A Galerkin approximation for integro-differential equations in electromagnetic scattering from a chiral medium

2016 ◽  
Vol 96 (1) ◽  
pp. 159-172 ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Thanh-Nhan Nguyen ◽  
Minh-Phuong Tran
Keyword(s):  
Differential Equations ◽  
Electromagnetic Scattering ◽  
Galerkin Approximation ◽  
Chiral Medium

scholarly journals Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 49 ◽  
Author(s):  
Carlo Garoni ◽  
Mariarosa Mazza ◽  
Stefano Serra-Capizzano
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Discontinuous Galerkin ◽  
Spectral Distribution ◽  
Galerkin Approximation ◽  
Higher Order ◽  
Numerical Discretization

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices An arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices An give rise to a sequence {An}n, which often turns out to be a GLT sequence or one of its “relatives”, i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.

Mechanical Behavior of an Electrostatically Actuated Microplate

2003 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Finite Dimension ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Mode Shapes ◽  
Design Parameters ◽  
Electrostatically Actuated ◽  
Linear Eigenvalue Problem ◽  
Electrically Actuated

We present a nonlinear model of electrically actuated microplates. The model accounts for the nonlinearity in the electric forcing as well as mid-plane stretching of the plate. We use a Galerkin approximation to reduce the partial-differential equations of motion to a finite-dimension system of nonlinearly coupled second-order ordinary-differential equations. We find the deflection of the microplate under DC voltage and study the pull-in phenomenon. The natural frequencies and mode shapes are then obtained around the deflected position of the microplate by solving the linear eigenvalue problem. The effect of various design parameters on both the static response and the dynamic characteristics are studied.

WAVELET SOLUTIONS FOR TIME HARMONIC ACOUSTIC WAVES IN A FINITE OCEAN

1993 ◽  
Vol 01 (01) ◽  
pp. 31-60 ◽  
Author(s):  
R. P. GILBERT ◽  
WEI LIN
Keyword(s):  
Partial Differential Equations ◽  
Wavelet Analysis ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Galerkin Approximation ◽  
Partial Differential ◽  
Adaptive Wavelet ◽  
Time Harmonic ◽  
Variational Form ◽  
Approximate Wave

In this paper, we show how wavelet analysis may be used to solve the parabolic approximate wave equation. The paper is naturally subdivided into three parts. The first entails a crash course in wavelet analysis with the aim of using it to solve partial differential equations. The second part develops the wavelet-Galerkin approximation for solving partial differential equations in variational form. Finally, the third section derives a range-depth adaptive wavelet approach, and, moreover, provides an algorithm for solving the propagation problem.

Ring Microgyroscope Modeling and Performance Evaluation

2005 ◽  
Author(s):  
Mehdi Esmaeili ◽  
Mohammad Durali ◽  
Nader Jalili
Keyword(s):  
Performance Evaluation ◽  
Differential Equations ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Ring Structure ◽  
Frequency Equation ◽  
System Sensitivity ◽  
Extended Hamilton’S Principle ◽  
And Performance

This paper discusses the effects of substrate motions on the performance of a microgyroscope modeled as a ring structure. Using Extended Hamilton’s Principle, the equations of motion are derived. The natural frequency equation and response of gyroscope are then extracted in closed-form for the case where substrate undergoes normal rotation. The Galerkin approximation is used for discretizing the partial differential equations of motion into ordinary differential equations. In these equations, the effects of angular accelerations, centripetal and coriolis accelerations are well apparent. The response of the system to different inputs is studied and the system sensitivity to input parameter changes is examined. Finally, the sources of error in the measurement of input rotational rate are recognized. The study demonstrates the importance of errors caused by cross axes inputs on the gyroscope output measurements.

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