This paper concerns a harmonic projection method for computing an approximation to an eigenpair (λ, x) of a large matrix A. Given a target point τ and a subspace W that contains an approximation to x, the harmonic projection method returns an approximation (μ + τ, x̃) to (λ, x). Three convergence results are established as the deviation of x from W approaches zero. First, the harmonic Ritz value...

We propose a new method to deal with the essential boundary conditions encountered in deep learning-based numerical solvers for partial differential equations. The trial functions representing by neural networks are non-interpolatory, which makes enforcement of nontrivial matter. Our resorts Nitsche's variational formulation this difficulty, is consistent, and does not require significant extra...

this article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. the electrostatic actuation was induced by applying ac-dc voltage between the microbeam and electrode plate. in contrast to previous works, it was assumed that length of the electrode plate was smaller than that of the microbeam. in additio...

Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm [8], has been proposed. The main computational cost of the AIRGA algorithm is solving a sequence of linear systems. Usually, direct methods (e.g., LU) are used for solving these systems. As model sizes grow, direct meth...

This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X of a general matrix A from a subspace W that contains an approximation to X . The method produces a pair (N, X̃) that purports to approximate a pair (L,X), where X is a basis for X and AX = XL. In this paper we consider the convergence of (N, X̃) as the sine of the angle between X andW approaches zero. ...

A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...

Abstract. This paper presents a theoretical approach for constructing a reduced model in the medium frequency range in the area of structural dynamics for a general three-dimensional anisotropic and inhomogeneous viscoelastic bounded medium. All the results presented can be used for beams, plates and shells. The boundary value problem in the frequency domain and its variational formulation are ...

Article history: Received 9 August 2012 Received in revised form 12 December 2012 Accepted 24 January 2013 Available online 14 February 2013