Asymptotic Evaluation Research Articles

Temperature distribution analysis of piezoelectric transformer with heat couple component

ABSTRACTThe use of a heat transfer structure can effectively improve the power of a piezoelectric transformer (PT). A heat couple component (HCC) serves as the core element in the heat transfer structure and improves temperature distribution of PT. The finite element method and experimental measurement are conducted to determine the influence of HCC to the temperature distribution of PT in this study. The heat sources are mechanical vibration, piezoelectric, dielectric losses of PT, as well as the friction heat. The thermal contact conductance coefficient between HCC and PT is determined by the asymptotic waveform evaluation method.

Analysis of Fourier and Non-Fourier heat conduction using Tiknonov based Well-conditioned Asymptotic Waveform Evaluation Technique

Analysis of Fourier and Non-Fourier heat conduction using Tiknonov based Well-conditioned Asymptotic Waveform Evaluation Technique

An inductive method of calculation of the deflection of the truss regular type

In this paper, the author proposes a regular option of statically determinate flat truss with a lattice of Shukhov's type working under beam scheme. By induction, using Maple computer algebra system, the exact formula for the mid-span deflection under the action of the uniform load is obtained. The deflection of the elastic structure is defined by the formula of Maxwell – Mohr. Forces in the rods are found using cut nodes method with the composition of the management of the matrix of equations in vector form. The analysis of the coefficients in the truss evaluation with a different number of panels revealed the recurrence equation satisfied by these coefficients, and then the determined operators of a specialized package genfunc give a solution of the resulting equation that determines the required general formula. The case of a uniform load on the top horizontal zone is considered. The author obtained a simple asymptotic evaluation of this solution, proving the cubic nature of the growth of deflection for a fixed span length and a given nodal load. The solution found for an even number of panels and rods of the same cross-section, has a polynomial form; the dependence is non-monotonic and detects extremum, which allows optimizing the design.

Delay Analysis and Design Optimization for Low-Swing RC-Limited Global Interconnects

On-chip global interconnects are becoming speed and power bottlenecks in state-of-the-art chips. Low-swing signaling is used to improve delay performance and reduce power consumption. This paper first performs a delay analysis for different low-swing circuits based on the Asymptotic Waveform Evaluation (AWE). In addition, new delay metrics are presented and analyzed. The new delay metrics demonstrate that optimal designs can be obtained in low-swing signaling. To verify our analysis, a simulation environment is established. The simulation results indicate that the optimal designs can increase the 3[Formula: see text]dB bandwidth of a wire by more than 40% in resistively driven or capacitively driven 10[Formula: see text]mm global links. Thus, these optimal design methods can effectively improve the bandwidth of global wires.

Analytic-Numerical Approach to Solving Singularly Perturbed Parabolic Equations with the Use of Dynamic Adapted Meshes

The main objective of the paper is to present a new analytic-numerical approach to singularly perturbed reaction-diffusion-advection models with solutions containing moving interior layers (fronts). We describe some methods to generate the dynamic adapted meshes for an efficient numerical solution of such problems. It is based on a priori information about the moving front properties provided by the asymptotic analysis. In particular, for the mesh construction we take into account a priori asymptotic evaluation of the location and speed of the moving front, its width and structure. Our algorithms significantly reduce the CPU time and enhance the stability of the numerical process compared with classical approaches. The article is published in the authors’ wording.

Fast frequency sweep method for indirect boundary element models arising in acoustics

This paper presents an efficient approach for computing frequency sweeps with fine increments of acoustic systems described by the variational indirect boundary element method. The matrices arising from such boundary element discretizations are fully populated and their assembly is computationally demanding as it involves the calculation of double surface integrals for each system matrix entry. Therefore, the two operations performed when computing the response at one frequency, namely assembling the system matrix and solving the associated linear system, may be of the same order of magnitude in terms of the required computational time. The proposed fast frequency sweep approach accelerates both operations. First, it avoids forming the system matrices for each individual frequency. Matrices are only assembled at a few master frequencies, while for the rest, interpolation is used on scaled quantities determined at the master frequencies. Second, it avoids solving a dense linear system at each frequency. Padé approximants constructed via the well-conditioned asymptotic waveform evaluation algorithm are used to extrapolate the response around expansion frequencies using derivative information. The proposed method was tested on an exterior acoustics application representing an academic test case, as well as on an interior/exterior application representing an industrial test case.

Fast Frequency Sweep Using Asymptotic Waveform Evaluation Technique and Thin Dielectric Sheet Approximation

The thin dielectric sheet (TDS) surface integral equation (SIE) combined with the asymptotic waveform evaluation (AWE) technique is proposed to efficiently analyze wideband properties of thin dielectric layers such as radome and composite materials. The TDS SIE is an efficient method for analyzing the thin dielectric layer because the number of unknowns of the TDS SIE is fewer than that of the volume integral equation (VIE) and the condition number of the TDS impedance matrix is small. In addition, the AWE technique based on a Taylor series and the Pade approximation is a well-known method for fast frequency sweep. Therefore, the combination of these two methods makes analysis of the thin dielectric layer efficient in the wide frequency region because the advantages of each method are shown at the same time. In order to determine the valid bandwidth of the approximated results for arbitrary problems using the TDS combined with the AWE, the bandwidth estimation approach for the AWE is applied. The results of the proposed method for closed and open structures agree very well with the exact solutions and reveal the capability for fast frequency sweep.

Direct calculation of wind turbine tip loss

The usual method to account for a finite number of blades in blade element calculations of wind turbine performance is through a tip loss factor. Most analyses use the tip loss approximation due to Prandtl which is easily and cheaply calculated but is known to be inaccurate at low tip speed ratio. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation of those sums by Kawada. The third uses the approximation due to Okulov which avoids the sums altogether. These methods are compared to the tip loss determined independently and exactly for an ideal three-bladed rotor at tip speed ratios between zero and 15. Kawada's asymptotic approximation and Okulov's equations are preferable to the Prandtl factor at all tip speed ratios, with the Okulov equations being generally more accurate. In particular the tip loss factor exceeds unity near the axis of rotation by a large amount at all tip speed ratios, which Prandtl's factor cannot reproduce. Neither the Kawada nor the Okulov equations impose a large computational burden on a blade element program.

The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals

The divergent integral ∫abf(x)(x−x0)−n−1dx, for −∞ < a < x0 < b < ∞ and n = 0, 1, 2, …, is assigned, under certain conditions, the value equal to the simple average of the contour integrals ∫C±f(z)(z − x0)−n−1dz, where C+ (C−) is a path that starts from a and ends at b and which passes above (below) the pole at x0. It is shown that this value, which we refer to as the analytic principal value, is equal to the Cauchy principal value for n = 0 and to the Hadamard finite-part of the divergent integral for positive integer n. This implies that, where the conditions apply, the Cauchy principal value and the Hadamard finite-part integral are in fact values of absolutely convergent integrals. Moreover, it leads to the replacement of the boundary values in the Sokhotski-Plemelj-Fox theorem with integrals along some arbitrary paths. The utility of the analytic principal value in the numerical, analytical, and asymptotic evaluations of the principal value and the finite-part integral is discussed and demonstrated.

Fast scattering analysis over a wide frequency band using Clenshaw–Lord‐type Pade–Chebyshev approximation

Pade–Chebyshev approximation of Clenshaw–Lord type with method of moments is proposed for wide-band analysis of an arbitrary-shaped perfect electric conductor structure. Moreover, various Chebyshev polynomials, such as first, third, and fourth kinds, are used to express the singular points in the graph to display the expected result for scattering characteristics. The proposed algorithm has a wide radius of convergence due to the use of Chebyshev polynomials and improves calculation speed because Clenshaw–Lord-type Pade approximation requires fewer sampling points than Maehly-type Pade approximation in the derivation of the rational function. The results of the proposed method agree very well with the exact solution and reveal its possibility of obtaining more accurate solution than the asymptotic waveform evaluation technique.

Frequency sweep computation of half‐space scattering using asymptotic waveform evaluation

ABSTRACTThe asymptotic waveform evaluation (AWE) technique is applied to mixed potential integral equation (MPIE) for fast frequency sweep in half‐space scattering analysis. The AWE procedure requires the evaluation of high order derivative of impedance matrices that consist of complicated Green's function of layered media. Pseudo‐spectral method, a numerical differentiation approach, is employed to calculate these derivatives. Numerical experiments show that AWE technique improves the efficiency of scattering computation in half‐space structure. Furthermore, the presented approach can handle dispersive media. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:495–498, 2016

Tickhonov based well-condition asymptotic waveform evaluation for dual-phase-lag heat conduction

The Tickhonov based well condition asymptotic waveform evaluation (TWCAWE) is presented here to study the non-Fourier heat conduction problems with various boundary conditions. In this paper, a novel TWCAWE method is proposed to overwhelm ill-conditioning of the asymptotic waveform evaluation (AWE) technique for thermal analysis and also presented for time-reliant problems. The TWCAWE method is capable to evade the instability of AWE and also efficaciously approximates the initial high frequency and delay similar as well-established numerical method, such as Runge-Kutta (R-K). Furthermore, TWCAWE method is found 1.2 times faster than the AWE and also 4 times faster than the traditional R-K method.

Rates of Convergence to Scaling Profiles in a Submonolayer Deposition Model and the Preservation of Memory of the Initial Condition

We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of $j$-clusters....

A combinatorial study of two-periodic random walks

ABSTRACTTwo-periodic random walks have up-steps and down-steps of one unit as usual, but the probability of an up-step is α after an even number of steps and β = 1 − α after an odd number of steps, and reversed for down-steps. This concept was studied by Böhm and Hornik[2]. We complement this analysis by using methods from (analytic) combinatorics. By using two steps at once, we can reduce the analysis to the study of Motzkin paths, with up-steps, down-steps, and level-steps. Using a proper substitution, we get the generating functions of interest in an explicit and neat form. The parameters that are discussed here are the (one-sided) maximum (already studied by Böhm and Hornik[2]) and the two-sided maximum. For the asymptotic evaluation of the average value of the two-sided maximum after n random steps, more sophisticated methods from complex analysis (Mellin transform, singularity analysis) are required. The approach to transfer the analysis to Motzkin paths is, of course, not restricted to the two parameters under consideration.

A hybrid broadband analysis approach for surface-wire junctions structures by applying AIM and asymptotic waveform evaluation technique

The asymptotic waveform evaluation (AWE) technique is utilized to deal with broadband electromagnetic problems of surface–wire junction geometries in this paper. To ensure the current continuity, triangles-to-segments junction model is used and the Rao–Wilton–Glisson (RWG) and triangular basis functions are used to solve the distributions of current on perfect electric conductor and wire, respectively. Then, the current on surface conductor, wire, and junctions are expanded in a rational function via Padé approximation. The AWE technique needs to store the high-order derivatives of the self-impedance and mutual-impedance matrices of surface–wire, which increase the memory requirements. Thus, the adaptive integral method is employed to reduce memory requirements and to accelerate the matrix-vector multiplications in an iterative solver. Finally, some numerical examples are shown to demonstrate the efficiency and accuracy of the proposed method

The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane.

Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.

Asymptotic evaluations for some double sums in number theory

In this paper, we indicate a method to obtain asymptotic evaluations for double sums from the asymptotic evaluations of a single sum. As applications, we show that all results in the recent paper [New extensions of some classical theorems in number theory, J. Number Theory133(13) (2013) 3771–3795] can be used to obtain some asymptotic evaluations for double sums. Further, we give asymptotic evaluations for double sums which involve the divisor and the Euler totient function.

Efficient Analysis of Surface‐Wire Configurations Using AIM and Best Uniform Rational Approximation

The Adaptive integral method (AIM) in conjunction with the best uniform approximation technique is applied to analyze the electromagnetic problems of surface-wire junction geometries over a wide frequency band. To improve the computation efficiency, the best uniform approximation method is utilized. The AIM can reduce memory requirements and accelerate the matrix-vector multiplications in iterative process. Some numerical examples are shown to demonstrate the efficiency and accuracy of the proposed method. Compared with the direct solution method and Asymptotic waveform evaluation (AWE) technique, the proposed technique is found to be efficient in a broadband with the lower Central processing unit (CPU) time required and without loss of accuracy.

Efficient analysis of lossy SIW structures based on the parallel plates waveguide Green's function and fast frequency sweep

ABSTRACTA fast frequency analysis of lossy substrate‐integrated waveguides based on the asymptotic waveform evaluation (AWE) and Padè approximant technique in conjunction with the dyadic Green's function technique, is presented. The derivatives needed to evaluate moments in the AWE method are computed in a simple way thanks to an efficient method that reduces their computational cost. Numerical results demonstrate the efficiency and the accuracy of the proposed approach. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:2435–2437, 2015

Endpoint contribution to the instantaneous ionization rate for tunneling ionization

We examine the instantaneous ionization amplitudes and instantaneous ionization rates for the process of tunneling ionization. We show that the endpoint contribution usually neglected in the asymptotic evaluation of the amplitudes, may be significant. For weak fields the instantaneous ionization rate is largely defined by this contribution. For higher field strengths of the order of 0.1 a.u., the account of this contribution allows one to reproduce numerically computed instantaneous ionization rates with higher accuracy.