scholarly journals Acceleration of Augmented EFIE Using Multilevel Complex Source Beam Method

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lianning Song ◽  
Yongpin Chen ◽  
Ming Jiang ◽  
Jun Hu ◽  
Zaiping Nie
Keyword(s):  
Computational Cost ◽  
Low Frequency ◽  
Electric Field Integral Equation ◽  
Vector Potentials ◽  
Multilevel Algorithm ◽  
Complex Source ◽  
The Matrix ◽  
Aggregation And Disaggregation ◽  
Scalar Potentials ◽  
Fast Multipole Algorithm

The computation of the augmented electric field integral equation (A-EFIE) is accelerated by using the multilevel complex source beam (MLCSB) method. As an effective solution of the low-frequency problem, A-EFIE includes both current and charge as unknowns to avoid the imbalance between the vector potentials and the scalar potentials in the conventional EFIE. However, dense impedance submatrices are involved in the A-EFIE system, and the computational cost becomes extremely high for problems with a large number of unknowns. As an exact solution to Maxwell’s equations, the complex source beam (CSB) method can be well tailored for A-EFIE to accelerate the matrix-vector products in an iterative solver. Different from the commonly used multilevel fast multipole algorithm (MLFMA), the CSB method is free from the problem of low-frequency breakdown. In our implementation, the expansion operators of CSB are first derived for the vector potentials and the scalar potentials. Consequently, the aggregation and disaggregation operators are introduced to form a multilevel algorithm to reduce the computational complexity. The accuracy and efficiency of the proposed method are discussed in detail through a variety of numerical examples. It is observed that the numerical error of the MLCSB-AEFIE keeps constant for a broad frequency range, indicating the good stability and scalability of the proposed method.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

SYNTHESIS OF ALLOY METAL NANOCLUSTERS IN SILICA GLASS BY SEQUENTIAL ION IMPLANTATION

2007 ◽  
Vol 06 (06) ◽  
pp. 423-430 ◽  
Author(s):  
B. JOSEPH ◽  
H. P. LENKA ◽  
P. K. KUIRI ◽  
D. P. MAHAPATRA ◽  
R. KESAVAMOORTHY
Keyword(s):  
Ion Implantation ◽  
Silica Glass ◽  
Metallic Nanoparticles ◽  
Rutherford Backscattering Spectrometry ◽  
Low Frequency ◽  
Peak Position ◽  
Negative Ion ◽  
Metal Nanoclusters ◽  
Cross Sectional ◽  
The Matrix

High fluence low energy negative ion implantation has been used to synthesize embedded metal nanoclusters of Au , Ag and Sb in silica glass. The Au - and Ag -implanted samples showed peaks, corresponding to surface plasmon resonance (SPR) in the optical absorption (OA) spectra, confirming the formation of metallic nanoparticles in the matrix. No SPR peak was observed in case of Sb -implanted samples which is attributed to the absence of pure metallic precipitates which could be detected in the OA spectrum. Low frequency Raman scattering (LFRS) measurements also confirm this. Cross-sectional transmission electron microscopy has been used to infer about the size distribution of the nanoparticles. Sequential implantations of Au and Ag or Au and Sb have been found to result in SPR peaks at locations in between those for nanoparticles of the constituent atoms, indicating the formation of alloy nanoparticles in the system. In case of the Au + Ag system, Rutherford backscattering spectrometry has been used to infer about the composition of the nanoparticles in terms of the concentrations of the metallic constituents. A direct, one-to-one correspondence between the SPR peak position and composition has been observed.

Subsurface reflectivity estimation from imaging of primaries and multiples using amplitude-normalized separated wavefields

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S101-S117 ◽  
Author(s):  
Alba Ordoñez ◽  
Walter Söllner ◽  
Tilman Klüver ◽  
Leiv J. Gelius
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Computational Cost ◽  
Image Point ◽  
Point Location ◽  
Multiple Reflections ◽  
Frequency Space ◽  
Propagation Effects ◽  
The Matrix ◽  
Spatial Domains

Several studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors. However, to characterize the reflector properties, there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples. From this perspective and based on the wave equation and Rayleigh’s reciprocity theorem, recent works have suggested computing the subsurface image from the Green’s function reflection response (or reflectivity) by inverting a Fredholm integral equation in the frequency-space domain. By following Claerbout’s imaging principle and assuming locally reacting media, the integral equation may be reduced to a trace-by-trace deconvolution imaging condition. For a complex overburden and considering that the structure of the subsurface is angle-dependent, this trace-by-trace deconvolution does not properly solve the Fredholm integral equation. We have inverted for the subsurface reflectivity by solving the matrix version of the Fredholm integral equation at every subsurface level, based on a multidimensional deconvolution of the receiver wavefields with the source wavefields. The total upgoing pressure and the total filtered downgoing vertical velocity were used as receiver and source wavefields, respectively. By selecting appropriate subsets of the inverted reflectivity matrix and by performing an inverse Fourier transform over the frequencies, the process allowed us to obtain wavefields corresponding to virtual sources and receivers located in the subsurface, at a given level. The method has been applied on two synthetic examples showing that the computed reflectivity wavefields are free of propagation effects from the overburden and thus are suited to extract information of the image point location in the angular and spatial domains. To get the computational cost down, our approach is target-oriented; i.e., the reflectivity may only be computed in the area of most interest.

scholarly journals CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS

2000 ◽  
Vol 12 (02) ◽  
pp. 181-225 ◽  
Author(s):  
KURT BRODERIX ◽  
DIRK HUNDERTMARK ◽  
HAJO LESCHKE
Keyword(s):  
Brownian Bridge ◽  
Integral Kernel ◽  
Dirichlet Boundary Conditions ◽  
Dimensional Euclidean Space ◽  
Kato Class ◽  
Vector Potentials ◽  
Continuity Properties ◽  
Scalar Potentials ◽  
General Configuration ◽  
Zero Vector

The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.

A Computationally Efficient Rayleigh–Ritz Model for Heterogeneous Oceanic Waveguides Using Fourier Series of Sound Speed Profile

2021 ◽  
pp. 2150015
Author(s):  
A. D. Chowdhury ◽  
S. K. Bhattacharyya ◽  
C. P. Vendhan
Keyword(s):  
Fourier Series ◽  
Sound Speed ◽  
Transmission Loss ◽  
Ritz Method ◽  
Computational Cost ◽  
Least Square ◽  
Speed Profile ◽  
Matrix Elements ◽  
Sound Speed Profile ◽  
The Matrix

The normal mode method is widely used in ocean acoustic propagation. Usually, finite difference and finite element methods are used in its solution. Recently, a method has been proposed for heterogeneous layered waveguides where the depth eigenproblem is solved using the classical Rayleigh–Ritz approximation. The method has high accuracy for low to high frequency problems. However, the matrices that appear in the eigenvalue problem for radial wavenumbers require numerical integration of the matrix elements since the sound speed and density profiles are numerically defined. In this paper, a technique is proposed to reduce the computational cost of the Rayleigh–Ritz method by expanding the sound speed profile in a Fourier series using nonlinear least square fit so that the integrals of the matrix elements can be computed in closed form. This technique is tested in a variety of problems and found to be sufficiently accurate in obtaining the radial wavenumbers as well as the transmission loss in a waveguide. The computational savings obtained by this approach is remarkable, the improvements being one or two orders of magnitude.

scholarly journals Improved Generalized Single-Source Tangential Equivalence Principle Algorithm with Contact-Region Modeling Method for Array Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yao Han ◽  
Hanru Shao ◽  
Jianfeng Dong
Keyword(s):  
Equivalence Principle ◽  
Contact Region ◽  
Near Field ◽  
Single Source ◽  
Matrix Vector Multiplication ◽  
The Matrix ◽  
Array Structures ◽  
Fast Multipole Algorithm ◽  
Matrix Vector ◽  
Equivalence Principle Algorithm

An improved generalized single-source tangential equivalence principle algorithm (GSST-EPA) is proposed for analyzing array structures with connected elements. In order to use the advantages of GSST-EPA, the connected array elements are decomposed and computed by a contact-region modeling (CRM) method, which makes that each element has the same meshes. The unknowns of elements can be transferred onto the equivalence surfaces by GSST-EPA. The scattering matrix in GSST-EPA needs to be solved and stored only once due to the same meshes for each element. The shift invariant of translation matrices is also used to reduce the computation of near-field interaction. Furthermore, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiplication in the GSST-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Characteristics of Band Gap and Low-frequency Wave Propagation of Mechanically Tunable Phononic Crystals with Scatterers in Periodic Porous Elastomeric Matrices

2021 ◽  
pp. 1-34
Author(s):  
Shaowu Ning ◽  
Dongyang Chu ◽  
Fengyuan Yang ◽  
Heng Jiang ◽  
Zhanli Liu ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Coupling Effect ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Dynamic Responses ◽  
Acoustic Metamaterials ◽  
Frequency Wave ◽  
Strong Coupling Effect ◽  
The Matrix

Abstract The characteristics of passive responses and fixed band gaps of phononic crystals (PnCs) limit their possible applications. For overcoming this shortcoming, a class of tunable PnCs comprised of multiple scatterers and soft periodic porous elastomeric matrices are designed to manipulate the band structures and directionality of wave propagation through the applied deformation. During deformation, some tunable factors such as the coupling effect of scatterer and hole in the matrix, geometric and material nonlinearities, and the rearrangement of scatterer are activated by deformation to tune the dynamic responses of PnCs. The roles of these tunable factors in the manipulation of dynamic responses of PnCs are investigated in detail. The numerical results indicate that the tunability of the dynamic characteristic of PnCs is the result of the comprehensive function of these tunable factors mentioned above. The strong coupling effect between the hole in the matrix and the scatterer contributes to the formation of band gaps. The geometric nonlinearity of matrix and rearrangement of scatterer induced by deformation can simultaneously tune the band gaps and the directionality of wave propagation. However, the matrix's material nonlinearity only adjusts the band gaps of PnCs and does not affect the directionality of wave propagation in them. The research extends our understanding of the formation mechanism of band gaps of PnCs and provides an excellent opportunity for the design of the optimized tunable PnCs and acoustic metamaterials.

scholarly journals Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements

2019 ◽  
Vol 219 (1) ◽  
pp. 39-65
Author(s):  
Octavio Castillo-Reyes ◽  
Josep de la Puente ◽  
Luis Emilio García-Castillo ◽  
José María Cela
Keyword(s):  
High Performance ◽  
Computational Cost ◽  
Low Frequency ◽  
Computation Time ◽  
Multiple Scale ◽  
High Order ◽  
Physical Parameters ◽  
Adaptive Meshing ◽  
Controlled Source ◽  
High Order Schemes

SUMMARY We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell’s equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture.

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