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

Assyriological Comments on Some Difficult Passages

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A chironomid-based reconstruction of summer temperatures in NW Iceland since AD 1650

Few studies currently exist that aim to validate a proxy chironomid-temperature reconstruction with instrumental temperature measurements. We used a reconstruction from a chironomid percentage abundance data set to produce quantitative summer temperature estimates since AD 1650 for NW Iceland through a transfer function approach, and validated the record against instrumental temperature measurements from Stykkishólmur in western Iceland. The core was dated through Pb-210, Cs-137 and tephra analyses (Hekla 1693) which produced a well-constrained dating model across the whole study period. Little catchment disturbance, as shown through geochemical (Itrax) and loss-on-ignition data, throughout the period further reinforce the premise that the chironomids were responding to temperature and not other catchment or within-lake variables. Particularly cold phases were identified between AD 1683–1710, AD 1765–1780 and AD 1890–1917, with relative drops in summer temperatures in the order of 1.5–2°C. The timing of these cold phases agree well with other evidence of cooler temperatures, notably increased extent of Little Ice Age (LIA) glaciers. Our evidence suggests that the magnitude of summer temperature cooling (1.5–2°C) was enough to force LIA Icelandic glaciers into their maximum Holocene extent, which is in accordance with previous modelling experiments for an Icelandic ice cap (Langjökull)

Diseases of mahi mahi or common dolphin fish, Coryphaena hippurus in Australia

The diseases encountered in mahi mahi, Coryphaena hippurus, in a land-based hatchery, grow-out sea-cages, and from wild populations between 1987 and 1990 were predominately due to protozoan and metazoan parasites. Milky flesh , or flesh liquefaction post-mortem, due to Kudoa thyrsites, Trichodina gill infections, and eye lesions induced by Benedenia were the most serious infectious diseases of cultured fish. Bacterial diseases were limited to secondary opportunistic infections and fin rot , and no fungal or viral conditions were detected. Non-infectious diseases included vitamin E deficiency in fry, lateral canal erosions, and miscellaneous dietary and therapeutic toxicities

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells

An efficient frequency-independent numerical method for computing the far-field pattern induced by polygonal obstacles

For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent) set of canonical incident angles. Although these remarkable formulae are exact in theory, here we demonstrate that: (i) they are highly sensitive to numerical errors in practice, and; (ii) direct calculation of the coefficients in these formulae may be impossible for particular sets of canonical incident angles, even in exact arithmetic. Only by overcoming these practical issues can embedding formulae provide a highly efficient approach to computing the far-field pattern induced by a large number of incident angles. Here we propose solutions for problems (i) and (ii), backed up by theory and numerical experiments. Problem (i) is solved using techniques from computational complex analysis: we reformulate the embedding formula as a complex contour integral and prove that this is much less sensitive to numerical errors. In practice, this contour integral can be efficiently evaluated by residue calculus. Problem (ii) is addressed using techniques from numerical linear algebra: we oversample, considering more canonical incident angles than are necessary, thus expanding the space of valid coefficients vectors. The coefficients vectors can then be selected using either a least squares approach or column subset selection

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings