Space-FFT-accelerated marching-on-in-degree methods for finite periodic structures

2009 ◽  
Vol 1 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Amir Geranmayeh ◽  
Wolfgang Ackermann ◽  
Thomas Weiland
Keyword(s):  
Periodic Structures ◽  
Computational Cost ◽  
Stable Solution ◽  
Time Variable ◽  
One Dimensional ◽  
Multi Level ◽  
Temporal And Spatial ◽  
And Storage ◽  
Electric Field Integral Equations ◽  
Field Integral

A fast, yet unconditionally stable, solution of time-domain electric field integral equations (TD EFIE) pertinent to the scattering analysis of uniformly meshed and/or periodic conducting structures is introduced. A one-dimensional discrete fast Fourier transform (FFT)-based algorithm is proffered to expedite the calculation of the recursive spatial convolution products of the Toeplitz–block–Toeplitz retarded interaction matrices in a new marching-without-time-variable scheme. Additional saving owing to the system periodicity is concatenated with the Toeplitz properties due to the uniform discretization in multi-level sense. The total computational cost and storage requirements of the proposed method scale as O(Nt2Nslog Ns) and O(Nt Ns), respectively, as opposed to O(Nt2Ns2) and O(NtNs2) for classical marching-on-in-order methods, where Nt and Ns are the number of temporal and spatial unknowns, respectively. Simulation results for arrays of plate-like and cylindrical scatterers demonstrate the accuracy and efficiency of the technique.

Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials

2004 ◽  
Vol 70 (16) ◽  
Author(s):  
A. Mandatori ◽  
C. Sibilia ◽  
M. Bertolotti ◽  
S. Zhukovsky ◽  
J. W. Haus ◽  
...  
Keyword(s):  
Periodic Structures ◽  
One Dimensional

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

scholarly journals A Parameter Study of Localization

1996 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Sandor Stephen Mester ◽  
Haym Benaroya
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Vibration Characteristics ◽  
Periodic Pattern ◽  
Parameter Study ◽  
Structural Damping ◽  
One Dimensional

Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections.

scholarly journals Periodic and Near-Periodic Structures

1995 ◽  
Vol 2 (1) ◽  
pp. 69-95 ◽  
Author(s):  
S. S. Mester ◽  
H. Benaroya
Keyword(s):  
State Physics ◽  
Solid State ◽  
Periodic Structures ◽  
Vibration Characteristics ◽  
Aerospace Engineering ◽  
Structural Damping ◽  
Solid State Physics ◽  
One Dimensional ◽  
Fields Of Study ◽  
Effects Of Disorder

Extensive work has been done on the vibration characteristics of perfectly periodic structures. This article reviews the different methods of analysis from several fields of study, for example solid-state physics and civil, mechanical, and aerospace engineering, used to determine the effects of disorder in one-dimensional (1-D) and 2-D periodic structures. In the work examined, disorder has been found to lead to localization in 1-D periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. The implications of localization for control are also examined.

Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models

2014 ◽  
Author(s):  
Erasmo Carrera ◽  
Enrico Zappino
Keyword(s):  
Mechanical Design ◽  
Computational Cost ◽  
Advanced Materials ◽  
Complex Structures ◽  
Displacement Fields ◽  
One Dimensional ◽  
Classical Models ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Dimensional Models

One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.

scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot ◽  
A. S. Tijsseling ◽  
M. C. M. Rutten ◽  
F. N. van de Vosse
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
One Dimensional ◽  
Arterial Blood

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

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