Automatic mesh generation using the symmetric axis transformationof polygonal domains

An automatic method for generating finite element meshes for multiply connected planar domains with polygonal boundaries (i.e. planar polygons with polygonal holes) is described. The symmetric axis transform is used to obtain a planar graph that partitions the given domain. This transformation may introduce edges in the graph that are too long or too short for generating good meshes. A silver processing algorithm, which transforms the graph into another graph devoid of such edges, is presented. Finally, additional modes are placed on the edges of the graph to obtain a triangulation, and this process is applied iteratively, yielding the final mesh. The method automatically increases the mesh density in regions of rapid change in shape and allows both global and local control of the mesh density. The method also admits the imposition of node compatibility constraints along domain boundaries, thus making the method suitable for meshing planar cell complexes (i.e multiple polygonal domains with shared boundaries in two-dimensional space) and for generating boundary elements for polyhedra in three-dimensional space     

Limiting stable currents in bounded electron and ion streams

The classical static analysis of the infinite planar diode has been extended to include the effects of finite transverse beam size. Simple expressions have been found for the increase in maximum stable current density over that of an infinite stream for finite cylindrical and strip streams flowing between plates of infinite diodes. The results are also given in terms of stream perveance. The effect of a nonuniform distribution of current across the stream is shown to be relatively small. Experimental values of maximum stable current agree with those obtained from the analysis. A further extension of the static analysis has been made to include the effects of additional conducting plane boundaries parallel to the stream motion. For length-to-width ratios L/D less than 0.25 the tube is adequately described by the results for the infinite planar diode and for L/D greater than 4, the infinitely-long drift tube theory suffices. At intermediate values of L/D, the maximum amount of current that can be stably passed through the tube is greater than that predicted by either asymptotic theory.     

On the GTD scattering by a polygonal cylinder

Using Keller's geometrical theory of diffraction (GTD) the field diffracted by a wedge is infinite at the shadow and reflection boundaries. In general, uniform diffraction coefficients must be used to provide continuous fields at these boundaries. In this communication it is shown that by properly adding the singular contributions from a pair of adjacent edges, Keller's diffraction coefficients yield a continuous far-zone field at the reflection boundaries of a polygonal cylinder illuminated by a plane wave. Furthermore the procedure is justified by noting that the uniform diffraction coefficients reduce to the Keller diffraction coefficients for this case.     

High-Frequency Green's Function for Planar Periodic Phased Arrays With Skewed Grid and Polygonal Contour

The derivation of an uniform high-frequency asymptotic representation of the array Green's function (AGF) for finite planar periodic phased arrays with arbitrary polygonal contour and skewed grid is presented. This result generalizes those obtained, in a series of recent papers, in the case of rectangular phased arrays with rectangular grid. For the treatment of the high-frequency phenomena, the actual finite array is rigorously decomposed in terms of canonical constituents, i.e., infinite, semi-infinite and sectoral arrays. The final result is a representation of the AGF in terms of spatially truncated Floquet waves (FWs) and FW-induced diffracted fields arising from the edges and vertices of the polygonal rim of the array. Consequently, the number of field contributions necessary to reconstruct the total field is independent of the number of elements of the array, leading to a very efficient algorithm. A series of numerical results is provided to demonstrate the effectiveness of the high-frequency representation     

Incremental diffraction coefficients for planar surfaces

Exact expressions for incremental diffraction coefficients at arbitrary angles of incidence and scattering are derived directly in terms of the corresponding two-dimensional, cylindrical diffraction coefficients. The derivation is limited to perfectly conducting scatterers that consist of planar surfaces, such as the wedge, the slit in an infinite plane, the strip, parallel or skewed planes, polygonal cylinders, or any combination thereof; and requires a known expression (whether exact or approximate) for the two-dimensional diffraction coefficients produced by the current on each different plane. Specifically, if one can supply an expression for the conventional diffraction coefficients of a two-dimensional planar scatterer, one can immediately find the incremental diffraction coefficients through direct substitution. No integration, differentiation, or specific knowledge of the current is required. Special attention is given to defining ambiguously all real angles and their analytic continuation into imaginary values required by the incremental diffraction coefficients     

Analysis and optimization of an array of miltimode plane waveguides excited by TM waves in order to form sectorial partial directional patterns

An electrodynamic analysis of an infinite periodic array of radiating planar multimode waveguide sections of finite length, each of which is excited by TM waves through a pair of input planar waveguides, is carried out. A numerical algorithm based on the method of projective field matching at the boundaries of partial domains, making it possible to calculate the partial directional pattern of the array and the amplitudes of the reflected waves in the input waveguides, is developed. Three circuits for the excitation of the array are considered, and the optimization of the length of the radiating sections and the parameters of the excitation circuits in order to form sectorial partial directional patterns of the array is performed. Results characterizing the comparative efficiency of the considered circuits for different periods of array are presented.     

Novel method to obtain the optimal polygonal approximation of digital planar curves based on Mixed Integer Programming

Polygonal approximations of digital planar curves are very useful for a considerable number of applications in computer vision. A great interest in this area has generated a huge number of methods for obtaining polygonal approximations. A good measure to compare these methods is known as Rosin’s merit. This measure uses the optimal polygonal approximation, but the state-of-the-art methods require a tremendous computation time for obtaining this optimal solution.We focus on the problem of obtaining the optimal polygonal approximation of a digital planar curve. Given N ordered points on a Euclidean plane, an efficient method to obtain M points that defines a polygonal approximation with the minimum distortion is proposed.The new solution relies on Mixed Integer Programming techniques in order to obtain the minimum value of distortion. Results, show that computation time for the new method dramatically decreases in comparison with state-of-the-art methods for obtaining the optimal polygonal approximation.     

Stochastic processes that generate polygonal and related randomfields

A reversible, ergodic, Markov process taking values in the space of polygonally segmented images is constructed. The stationary distribution of this process can be made to correspond to a Gibbs-type distribution for polygonal random fields as introduced by Arak and Surgailis (1989) and a few variants thereof, such as those arising in Bayesian analysis of random fields. Extensions to generalized polygonal random fields are presented where the segmentation boundaries are not necessarily straight line segments     

Surface currents induced on a wedge under plane wave illumination: An approximation

An approximate transform for the surface current induced on an infinite wedge is presented. The transform readily allows the investigation of the pulse response of a large class of cylindrical structures of general polygonal cross section. The results for the polarization of the excitation both parallel and normal to the axis of the infinite wedge are presented.     

Non-local singularities as the point-source images in thegeneralized method of D. A. Grave for solving wave-scattering problems.(On the possible origin of a legend about optical properties ofwerewolves and ghosts)

The method of D. A. Grave (1885) in the theory of two-dimensional boundary-value problems for the Laplace equation in domains with smooth analytical (algebraic) boundaries represents the solution as an infinite superposition of static fields of external sources with alternating signs, located along an infinite curve orthogonal to the boundary. This method is a generalization of the classical method of images for the simplest boundaries (half-plane, flat strip, circular, and rectangular cylinders). All of the images are local singularities of the pole type of the solution continuation outside the boundary. The type of solution of D. A. Grave may be obtained for convex algebraic boundaries as a result of a certain regular procedure. In the case of the Helmholtz equation, a generalization of this method for curved boundaries is also possible, but leads to more complicated non-local singularities. Besides the poles, it also contains a series of weak singularities, distributed along an infinite set of segments     

Improved boundary element techniques for two-dimensional scattering problems with circular boundaries

The application of the boundary element method (BEM) in two-dimensional scattering problems with circular boundaries is considered. Uniform discretization of the boundaries results in circulant or block-circulant matrices which provide a great economy in memory storage requirements, and through the use of fast Fourier transform (FFT) techniques, reduction in computation time. Some of the described methods can be applied in problems with regular polygonal boundaries.     

强激光诱导的应力波在靶板中衰减特性数值模拟

利用ABAQUS 数值模拟软件对脉宽为ns量级的强激光诱导的应力波在铜靶中传播特性进行了模拟研究。建立了适合于高压高应变率下一维平面应力波在铜靶中传播的有限元分析模型,模拟了两种不同激光冲击波峰值压力诱导的应力波在铜靶中衰减的特性。结果显示,峰值压力为0.35 GPa和3.5 GPa 下驱动的应力波在铜靶中的传播速度分别为4 600 m/s,4 000 m/s。峰值压力为3.5 GPa 冲击波在靶体内诱导的应力波出现了弹性波和塑性波的双波结构。应力波峰值的衰减规律呈指数形式衰减。模拟计算的结果与理论和实验结果较为一致。     

FDTD analysis of E-sectoral horn antennas for broad-bandapplications

The finite-difference time-domain (FDTD) method is applied to study the performance of E-plane sectoral horn antennas designed for broad-band applications. These antennas (proposed for 6-18 GHz phased arrays) have a large bandwidth, and they are easily array integrated. These antennas have a highly complicated geometry that is modeled using a polygonal approximation in the curved boundaries. Perfect matched layers (PMLs) combined with first-order absorbing boundaries are employed to simulate the free-space environment in the FDTD mesh     

A polygonal approximation of shape boundaries of marine plankton based-on genetic algorithms

Polygonal approximation of a shape boundary can provide a minimalistic representation of the shape. It can also accelerate the processing speed of feature extraction. Our interest is in applying such a method to approximate the boundaries of plankton shapes. A polygonal approximation method based on genetic algorithms has been designed to compactly describe the plankton shapes by polygons. Firstly, two artificial digital curves are used to test the performance of our algorithm. Results are compared with other existing algorithms which show that our algorithm has efficient performance for solving the problem of the polygonal approximation. Secondly, the proposed method is applied to a selection of plankton images under three different approximation levels to a polygonal fit and then five evaluation criteria are applied to determine which approximation level of a particular image is most suitable for describing the shape. The stability and robustness of three approximation levels are also tested.     

A new approach to diffraction analysis of conductor grids. I.Parallel-polarized incident plane waves

Diffraction analysis is presented for infinite planar conducting-cylinder grids illuminated by normally incident (parallel-polarized) plane waves, the electric fields of which are parallel to the cylinder axes. The Green's function kernel integral equations are used for the induced currents, which are based on the equivalent waveguide theory and solved for the currents by the moment method. This is a universal analysis approach, applicable to infinite planar grids made of conducting cylinders of arbitrary cross section, uniform or periodic, dense or sparse, single layer or multilayer     

Modal conversion in a gradient-index channel waveguide due to boundary perturbations

The effect of boundary perturbations on channel waveguides has been calculated following the effective-index method. As required by this approach, the index perturbations are assumed separable-a form describing defects expected using planar waveguide fabrication techniques. For sinusoidal perturbations, coupling occurs to, at most, one other guided mode and to a small band of radiation modes. As in the planar case, losses at step-index boundaries are greater than those at graded-index boundaries.     

Singularity expansion method analysis of regular polygonal loops

The singularity expansion method parameters (natural frequencies, natural modes, and coupling coefficients) for regular planar polygonal loops (equilateral triangle, square, regular pentagon, and regular hexagon) are computed and compared to those determined for the regular 60-gon (pseudo-circular) loop. Common characteristics of these geometries are compared and contrasted with respect to their use as radiating antenna structures or scatterers. The approach results in new insights for these canonical loop structures     

Properties of a cylindrical antenna in an infinite planar or collinear array

A solution is given for the active impedance and current distribution on a cylindrical antenna in a uniform, infinite, planar, or collinear array. The analysis is applicable to the case in which the distance in the collinear direction between the ends of adjacent elements is small. The current distribution on the collinear array is found by relating the antenna current and electric-field variation on the cylindrical surface of infinite length which contains the array. This analysis is then extended to consider a planar array. Results obtained are applicable to any combination of element length and array phasing, for arrays with or without a ground plane. Comparisons with other investigations based upon sinusoidally distributed currents reveal substantial discrepancies for some configurations.     

A new approach to diffraction analysis of conductor grids. II.Perpendicular-polarized incident plane waves

For pt.I see ibid., vol.37, no.1, p.84-88 (1988). Diffraction analysis is given for infinite planar conducting-strip grids illuminated by normally incident (perpendicular-polarized) plane waves, the electric fields of which are perpendicular to the strip axes. Iris-surface electric field integral equations are used which are based on the equivalent waveguide theory, and then the electric field is solved for using the moment method. This is a universal approach applicable to infinite planar grids made of conducting strips of rectangular cross section, uniform or periodic, dense or sparse, single layer or multilayer     

Infinite phased dipole array

By means of a Poisson sum formula and an integral-equation technique, an accurate solution for an infinite phased dipole array is obtained. The elements of the array are spaced uniformly and are excited with increasing phases. The technique can be applied to an infinite collinear array and to an infinite planar array either in free space or over a ground plane. The integral equation is solved both by a Fourier method and by an approximate five-term procedure. It is found that the latter is as good as the former. The current distributions and the active admittances are investigated.