Joseph J. Shirron

A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems

We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not. We find that the accuracy of the ABCs decreases with increasing frequency, and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the IEMs. We show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field.

A numerical integration scheme for special finite elements for the Helmholtz equation

The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissae and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved.

Mid-frequency structural acoustic and vibration analysis in arbitrary, curved three-dimensional domains

Abstract A high-order finite element infrastructure is described for the numerical solution of the vibratory response of fluid–structure systems in the mid-frequency range. Underlying variational forms along with the use of an unstructured, topology-based, variable-degree, polymorphic finite element discretization scheme is described. Accurate numerical solutions to practical problems, including rigid and elastic acoustic scattering and interior acoustics, are presented to demonstrate the accuracy and flexibility of the infrastructure.

Image enhancement for underwater pulsed laser line scan imaging system

Recent progress in system hardware such as laser, photon detectors and other electronic and optical components resulted in significant improvement for the underwater serial laser imaging system. Nevertheless, during normal system operation, system issues such as laser instability, electronic noise, and environmental conditions such as imaging in highly turbid water can still put constraint on the performance of imager. In this work, post-processing to take advantage of the improvement hardware to further reduce image noise and enhance the image quality as a critical aspect of the overall system design is studied. A novel realization of the bilateral principle based image/pulse noise reduction and image deconvolution using point spread function (PSF) predicted with EODES radiative transfer model is used to implement the processing chain. The concept is further extended to a multichannel deconvolution to exploit the benefit offered by the new multi element PMT configuration developed in HBOI. Two datasets were used to test the developed techniques respectively.

Acoustic infinite elements for non-separable geometries

We present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long, slender bodies. The new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer. These elements need not begin on a level surface of the prolate spheroidal coordinate system. Instead, they may be attached to any convex surface, including that of the scatterer itself. This scheme reduces, or even completely eliminates, finite element modeling of the exterior medium. The formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid. We present both conjugated and unconjugated formulations without any weighting factors, although it would be simple to include them. We describe a fast numerical scheme for computing the element integrals based on Chebychev approximation. We include numerical results for scattering from spheres and capped cylinders. These results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element/infinite element methods.

A hierarchic p‐version boundary‐element method for axisymmetric acoustic scattering and radiation

A rapidly convergent boundary‐element method that has a high‐accuracy capability is developed for the solution of the exterior Neumann problem for the Helmholtz equation. The approach makes use of the boundary‐operator combination idea of Burton and Miller [A. J. Burton and G. F. Miller, Proc. R. Soc. London Ser. A 323, 201–210 (1971)] to avoid the classical irregular frequency difficulties together with p‐version boundary elements to obtain a high rate of convergence. The entire algorithm is designed to be fully hierarchic to minimize the cost of multiple solutions, which are necessary for a posteriori assessment of accuracy. A new hierarchic singular‐kernel quadrature rule is developed for this purpose. Numerical examples demonstrate the accuracy and convergence rate of the method.

Efficient laser pulse dispersion codes for turbid undersea imaging and communications applications

The objective of this work was to develop and validate approaches to accurately and efficiently model channel characteristics in a range of environmental and operational conditions for underwater laser communications systems that use high frequency amplitude modulation (AM) or coded pulse trains. Two approaches were investigated: 1) a Monte Carlo model to calculate impulse responses for a particular system hardware design over a large range of environmental and operational conditions, and 2) a semi-analytic model which has the potential to be more computationally efficient than the Monte Carlo model. The formulation of the Monte Carlo code is presented in this paper, together with test results used to evaluate the range of accuracy of the model against 500ps laser-pulse propagation measurements from well-controlled and characterized particle suspensions in a 12.5m test tank. A multiple scattering study using the Monte Carlo simulation code was also performed and some results are presented. Results from the semi-analytic model will be compared with these test tank measurements and the Monte Carlo model in a later paper.

A model for sonar interrogation of complex bottom and surface targets in shallow-water waveguides

Many problems of current interest in underwater acoustics involve low-frequency broadband sonar interrogation of objects near the sea surface or sea floor of a shallow-water environment. When the target is situated near the upper or lower boundary of the water column the acoustic interactions with the target objects are complicated by interactions with the nearby free surface or fluid-sediment interface, respectively. A practical numerical method to address such situations is presented. The model provides high levels of accuracy with the flexibility to handle complex, three-dimensional targets in range-independent environments. The model is demonstrated using several bottom target scenarios, with and without locally undulating seabeds. The impact of interface and boundary interactions is considered with an eye toward using the sonar return signal as the basis for acoustic imaging or spectral classification.

Numerical simulation of the incoherent electro-optical imaging process in plane-stratified media

A high-fidelity numerical model is developed for the incoherent electro-optical imaging process in media where the inherent optical properties vary with range. Four contributions to the image data are considered: laser light reflected from the scene, volume backscatter of laser light, reflected solar light, and solar backscatter. The model implements rigorous mathematical formulations, incorporates adaptive error control, uses computationally efficient algorithms, and has been rigorously validated. The model is flexible enough to handle many different sensor configurations and sampling techniques, continuous-wave and pulsed laser sources, and range-dependent properties of the optical environment. The derivation of relevant mathematical models is reviewed and unified into a comprehensive and flexible system that can be tailored to fit the various incoherent electro-optical imaging systems currently in use or in development. The numerical implementations are described for each key component of the overall model, and a sampling of new verification and validation results is provided.

An integration scheme for electromagnetic scattering using plane wave edge elements

Finite element techniques for the simulation of electromagnetic wave propagation are, like all conventional element based approaches for wave problems, limited by the ability of the polynomial basis to capture the sinusoidal nature of the solution. The Partition of Unity Method (PUM) has recently been applied successfully, in finite and boundary element algorithms, to wave propagation. In this paper, we apply the PUM approach to the edge finite elements in the solution of Maxwells equations. The electric field is expanded in a set of plane waves, the amplitudes of which become the unknowns, allowing each element to span a region containing multiple wavelengths. However, it is well known that, with PUM enrichment, the burden of computation shifts from the solver to the evaluation of oscillatory integrals during matrix assembly. A full electromagnetic scattering problem is not simulated or solved in this paper. This paper is an addition to the work of Ledger and concentrates on efficient methods of evaluating the oscillatory integrals that arise. A semi-analytical scheme of the Filon character is presented.