatorics , database , programming language
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 N trace = 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 N trace 2.6 log N trace . 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.