The parallel computation of the smallest eigenpair of an acoustic problem with damping

Acoustic problems with damping may give rise to large quadratic eigenproblems. Efficient and parallelizable algorithms are required for solving these problems. The recently proposed Jacobi-Davidson method is well suited for parallel computing: no matrix decomposition and no back or forward substitutions are needed. This paper describes the parallel solution of the smallest eigenpair of a realistic and very large quadratic eigenproblem with the Jacobi-Davidson method

Spectral Clustering of Graphs with the Bethe Hessian

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the non-backtracking walk on the graph, leads to improved performance in detecting clusters, and even to optimal performance for the stochastic block model. Here, we propose to use instead a simpler object, a symmetric real matrix known as the Bethe Hessian operator, or deformed Laplacian. We show that this approach combines the performances of the non-backtracking operator, thus detecting clusters all the way down to the theoretical limit in the stochastic block model, with the computational, theoretical and memory advantages of real symmetric matrices.Comment: 8 pages, 2 figure

Frequency-domain sensitivity analysis of stability of nonlinear vibrations for high-fidelity models of jointed structures

For the analysis of essentially nonlinear vibrations it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including: friction, gaps, and cubic elastic nonlinearity

Shift Strategy for Non-overdamped Quadratic Eigen-problems

ABSTRACT In this paper we study properties of non-overdamped quadratic eigenproblems. For the non-overdamped Eigen-value problems we cannot apply variational characterization in full. One of the subintervals of the interval in which we can apply variational characterization for Eigen-values of a negative type is known. In this paper we expand this subinterval by giving better right boundry of the variational characterization interval. This is achieved by getting bigger lower boundary for δ +. New strategy is seen in fact that we join suitably selected hyperbolic quadratic pencil to non-overdamped quadratic pencil. From the variational characterization of the hyperbolic eigenproblem we get better lower boundary for δ +

Acoustic modal analysis with heat release fluctuations using nonlinear eigensolvers

Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different approaches have been developed by the researchers over the years. In this work we focus on the Helmholtz wave equation based solver which is found to be relatively fast and accurate for most applications. This solver has been a subject of study in many previous works. The Helmholtz wave equation in frequency space reduces to a nonlinear eigenvalue problem which needs to be solved to compute the acoustic modes. Most previous implementations of this solver have relied on linearized solvers and iterative methods which as shown in this work are not very efficient and sometimes inaccurate. In this work we make use of specialized algorithms implemented in SLEPc that are accurate and efficient for computing eigenvalues of nonlinear eigenvalue problems. We make use of the n-tau model to compute the reacting source terms in the Helmholtz equation and describe the steps involved in deriving the Helmholtz eigenvalue equation and obtaining its solution using the SLEPc library

Pure spin current generation in a Rashba-Dresselhaus quantum channel

We demonstrate a spin pump to generate pure spin current of tunable intensity and polarization in the absence of charge current. The pumping functionality is achieved by means of an ac gate voltage that modulates the Rashba constant dynamically in a local region of a quantum channel with both static Rashba and Dresselhaus spin-orbit interactions. Spin-resolved Floquet scattering matrix is calculated to analyze the whole scattering process. Pumped spin current can be divided into spin-preserved transmission and spin-flip reflection parts. These two terms have opposite polarization of spin current and are competing with each other. Our proposed spin-based device can be utilized for non-magnetic control of spin flow by tuning the ac gate voltage and the driving frequency.Comment: 6 pages, 3 figure