Related papers: Frequency- and Time-Limited Balanced Truncation fo…
Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less,…
Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as tearing and reconstruction. On the other hand, commutativity of cascade connected systems have…
We show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user.…
A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this paper, we first propose a second-order implicit difference…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations…
We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…