EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION

2000 ◽  
Vol 08 (01) ◽  
pp. 223-240 ◽  
Author(s):  
MANISH MALHOTRA ◽  
PETER M. PINSKY
Keyword(s):  
Transfer Function ◽  
Near Field ◽  
Padé Approximation ◽  
Linear Operators ◽  
Far Field ◽  
Efficient Computation ◽  
Pade Approximation ◽  
Wide Range ◽  
Multiple Frequencies ◽  
Element Matrix

For many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Padé approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods.

Long-offset moveout for VTI using Padé approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C219-C227 ◽  
Author(s):  
Hanjie Song ◽  
Yingjie Gao ◽  
Jinhai Zhang ◽  
Zhenxing Yao
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Practical Applications ◽  
Long Offset ◽  
Wide Range ◽  
Isotropic Media ◽  
Transversally Isotropic ◽  
Error Accumulation ◽  
Anisotropy Parameters ◽  
Vti Media

The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation based on the higher order Taylor series coefficients for VTI media. For a given anellipticity parameter, we have the best accuracy when the numerator is one order higher than the denominator (i.e., [[Formula: see text]]); thus, we suggest using [4/3] and [7/6] orders for practical applications. A [7/6] Padé approximation can handle a much larger offset and stronger anellipticity parameter. We have further compared the relative traveltime errors between the Padé approximation and several approximations. Our method shows great superiority to most existing methods over a wide range of offset (normalized offset up to 2 or offset-to-depth ratio up to 4) and anellipticity parameter (0–0.5). The Padé approximation provides us with an attractive high-accuracy scheme with an error that is negligible within its convergence domain. This is important for reducing the error accumulation especially for deeper substructures.

Model Reduction of Transfer Functions Using a Dominant Root Method

1990 ◽  
Vol 112 (3) ◽  
pp. 547-554 ◽  
Author(s):  
J. E. Seem ◽  
S. A. Klein ◽  
W. A. Beckman ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Padé Approximation ◽  
Computational Effort ◽  
Pade Approximation ◽  
Bilinear Transformation ◽  
Transfer Problems

Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.

Derivation of Far-field Gain Using a Gain Reduction Effect in the Fresnel Region

2020 ◽  
Vol 35 (10) ◽  
pp. 1137-1143
Author(s):  
Ilkyu Kim ◽  
Sun-Gyu Lee ◽  
Jeong-Hae Lee
Keyword(s):  
Power Transmission ◽  
Near Field ◽  
Separation Distance ◽  
Far Field ◽  
Preliminary Measurement ◽  
Microwave Antennas ◽  
Fresnel Region ◽  
Wide Range ◽  
Reduction Effect ◽  
Reference Parameters

A handy method of calculating far-field gain based on the magnitude of the power transmission in a Fresnel region is presented, which can be applied to the phaseless near-field measurement. Due to the short range inside an anechoic chamber, the probe antenna is often placed in the Fresnel region of the antenna under test (AUT). It is well-known that far-field gain of an antenna gradually reduces when one antenna moves to the other one placed in a proximity distance. This fact can be advantageously applied to estimate the far-field gain in a far-field region. The proposed method offers rapid estimation of the far-field gain based on the simple input knowledge such as the probe antenna gain and the magnitude of the power transmission and the separation distance between AUT and probe antenna. The proposed method can be applicable to a wide range of microwave antennas. This feature makes it possible to offer preliminary measurement results and reference parameters of the measurement for the various types of microwave antennas.

Signature of coseismic off-fault damage in intermediate- and far-field radiation

2020 ◽  
Author(s):  
Kurama Okubo ◽  
Harsha S. Bhat ◽  
Esteban Rougier ◽  
Marine A. Denolle
Keyword(s):  
High Frequency ◽  
Near Field ◽  
Fault System ◽  
Far Field ◽  
Earthquake Rupture ◽  
Length Scales ◽  
Earthquake Sources ◽  
Planar Fault ◽  
Wide Range ◽  
Field Radiation

<p>Off-fault damage is observed around fault cores in a wide range of length scales, which is identified as an aggregation of localized fractures via geological and geodetic observations, or as low-velocity zone via seismological tomography. However, its seismological observables in earthquake traces, e.g. change in source spectra and/or radiation pattern, remains to be investigated. </p><p>Okubo et al. (2019) proposed an approach framework of physics-based dynamic earthquake rupture modeling with coseismic off-fault damage using the combined finite-discrete element method (FDEM). It shows a non-negligible contribution of coseismic damage to rupture dynamics, high-frequency radiation and overall energy budget, whereas the model domain is limited in the near-field region. This study efficiently computes intermediate- and far-field radiation propagating from earthquake sources with coseismic off-fault damage, and to identify its signature in the seismic traces.</p><p>We first conduct the dynamic earthquake rupture with coseismic damage and compute synthetic near-field radiation using FDEM-based software tool, HOSSedu, developed by Los Alamos National Laboratory. We then couple the output of HOSSedu to SPECFEM2D in order to compute intermediate- and far-field radiation. The HOSS-SPECFEM2D coupling can resolve complexities over wide range of length scales associated with earthquake sources with coseismic damage and wave propagation.</p><p>We conduct 2D dynamic earthquake rupture modeling with a finite planar fault as canonical simplest model. The comparison between the cases with and without allowing for coseismic off-fault damage shows differences in intermediate- and far-field radiation. 1) High-frequency components in ground motion are enhanced all around the fault. 2) The rupture arresting phase, which clearly appears at the stations located orthogonal to the fault for the case without off-fault damage, is damped due to the smoothed rupture arrest by coseismic damage around fault edges. 3) Radiated energy is enhanced in the direction parallel to the fault due to the substantial damage around fault edges.</p><p>These fundamental observables will help identify the existence of coseismic off-fault damage in real earthquakes. It would also contribute to resolve the mechanisms of earthquake sources and the potential distribution of aftershock locations. We also attempt to replace the planar fault to the real fault geometry, e.g. the fault system associated with the 2019 Ridgecrest earthquake sequence, and will investigate the signature of off-fault damage in the seismic traces recorded in intermediate- and far-field range.</p>

scholarly journals Near-Tip Field and the Associated Path-Independent Integrals for Anisotropic Composite Wedges

2001 ◽  
Vol 17 (1) ◽  
pp. 21-28
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Boundary Conditions ◽  
Near Field ◽  
Far Field ◽  
Anisotropic Composite ◽  
Wide Range ◽  
Composite Wedge ◽  
Asymptotic Fields

ABSTRACTThe asymptotic fields in an elastic anisotropic composite wedge are considered for a wide range of boundary conditions. It is shown that the eigenfunctions for the near-field and far-field are dual as they are generated by the same set of eigenvalues in general. If the boundary conditions on the wedge faces are the same, an additional eigenfunction may appear in the far-field. Moreover the dual eigenfunctions are used to derive path-independent integrals that relate the near-field to the far-field.

An Innovative Package EMC Solution Using a Highly Cost-Effective Sputtered Conformal Shield

2016 ◽  
Vol 2016 (DPC) ◽  
pp. 002152-002181 ◽  
Author(s):  
Nozad Karim ◽  
Rong Zhou ◽  
Jun Fan
Keyword(s):  
High Speed ◽  
Metal Layer ◽  
Near Field ◽  
Cost Effective ◽  
Circuit Board ◽  
System Level ◽  
Normal Operation ◽  
Far Field ◽  
Wide Range ◽  
The Cost

High-speed digital and wireless devices radiate undesired electromagnetic noises that affect the normal operation of other devices causing electromagnetic interference (EMI) problems. Printed circuit board (PCB) and system-level shielding may alleviate inter-system EMI between the PCB board and the outside environment, but does not prevent intra-system EMI within the shielding enclosure. Package and System in Package (SiP) level shielding is often used to minimize intra-system EMI issues. An external metal lid is traditionally employed to prevent noise emission from a device, but the cost and size of this technique makes it unattractive for modern electronics. Conformal shielding is gaining momentum due to its size and height advantages. However, high cost and complexity of the sprayed coating shield prevents it from being used for a wide range of low cost commercial applications. In this paper, an innovative shielding technology with sputtered metal conformal shield is investigated using a specially designed test vehicle. By sputtering a conductive material onto a package, a very thin (typically a few μm) metal layer is constructed on the top and around four sides of the package. This thin sputtered metal layer adds virtually zero penalty to the package size. The cost and complexity of the sputtering process is significantly lower compared to a spraying process. Several types of shielded and unshielded modules were built and extensively tested for both far-field and near-field shielding effectiveness (SE) in a semi-anechoic chamber. The performance of the sputtered conformal shield is compared to that of an unshielded module and the sprayed shield. The measured results show that the sputtered shield performs equally well to a sprayed shield, in far field test, with most measurements better than 40 dB of SE. In near field testing, sputtered shields mostly outperform the sprayed shield, especially when compared in the entire scanned region. A well-designed sputtered conformal shield can, therefore, be a very cost-effective EMI solution for a wide range of packages, such as SiP. Also in the paper, a full wave 3D HFSS model is presented and simulated results for both far and near field are compared with measured data.

An Evaluation of a Two-Fluid Eulerian-Liquid Eulerian-Gas Model for Diesel Sprays

2003 ◽  
Vol 125 (4) ◽  
pp. 660-669 ◽  
Author(s):  
Venkatraman Iyer ◽  
John Abraham
Keyword(s):  
Fluid Model ◽  
Near Field ◽  
Far Field ◽  
Diesel Sprays ◽  
Jet Breakup ◽  
Wide Range ◽  
Numerical Grid ◽  
Two Fluid Model ◽  
Grid Independence ◽  
Two Fluid

A two fluid Eulerian-liquid Eulerian-gas (ELEG) model for diesel sprays is developed. It is employed to carry out computations for diesel sprays under a wide range of ambient and injection conditions. Computed and measured results are compared to assess the accuracy of the model in the far field, i.e., at axial distances greater than 300 orifice diameters, and in the near field, i.e., at axial distances less than 100 orifice diameters. In the far field, the comparisons are of drop mean velocities and drop fluctuation velocities and in the near field they are of entrainment velocities and entrainment constants. Adequate agreement is obtained quantitatively, within 30 percent, and qualitatively as parameters are changed. Unlike in traditional Lagrangian-drop Eulerian-fluid (LDEF) approaches that are employed for diesel spray computations, adequate resolution can be employed in the near field to achieve numerical grid independence when the two-fluid model is employed. A major source of uncertainty in the near field is in the modeling of liquid jet breakup and atomization.

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