Peter L. Levin

Finite element formulation of acoustic scattering phenomena with absorbing boundary condition in the frequency domain

This paper discusses a finite element formulation with an absorbing boundary condition to simulate acoustic scattering phenomena in a general situation, that is, including density as well as sound velocity variations of single and multi‐scatterers of arbitrary two‐dimensional cross sections. In this model, a Galerkin finite element formulation is incorporated with an absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to the near field. By applying the absorbing boundary operator on the artificial boundary of the finite domain, the truncation errors as well as the artificial reflected power is minimized without compromising the sparsity of the finite element matrix. Performance analysis indicates that the absorbing boundary operator increases the accuracy from O(1/r3/2) to O(1/r9/2). The numerical results are compared with analytical solutions of cylindrical scatterers of different sizes and at different frequenci...

Nonlinear Diffractive Inverse Scattering for Multiple-Scattering in Inhomogeneous Acoustic Background Media

This paper discusses a nonlinear diffractive inversion of the Helmholtz equation for multiscattering configurations, where the scatterers are embedded in an inhomogeneous background medium. Using the finite element model to iteratively compute the scattered field in conjunction with a novel discrete cosine transform (DCT) representation of the object function permits the development of an efficient nonlinear inversion algorithm. The object function expansion is obtained by applying the DCT to sampling points which are chosen at the zeros of the Chebyshev polynomials, and achieves an accuracy comparable to the more popular sinc basis with far fewer expansion terms. After the inverse scattering formulation is converted into a nonlinear parameter estimation problem, the final matrix equation is linearized and solved by a standard least‐squares algorithm. Several examples of two‐dimensional single‐ and multiple‐scattering configurations for both homogeneous and inhomogeneous acoustic backgrounds will illustra...

Analytical and numerical treatment of pulsed wave propagation into a viscous fluid

A transient analytical expression for the propagation of pulsed ultrasound through a viscous fluid is derived by evaluating the Laplace transform in the complex domain. The numerical solution of the viscous wave equation without any restricting approximations is developed for a full space with an impulsive excitation at the origin. Different values of the viscosity coefficient for a given sound speed clearly delineate the transition from a pure parabolic, or diffusive to a pure hyperbolic or wave propagation behavior. This region is often of crucial importance from a practical point of view as ultrasonic instrumentation in medical imaging and nondestructive testing must compensate not only for phase differences due to propagation delays but also for pulse distortion due to attenuation mechanisms in the medium of interest.<<ETX>>

On conforming Delaunay mesh generation

Abstract Some of the complications of automatic Delaunay mesh generation can be resolved using an edge based representation. In particular, difficult tasks such as maintaining object boundaries, region identification, and application specific issues such as rapid construction of stiffness matrices in finite element analysis become straightforward. In this paper we propose such a data structure which was successfully implemented for E 2 and is amenable to E 3 applications.

Using GPS to calibrate Loran-C

Various techniques for using simultaneous Global Positioning System (GPS)/Loran data to estimate the propagation uncertainties that limit the absolute accuracy of Loran-C are discussed. Significant improvements in the absolute accuracy of Loran can be achieved with very simple calibrations. The absolute accuracy of Loran in the Gulf of Maine without calibration is presented. The maximum and RMS absolute errors are between 700 and 500 m, depending on the choice of land model. Simple calibrations greatly improve the absolute accuracy of Loran. As shown, if the land conductivities are fixed a priori and a single parameter is optimized, the maximum and RMS absolute errors fall to around 250 and 60 m, respectively. Alternatively, land can be treated as a single conductivity which can be adjusted to reduce offshore additional secondary phase factor errors. The performance of this practice is summarized in tables which show maximum and RMS errors of around 300 to 100 m, respectively. >

Minimum airgap-permeance data for the doubly-slotted pole structures common in variable-reluctance-motors

Minimum airgap-permeance data for double-salient pole structures, such as those common in variable-reluctance motors (VRMs), are presented. The data are derived from a finite-element analysis of a family of doubly salient pole structures. The ratio of the rotor interpolar arc to the stator pole arc and the ratio of the rotor pole undercut to rotor interpolar arc length are identified as the critical parameters governing minimum airgap permeance. The data are normalized to the active axial length of the motor, and are independent of the active radius of the motor. The permeance data are used to compute minimum inductance for three VRMs which have been experimentally characterized. Comparison of the computed and measured values indicates that end turn effects comprise a significant portion of the measured minimum inductance for motors with a short axial length. A second comparison is made between the data presented and the conventional flux tube analysis, indicating that the finite-element data are about as accurate as those obtained with flux tubes but are easier to implement.<<ETX>>

Comparison of the donor cell method to other computational techniques for the duct electrostatic precipitator

Abstract As modelling capabilities and computational resources have become more powerful and accessible, the duct electrostatic precipitator has been readdressed in the light of more sophisticated physical and numerical descriptions of its behavior. Some recent advances are discussed in this paper, which focuses attention on how the transport phenomena of migration, convection, and turbulent diffusion have been approximated by the donor cell technique, and compares this model with other computational approaches.

On the creation of sparse boundary element matrices for two dimensional electrostatics problems using the orthogonal Haar wavelet

This paper describes the creation of sparse boundary element matrices arising from Laplaces equation with mixed boundary conditions using an orthogonal wavelet basis. In contrast to previous work which employed a similarity transform that changed the finite dimensional basis a posteriori, the method described here can produce the sparse matrix directly. This has obvious advantages for large problems, where quadratic growth of the storage space required for the matrix coefficients can be prohibitively expensive.

Multiscale compression of BEM equations for electrostatic systems

This paper describes the use of wavelet bases to create a sparse approximation of the fully populated matrix that one obtains using an integral formulation like charge simulation or surface charge simulation for numerically solving Laplaces equation with mixed boundary conditions. The sparse approximation is formed by a similarity transform of the N/spl times/N coefficient matrix, and the cost of the one employed here is of optimal order N/sup 2/. We must emphasize that benefits of computing with a sparse matrix typically do not justify the costs of the transformation, unless the problem has multiple right hand sides, i.e. one wants to simulate multiple excitation modes. The special orthogonal matrices we need for the similarity transform are built from wavelet bases. Wavelets are a well studied and mature topic in pure and applied mathematics, however, the fundamental ideas are probably new to many researchers interested in electrostatic field computation. Towards this end an important purpose of this paper is to describe some of the basic concepts of multiresolutional analysis using wavelet bases.

On adaptive refinement for boundary integral methods in electrostatics

Numerical techniques based upon boundary integral methods like charge simulation or Galerkin boundary elements are still warmly received in the HV community because they are relatively easy to implement and use, and because they are accurate. However, the results can be sensitive to the quality of the discretization. In this work we introduce an efficient refinement scheme that automatically chooses the sections of conducting and dielectric boundaries where new nodes should be placed. The numerical results compare favorably to canonical solutions, and the method is shown to be effective on more complicated practical geometries. >