Yangfeng Su

SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem

We first introduce a second-order Krylov subspace

Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method

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SAPOR: second-order Arnoldi method for passive order reduction of RCS circuits

(A,B;u) based on a pair of square matrices A and B and a vector u. The subspace is spanned by a sequence of vectors defined via a second-order linear homogeneous recurrence relation with coefficient matrices A and B and an initial vector u. It generalizes the well-known Krylov subspace

Model Order Reduction of Parameterized Interconnect Networks via a Two-Directional Arnoldi Process

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Solving Rational Eigenvalue Problems via Linearization

(A;v), which is spanned by a sequence of vectors defined via a first-order linear homogeneous recurrence relation with a single coefficient matrix A and an initial vector v. Then we present a second-order Arnoldi (SOAR) procedure for generating an orthonormal basis of

Parameterized model order reduction via a two-directional Arnoldi process

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RLCSYN: RLC Equivalent Circuit Synthesis for Structure-Preserved Reduced-order Model of Interconnect

(A,B;u). By applying the standard Rayleigh--Ritz orthogonal projection technique, we derive an SOAR method for solving a large-scale quadratic eigenvalue problem (QEP). This method is applied to the QEP directly. Hence it preserves essential structures and properties of the QEP. Numerical examples demonstrate that the SOAR method outperforms convergence behaviors of the Krylov subspace--based Arnoldi method applied to the linearized QEP.

On the Bose-Trautman condition for stability of two-dimensional linear systems

A structure-preserving dimension reduction algorithm for large-scale second-order dynamical systems is presented. It is a projection method based on a second-order Krylov subspace. A second-order Arnoldi (SOAR) method is used to generate an orthonormal basis of the projection subspace. The reduced system not only preserves the second-order structure but also has the same order of approximation as the standard Arnoldi-based Krylov subspace method via linearization. The superior numerical properties of the SOAR-based method are demonstrated by examples from structural dynamics and microelectromechanical systems.

Block SAPOR: block Second-order Arnoldi method for Passive Order Reduction of multi-input multi-output RCS interconnect circuits

The recently-introduced susceptance element exhibits many prominent features in modeling the on-chip magnetic couplings. For an RCS circuit, it is better to be formulated as a second-order system. Therefore, corresponding MOR (model-order reduction) techniques for second-order systems are desired to efficiently deal with the ever-increasing circuit scale and to preserve essential model properties. We first review the existing MOR methods for RCS circuits, such as ENOR and SMOR, and discuss several key issues related to numerical stability and accuracy of the methods. Then, a technique, SAPOR (second-order Arnoldi method for passive order reduction), is proposed to effectively address these issues. Based on an implementation of a generalized second-order Arnoldi method, SAPOR is numerically stable and efficient. Meanwhile, the reduced-order system also guarantees passivity.

Further results on stability of asynchronous discrete-time linear systems

This paper presents a multiparameter moment-matching-based model order reduction technique for parameterized interconnect networks via a novel two-directional Arnoldi process (TAP). It is referred to as a Parameterized Interconnect Macromodeling via a TAP (PIMTAP) algorithm. PIMTAP inherits the advantages of previous multiparameter moment-matching algorithms and avoids their shortfalls. It is numerically stable and adaptive. PIMTAP model yields the same form of the original state equations and preserves the passivity of parameterized RLC networks like the well-known method passive reduced-order interconnect macromodeling algorithm for nonparameterized RLC networks.