arXiv subjects

Yuncheng Xu

Publications and source records attributed to Yuncheng Xu.

5 recordsLinked to original sources

arXiv2026

Multistep Methods for Floquet Multipliers and Subspaces

Accurate and efficient computation of Floquet multipliers and subspaces is essential for analyzing limit cycles in dynamical systems and periodic steady states in radio frequency circuit simulation. This problem is typically addressed by solving a periodic linear eigenvalue problem, which is obtained by discretizing the linear time-periodic system using one-step collocation methods. Collocation methods become costly for large-scale problems. Our alternative approach is to use multistep methods. A multistep method leads to a periodic polynomial eigenvalue problem (pPEP) and introduces additional parasitic periodic eigenvalues. We prove that, as the stepsize decreases, the computed Floquet multipliers and their associated invariant subspace converge at the consistency order, while the parasitic periodic eigenvalues converge to zero geometrically and hence become separated from the nonzero Floquet multipliers. We design a memory-efficient algorithm, pTOAR, to solve the large-scale pPEP. Its arithmetic and memory costs are almost independent of the choice of multistep methods when the pPEP arises from an implicit multistep discretization. Numerical results agree with our convergence analysis and demonstrate the efficiency of pTOAR.

math.NA↗

arXiv2026

A Fourier-Aware Projection-Based Periodic Parareal Method for Time-Periodic Problems

Time-periodic problems arise when the desired solution is a periodic steady state rather than a transient trajectory. The periodic parareal algorithm with a periodic coarse problem (PP-PC) is a periodicity-preserving parallel-in-time approach for such problems. Projection-based correction can accelerate convergence of both parareal and PP-PC. In this paper, we propose a Fourier-aware construction of projection spaces and a new correction scheme to further accelerate the convergence of projection-based PP-PC. We develop a convergence analysis of projection-based PP-PC with the discrepancy-based correction scheme for general nonlinear time-periodic problems. For an arbitrary orthogonal projection, we derive a local one-step convergence estimate controlled by the unresolved error and explicit nonlinear contributions. A temporal Fourier decomposition bounds the unresolved error by a tail-leak quantity, which is small when dominant error modes are selected and their coefficients are captured by the projection space. For linear problems, the nonlinear contributions vanish, yielding a globally valid one-step tail-leak convergence estimate under weaker assumptions. Experiments on linear and nonlinear problems show that Fourier-aware PP-PC requires fewer outer iterations than Krylov-enhanced PP-PC. For the linear problems, the errors track the tail-leak bound. For the nonlinear problems, the experiments quantify the unresolved-error and explicit nonlinear contributions in the local one-step estimate and show that the evaluated tail-leak estimate follows the observed decay.

math.NA↗

arXiv2026

FlexRC: A Flexible Multi-Point Model Order Reduction Method for Many-Port RC Networks

Efficient model order reduction for many-port resistor-capacitor (RC) networks is essential in post-layout circuit simulation. Existing high-accuracy elimination-based methods have certain limitations, such as fixed frequency points, large reduced-order models, or high reduction cost. This paper proposes FlexRC, a flexible multi-point model order reduction method for many-port RC networks. FlexRC starts from the same elimination step as previous methods, and then constructs a nonorthogonal projection basis by a modified block rational Arnoldi process to generate a sparse banded reduced model. FlexRC features three adjustable components: user-specified frequency points, a tolerance-controlled port-reduction technique for the internal subsystem, and an optional sparsity-control strategy. We discuss passivity under port-reduction perturbations, analyze moment matching, and provide a conservative error estimate for port reduction. Numerical experiments on industrial RC examples and IBM power-grid examples demonstrate the effectiveness of FlexRC in terms of reduction time and transient simulation time.

eess.SY↗

arXiv2025

SMP-RCR: A Sparse Multipoint Moment Matching Method for RC Reduction

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching methods and elimination methods. High-order moment matching methods--characterized by high accuracy, such as PRIMA and TurboMOR--tend to generate large dense reduced-order systems when the number of ports is large, which impairs the efficiency of MOR. Another common type of MOR method for many--port circuits is based on Gaussian elimination, with the SIP method as a representative. The main limitation of this method lies in the inadequate matching of high--order moments. In this paper, we propose a sparse multipoint moment matching method and present comprehensive theoretical analysis results regarding the multi--frequency high--order moment matching property. Meanwhile, to enhance the algorithm's efficiency, sparse control and deflation techniques are introduced to further optimize the algorithm. Numerical experiments demonstrated that, compared to SIP, the accuracy is improved by more than two orders of magnitude at high frequency points without adding many extra linear components. Compared to TurboMOR methods, our method achieves a speed improvement of more than twice while maintaining the same level of precision.

eess.SY↗

arXiv2025

Memory Enhanced Fractional-Order Dung Beetle Optimization for Photovoltaic Parameter Identification

Accurate parameter identification in photovoltaic (PV) models is crucial for performance evaluation but remains challenging due to their nonlinear, multimodal, and high-dimensional nature. Although the Dung Beetle Optimization (DBO) algorithm has shown potential in addressing such problems, it often suffers from premature convergence. To overcome these issues, this paper proposes a Memory Enhanced Fractional-Order Dung Beetle Optimization (MFO-DBO) algorithm that integrates three coordinated strategies. Firstly, fractional-order (FO) calculus introduces memory into the search process, enhancing convergence stability and solution quality. Secondly, a fractional-order logistic chaotic map improves population diversity during initialization. Thirdly, a chaotic perturbation mechanism helps elite solutions escape local optima. Numerical results on the CEC2017 benchmark suite and the PV parameter identification problem demonstrate that MFO-DBO consistently outperforms advanced DBO variants, CEC competition winners, FO-based optimizers, enhanced classical algorithms, and recent metaheuristics in terms of accuracy, robustness, convergence speed, while also maintaining an excellent balance between exploration and exploitation compared to the standard DBO algorithm.

cs.NE↗