Search

Proper field sampling strategies are important in antenna measurements and diagnostics applications to reduce the overall testing time. We investigate the role of the source dimension in determining the sampling points locations by referring to circumference geometries. An inverse problem approach is adopted, and the spectral decomposition of the relevant operator is considered for a two-dimensional geometry. First, we introduce and discuss an approximation of the resulting Point Spread Functions, on which we found our approach. Next, a numerical strategy to discretize the field observation domain is presented, which results in a nonuniform angular step depending, in turn, on the source extension. Some numerical examples of source characterization show the effectiveness of the approach in comparison with the uniform angular sampling.

Inverse scattering problems stand at the center of many important imaging applications, such as geophysical explorations, radar imaging, and synthetic-aperture radar (SAR). Several methods have been proposed to solve them when the full data are available, usually providing satisfactory reconstructions. However, it is impossible to acquire the full data in many practical circumstances, such as target detection and ground penetrating radar (GPR); consequently, only limited data are available. Thus, this paper focuses on the mathematical analysis and some numerical simulations to estimate the achievable resolution in reconstructing an object from the knowledge of the scattered far-field when only limited data are available, with multi-view excitations at a single frequency. We focus on 2D full rectangular geometry as the investigation domain (ID). We also examine the number of degrees of freedom (NDF) and evaluate the point spread function (PSF). In particular, the NDF of the considered geometry can be estimated analytically. An approximated closed-form evaluation of the PSF is recalled, discussed, and compared with the exact one. Moreover, receiving, transmission, and angle sensing modes are considered to apply the analysis to more realistic scenarios to highlight the difference between the corresponding NDF and the resulting resolution performances. Finally, interesting numerical applications of the resolution analysis for the localization of a collection of point-like scatterers are presented to illustrate how it matches the expectations.

Field sampling should be devised in order to preserve the information required for the knowledge of the radiation of an antenna. In this paper, we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

We consider a fourth order singularly perturbed boundary value problem (BVP) in one-dimension and the approximation of its solution by the hp version of the Finite Element Method (FEM). The given problem's boundary conditions are not suitable for writing the BVP as a second order system, hence the approximation will be sought from a finite dimensional subspace of the Sobolev space H2. We construct suitable C1 hierarchical basis functions for the approximation and we show that the hp FEM on the Spectral Boundary Layer Mesh yields a robust approximation that converges exponentially in the energy norm, as the number of degrees of freedom is increased. Numerical examples that validate (and extend) the theory are also presented. © 2016 IMACS 104 81 97

In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O ( p 2 log ( N / p ) ) for one dimensional problems, O ( N p 2 ) for two dimensional problems, and O ( N 4 / 3 p 2 ) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O ( N p 2 ) for the one dimensional case, O ( N 1.5 p 3 ) for the two dimensional case, and O ( N 2 p 3 ) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p . Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions.

During the last few years, we have been witnessing a widespread adoption of touchless technologies in the context of surgical procedures. Touchless interfaces are advantageous in that they can preserve sterility around the patient, allowing surgeons to visualize medical images without having to physically touch any control or to rely on a proxy. Such interfaces have been tailored to interact with 2D medical images but not with 3D reconstructions of anatomical data, since such an interaction requires at least three degrees of freedom. In this paper, we discuss the results of a user study in which a mouse-based interface has been compared with two Kinect-based touchless interfaces which allow users to interact with 3D data with up to nine degrees of freedom. The experimental results show that there is a significant relation between the number of degrees of freedom simultaneously controlled by the user and the number of degrees of freedom required to perform, in a touchless way, an accurate manipulation task.

Cabinet vibrations during spinning cycles of washing machines are often perceived negatively by customers, both in acoustic and visual terms. Therefore, in a market that is more and more oriented towards customer satisfaction and appliance efficiency, reducing cabinet vibrations and noise is a very attractive target. Previous experimental campaigns have highlighted that currently installed dry-friction dampers have highly non-linear characteristics and they are the main source of broadband forcing on the cabinet panels. To overcome these negative effects, two innovative designs for the suspension system have been studied and are here presented: the first solution is a secondary suspension system, designed to filter out the high frequency force components introduced by the dampers and therefore to mitigate panel vibrations; the second solution is more radical and it consists in removing the existing dampers and to substitute them with a tuned mass damper (TMD), directly fixed to the oscillating group. These solutions are a compromise between cost and efficiency, since a linear oil damper would impact excessively on the final cost of the appliance. The secondary suspension system has been designed to meet the very strict requirements of the manufacturer: low cost (which implies small mass) and applicable to the existing machine without any modification of any part other than the dampers themselves. The desired results have been achieved increasing the mass of the damper rod and introducing a fixed-fixed (or hinged-hinged) beam spring. The prototype of the secondary suspension has been tested independently and assembled in the washing machine, and the vibratory and acoustic results will be reported. The introduction of a TMD and the contextual removal of the dry-friction dampers, on the contrary, requires the modification of the oscillating group in order to work efficiently. As a matter of fact, a principle for the design of oscillating groups is the space optimization, which usually leads to asymmetric distributions of mass of the oscillating group, that in their turn lead to asymmetrically coupled mode shapes. This dynamic characteristic does not suit the design of a simple and compact TMD, with a limited number of degrees of freedom. We show that careful mass distribution and a specifically designed 2-dofs TMD can efficiently substitute the original dampers. An elemental prototype of the so defined TMD has been tested on a shaking table, and it seems an effective alternative to classical suspension systems.