A Combined Perfectly Matching Layer and Infinite Element Formulation for Unbounded Wave Problems in the Frequency Domain

2014 ◽  
Author(s):  
Joseph S. Pettigrew ◽  
Anthony J. Mulholland ◽  
Jeffrey L. Cipolla ◽  
John Mould ◽  
Robert Banks
Keyword(s):  
Frequency Domain ◽  
Marked Improvement ◽  
Test Problem ◽  
Near Field ◽  
Element Formulation ◽  
Infinite Element ◽  
Matching Layer ◽  
Modal Response ◽  
New Type ◽  
Wave Problems

In this paper, Berenger’s Perfectly Matching Layer (PML) and Bettess’ Infinite Element (IE) scheme are combined to create a new type of element for unbounded acoustic wave problems. An assessment of this new element formulation is made through its use in the calculation of the acoustic modal response of a spherical radiator in the frequency domain. The performance of the PML+IE approach is contrasted with the IE only methodology by comparing them to the exact solution of this test problem in terms of the surface inertia and resistance in the near field. The results are encouraging and the PML+IE approach shows a marked improvement in performance, particularly at lower frequencies.

scholarly journals Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

2021 ◽  
pp. 108128652110408
Author(s):  
Joseph S. Pettigrew ◽  
Anthony J. Mulholland ◽  
Katherine M. M. Tant
Keyword(s):  
Finite Element ◽  
Elastic Wave ◽  
Three Dimensions ◽  
Element Formulation ◽  
Infinite Element ◽  
Matching Layer ◽  
Plane Wave Incident ◽  
The Time Domain ◽  
Wave Problems ◽  
Stress Free Boundary

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

Analysis of Structural and Non-Structural Problems by Coupling of Finite and Infinite Elements

2014 ◽  
Vol 578-579 ◽  
pp. 445-455
Author(s):  
Mustapha Demidem ◽  
Remdane Boutemeur ◽  
Abderrahim Bali ◽  
El-Hadi Benyoussef
Keyword(s):  
Numerical Technique ◽  
Near Field ◽  
Main Idea ◽  
Far Field ◽  
Mining Operations ◽  
Infinite Element ◽  
Infinite Elements ◽  
Structural Problems ◽  
Infinite Element Method ◽  
Element Method

The main idea of this paper is to present a smart numerical technique to solve structural and non-structural problems in which the domain of interest extends to large distance in one or more directions. The concerned typical problems may be the underground excavation (tunneling or mining operations) and some heat transfer problems (energy flow rate for construction panels). The proposed numerical technique is based on the coupling between the finite element method (M.E.F.) and the infinite element method (I.E.M.) in an attractive manner taking into consideration the advantages that both methods offer with respect to the near field and the far field (good accuracy and sensible reduction of equations to be solved). In this work, it should be noticed that the using of this numerical coupling technique, based on the infinite element ascent formulation, has introduced a more realistic and economic way to solve unbounded problems for which modeling and efficiency have been elegantly improved. The types of the iso-parametric finite elements used are respectively the eight-nodes (Q8) and the four-nodes (Q4) for the near field. However, for the far field the iso-parametric infinite elements used are the eight-nodes (Q8I) and the six-nodes (Q6I).

scholarly journals Frequency-Diverse Holographic Metasurface Antenna for Near-Field Microwave Computational Imaging

2021 ◽  
Vol 8 ◽  
Author(s):  
Jiaqi Han ◽  
Long Li ◽  
Shuncheng Tian ◽  
Xiangjin Ma ◽  
Qiang Feng ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Imaging System ◽  
Near Field ◽  
Horn Antenna ◽  
Computational Imaging ◽  
Simulation Studies ◽  
Field Patterns ◽  
Full Wave ◽  
Imaging Reconstruction ◽  
Iterative Shrinkage

This article presents a holographic metasurface antenna with stochastically distributed surface impedance, which produces randomly frequency-diverse radiation patterns. Low mutual coherence electric field patterns generated by the holographic metasurface antenna can cover the K-band from 18 to 26 GHz with 0.1 GHz intervals. By utilizing the frequency-diverse holographic metasurface (FDHM) antenna, we build a near-field microwave computational imaging system based on reflected signals in the frequency domain. A standard horn antenna is adopted to acquire frequency domain signals radiated from the proposed FDHM antenna. A detail imaging restoration process is presented, and the desired targets are correctly reconstructed using the 81 frequency-diverse patterns through full-wave simulation studies. Compressed sensing technique and iterative shrinkage/thresholding algorithms are applied for the imaging reconstruction. The achieved compressive ratio of this computational imaging system on the physical layer is 30:1.

Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

Optical Tomography With a Least Square Finite Element Formulation of the Collimated Irradiation in Frequency Domain

2010 ◽  
Author(s):  
Olivier Balima ◽  
Joan Boulanger ◽  
Andre´ Charette ◽  
Daniel Marceau
Keyword(s):  
Finite Element ◽  
Optical Properties ◽  
Frequency Domain ◽  
Complex Geometry ◽  
Numerical Study ◽  
Optical Tomography ◽  
Least Square ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Scattering Media

This paper presents a numerical study of optical tomography in frequency domain for the reconstruction of optical properties of scattering and absorbing media with collimated irradiation light sources. The forward model is a least square finite element formulation of the collimated irradiation problem where the intensity is separated into its collimated and scattered parts. This model does not use any empirical stabilization and moreover the collimated source direction is taken into account. The inversion uses a gradient type minimization method where the gradient is computed through an adjoint formulation. Scaling is used to avoid numerical round errors, as the output readings at detectors are very low. Numerical reconstructions of optical properties of absorbing and scattering media with simulated data (noised and noise-free) are achieved in a complex geometry with satisfactory results. The results show that complex geometries are well handled with the proposed method.

Corrugated SNOM probe with enhanced energy throughput

2008 ◽  
Vol 16 (4) ◽  
Author(s):  
T. Antosiewicz ◽  
T. Szoplik
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Energy Output ◽  
Dipolar Field ◽  
Two Dimensional ◽  
The Core ◽  
Dimensional Approximation ◽  
New Type ◽  
Difference Time ◽  
Main Factor

AbstractIn a previous paper we proposed a modification of metal-coated tapered-fibre aperture probes for scanning near-field optical microscopes (SNOMs). The modification consists in radial corrugations of the metal-dielectric interface oriented inward the core. Their purpose is to facilitate the excitation of surface plasmons, which increase the transport of energy beyond the cut-off diameter and radiate a quasi-dipolar field from the probe output rim. An increase in energy output allows for reduction of the apex diameter, which is the main factor determining the resolution of the microscope. In two-dimensional finite-difference time-domain (FDTD) simulations we analyse the performance of the new type of SNOM probe. We admit, however, that the two-dimensional approximation gives better results than expected from exact three-dimensional ones. Nevertheless, optimisation of enhanced energy throughput in corrugated probes should lead to at least twice better resolution with the same sensitivity of detectors available nowadays.

Sign in / Sign up

Export Citation Format

Share Document