A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high frequency asymptotics of the solution. Our numerical results suggest that fi�xed accuracy can be achieved at arbitrarily high frequencies with a frequency-independent computational cost. Our analysis does not capture this observed behaviour completely, but we provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom $N$ increases, and that to achieve any desired accuracy it is sufficient to increase $N$ in proportion to the square of the logarithm of the frequency as the frequency increases (standard boundary element methods require $N$ to increase at least linearly with frequency to retain accuracy). We also show how our method can be applied to the complementary "breakwater" problem of propagation through an aperture in an infinite sound-hard screen

Social Service and Urban-Renewal: A Case Illustration

The city of Stamford, Connecticut has an Urban Renewal project as have most Urban centers. The Family Relocation Divison of Stamford\u27s Urban Redevelopment Commission (URC) entered into a contract with the Family and Children\u27s Services (FCS) to provide one day a week consultation to the Relocation staff and client services to the families in the renewal area. This consultation involved in-service training programs geared toward helping the relocation staff increase their skills in identifying problems within families and in assisting families to obtain help. As a result of this consultation, the relocation workers frequently would discuss the problems of the families referred to the Family Service worker and accompany the caseworker to the initial interview. It was the result of one such referral of a couple living in a building taken over by the URC in an area slated for redevelopment, a building euphemistically called The Cumping Grounds , that the Family Service worker evolved a group work approach. The group included all the tenants in the building. This paper will highlight the development of this group over a two year period, focusing particular attention on the impact of the experience on the behavior of the participants. The group which developed included: Blacks, whites, Puerto Ricans; (single and married), elderly and middle aged members. Although the group work was a reality-oriented problem-solving endeavor, the therapeutic gains for the individuals were very dramatic

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Mechanical property evaluation of an Al-2024 alloy subjected to HPT processing

An aluminum-copper alloy (Al-2024) was successfully subjected to high-pressure torsion (HPT) up to five turns at room temperature under an applied pressure of 6.0 GPa. The Al-2024 alloy is used as a fuselage structural material in the aerospace sector. Mechanical properties of the HPT-processed Al-2024 alloy were evaluated using the automated ball indentation technique. This test is based on multiple cycles of loading and unloading where a spherical indenter is used. After two and five turns of HPT, the Al-2024 alloy exhibited a UTS value of ~1014 MPa and ~1160 MPa respectively, at the edge of the samples. The microhardness was measured from edges to centers for all HPT samples. These results clearly demonstrate that processing by HPT gives a very significant increase in tensile properties and the microhardness values increase symmetrically from the centers to the edges. Following HPT, TEM examination of the five-turn HPT sample revealed the formation of high-angle grain boundaries and a large dislocation density with a reduced average grain size of ~80 nm. These results also demonstrate that high-pressure torsion is a processing tool for developing nanostructures in the Al-2024 alloy with enhanced mechanical propertie