Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Solving complex optimal control problems at no cost with PSOPT

This paper introduces PSOPT, an open source optimal control solver written in C++. PSOPT uses pseudospectral and local discretizations, sparse nonlinear programming, automatic differentiation, and it incorporates automatic scaling and mesh refinement facilities. The software is able to solve complex optimal control problems including multiple phases, delayed differential equations, nonlinear path constraints, interior point constraints, integral constraints, and free initial and/or final times. The software does not require any non-free platform to run, not even the operating system, as it is able to run under Linux. Additionally, the software generates plots as well as LATEX code so that its results can easily be included in publications. An illustrative example is provided.

Preliminary leaf area index estimates from airborne small footprint full-waveform LiDAR data

This study has compared preliminary estimates of effective leaf area index (LAI) derived from fish-eye lens photographs to those estimated from airborne full-waveform small-footprint LiDAR data for a forest dataset in Australia. The full-waveform data was decomposed and optimized using a trust-region-reflective algorithm to extract denser point clouds. LAI LiDAR estimates were derived in two ways (1) from the probability of discrete pulses reaching the ground without being intercepted (point method) and (2) from raw waveform canopy height profile processing adapted to small-footprint laser altimetry (waveform method) accounting for reflectance ratio between vegetation and ground. The best results, that matched hemispherical photography estimates, were achieved for the waveform method with a study area-adjusted reflectance ratio of 0.4 (RMSE of 0.15 and 0.03 at plot and site level, respectively). The point method generally overestimated, whereas the waveform method with an arbitrary reflectance ratio of 0.5 underestimated the fish-eye lens LAI estimates.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Fixed point dual carrier modulation performance for wireless USB

Dual Carrier Modulation (DCM) is currently used as the higher data rate modulation scheme for Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) in the ECMA-368 defined Ultra-Wideband (UWB) radio platform. ECMA-368 has been chosen as the physical radio platform for many systems including Wireless USB (W-USB), Bluetooth 3.0 and Wireless HDMI; hence ECMA-368 is an important issue to consumer electronics and the user’s experience of these products. In this paper, Log Likelihood Ratio (LLR) demapping method is used for the DCM demaper implemented in fixed point model. Channel State Information (CSI) aided scheme coupled with the band hopping information is used as the further technique to improve the DCM demapping performance. The receiver performance for the fixed point DCM is simulated in realistic multi-path environments.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Whole crop cereals 1. Effect of method of harvest and preservation on chemical composition, apparent digestibility and energy value

A total of 133 samples (53 fermented unprocessed, 19 fermented processed. 62 urea-treated processed) of whole crop wheat (WCW) and 16 samples (five fermented unprocessed, six fermented processed, five urea-treated processed) of whole crop barley (WCB) were collected from commercial farms over two consecutive years (2003/2004 and 2004/2005). Disruption of the maize grains to increase starch availability was achieved at the point of harvest by processors fitted to the forage harvesters. All samples were subjected to laboratory analysis whilst 50 of the samples (24 front Year 1, 26 front Year 2 all WCW except four WCB in Year 2) were subjected to in vivo digestibility and energy value measurements using mature wether sheep. Urea-treated WCW had higher (P<0.05) pH, and dry matter (DM) and crude protein contents and lower concentrations of fermentation products than fermented WCW. Starch was generally lower in fermented, unprocessed WCW and no effect of crop maturity at harvest (as indicated by DM content) on starch concentrations was seen. Urea-treated WCW had higher (P<0.05) in vivo digestible organic matter contents in the DM (DOMD) in Year 1 although this was not recorded in Year 2. There was a close relationship between the digestibility values of organic matter and gross energy thus aiding the use of DOMD to predict metabolisable energy (ME) content. A wide range of ME values was observed (WCW. 8.7-11.8 MJ/kg DM; WCB 7.9-11.2 MJ/kg DM) with the overall ME/DOMD ratio (ME = 0.0156 DOMD) in line With Studies in other forages. There was no evidence that a separate ME/DOMD relationship was needed for WCB which is helpful for practical application. This ratio and other parameters were affected by year of harvest (P<0.05) highlighting the influence of environmental and Other undefined factors. The variability in the composition and nutritive value of WCW and WCB highlights the need for reliable and accurate evaluation methods to be available to assess the Value of these forages before they are included in diets for dairy cows. (C) 2008 Elsevier B.V. All rights reserved.

Development of a method fon non-destructive testing of fruits using scanning laser vibrometry (SLV)

Quality control on fruits requires reliable methods, able to assess with reasonable accuracy and possibly in a non-destructive way their physical and chemical characteristics. More specifically, a decreased firmness indicates the presence of damage or defects in the fruit or else that the fruit has exceeded its “best before date”, becoming unsuitable for consumption. In high-value exotic fruits, such as mangoes, where firmness cannot be easily measured from a simple observation of texture, colour changes and unevenness of fruits surface, the use of non-destructive techniques is highly recommendable. In particular, the application of Laser vibrometry, based on the Doppler effect, a non-contact technique sensitive to differences in displacements inferior to the nanometre, appears ideal for a possible on-line control on food. Previous results indicated that a phase shift can be in a repeatable way associated with the presence of damage on the fruit, whilst a decreased firmness results in significant differences in the displacement of the fruits under the same excitation signal. In this work, frequency ranges for quality control via the application of a sound chirp are suggested, based on the measurement of the signal coherence. The variations of the average vibration spectrum of a grid of points, or of point-by-point signal velocity allows the go-no go recognition of “firm” and “over-ripe” fruits, with notable success in the particular case of mangoes. The future exploitation of this work will include the application of this method to allow on-line control during conveyor belt distribution of fruits.