GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Efficient steady-state analysis based on matrix-free Krylov-subspace methods
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Matrix algorithms
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Design of millimeter-wave CMOS radios: a tutorial
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Design considerations for 60 GHz CMOS radios
IEEE Communications Magazine
A structured parallel periodic arnoldi shooting algorithm for RF-PSS analysis based on GPU platforms
Proceedings of the 16th Asia and South Pacific Design Automation Conference
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The verification of large radio-frequency/millimeter-wave (RF/MM) integrated circuits (ICs) has regained attention for high-performance designs beyond 90nm and 60GHz. The traditional time-domain verification by standard Krylov-subspace based shooting method might not be able to deal with newly increased verification complexity. The numerical algorithms with small computational cost yet superior convergence are highly desired to extend designers' creativity to probe those extremely challenging designs of RF/MM ICs. This paper presents a new shooting algorithm for periodic RF/MM-IC systems. Utilizing a periodic structure of the state matrix, a periodic Arnoldi shooting algorithm is developed to exploit the structured Krylov-subspace. This leads to an improved efficiency and convergence. Results from several industrial examples show that the proposed periodic Arnoldi shooting method, called PAS, is 1000 times faster than the direct-LU and the explicit GMRES methods. Moreover, when compared to the existing industrial standard, a matrix-free GMRES with non-structured Krylov-subspace, the new PAS method reduces iteration number and runtime by 3 times with the same accuracy.