1,722,098 research outputs found
On the Solution of the Nonsymmetric T-Riccati Equation
Full text linkThe nonsymmetric T-Riccati equation is a quadratic matrix equation where the linear part corresponds to the so-called T-Sylvester or T-Lyapunov operator that has previously been studied in the literature. It has applications in macroeconomics and policy dynamics. So far, it presents an unexplored problem in numerical analysis, and both theoretical results and computational methods are lacking in the literature. In this paper we provide some sufficient conditions for the existence and uniqueness of a nonnegative minimal solution, namely the solution with component-wise minimal entries. Moreover, the efficient computation of such a solution is analyzed. Both the small-scale and large-scale settings are addressed, and Newton-Kleinman-like methods are derived. The convergence of these procedures to the minimal solution is proven, and several numerical results illustrate the computational efficiency of the proposed methods
Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell's Equations
No full textA Reduced Basis Method for Microwave Semiconductor Devices with Geometric Variations
No full textPurpose - The Reduced Basis Method (RBM) generates low-order models of parametrized PDEs to allow for efficient evaluation of parametrized models in many-query and real-time contexts. The purpose of this paper is to investigate the performance of the RBM in microwave semiconductor devices, governed by Maxwell's equations. Design/methodology/approach - The paper shows the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction under geometry variation. Findings - The RBM reduces model order by a factor of $1,000 and more with guaranteed error bounds. Originality/value - Exponential convergence speed can be observed by numerical experiments, which makes the RBM a suitable method for parametric model reduction (PMOR). © Emerald Group Publishing Limited
Palindromic linearization and numerical solution of nonsymmetric algebraic T -Riccati equations
Full text linkWe identify a relationship between the solutions of a nonsymmetric algebraic T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arranging the coefficients of the T-NARE. The interplay between T-NAREs and palindromic pencils allows one to derive both theoretical properties of the solutions of the equation, and new methods for its numerical solution. In particular, we propose methods based on the (palindromic) QZ algorithm and the doubling algorithm, whose effectiveness is demonstrated by several numerical tests
A parallel, adaptive multi-point model order reduction algorithm
No full textThis paper describes a model order reduction technique for circuit simulation, based on the parallelization of the well-known multi-point PRIMA algorithm. In order to obtain an optimal accuracy of the reduced-order model in the entire frequency range of interest, the reduced models are computed on different expansion points in correspondence of which the errors, between the transfer functions of the original model and of the actual reduced one, exhibit the largest value, in a recursive way. Moreover, since the computation of the error is a computationally expensive routine, this task is parallelized, assuming that each error value is independent of the others and to work with modern multi-core computers or a cluster of workstations. The numerical results show that the parallelized model order reduction algorithm is able to provide accuracy and speed up with respect to the sequential one, for both dense and sparse data sets. © 2013 IEEE
On an integrated Krylov-ADI Solver for Large-Scale Lyapunov Equations
Full text linkOne of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this task. In particular, we illustrate how a single approximation space can be constructed to
solve all the shifted linear systems needed to achieve a prescribed accuracy in terms of Lyapunov residual norm. Moreover, we show how to fully merge the two iterative procedures in order to obtain a novel, efcient implementation of the low-rank ADI method, for an important class of equations. Many state-of-the-art algorithms for the shift computation can be easily incorporated into our new scheme, as well. Several numerical results illustrate the potential of our novel procedure when compared to an implementation of the low-rank ADI method based on sparse direct solvers for the shifted linear systems
Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems
Full text linkModel order reduction usually consists of two stages: the offline stage and the online stage. The offline stage is the expensive part that sometimes takes hours till the final reduced-order model is derived, especially when the original model is very large or complex. Once the reduced-order model is obtained, the online stage of querying the reduced-order model for simulation is very fast and often real-time capable. This work concerns a strategy to speed up the offline stage of model order reduction for large and complex systems. In particular, it is successful in accelerating the greedy algorithm that is often used in the offline stage for reduced-order model construction. We propose to replace the high-fidelity error estimator in the greedy algorithm with multi-fidelity error estimation. Consequently, the computational complexity of the greedy algorithm is reduced and the algorithm converges more than two times faster without incurring noticeable accuracy loss
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