Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

Impedance Analytical Method of Wave Run-up and Reflection from A Slotted-Wall Caisson Breakwater

An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

VIRTUAL-RAY METHOD AND ITS APPLICATION IN THE PLANE WAVE SCATTERING BY AN IMPEDANCE WEDGE

The virtual-ray method for treating HF electromagnetic scattering problems is derived from the plane wave of free space, and using this the plane wave scattering by an impedance wedge is studied. In the solution process a novel concept of generalized circle is introduced so that the complete amplitude function is obtained. And a reasonable physical interpretation for the term W2, which was neglected previously, is given. The calculated results agree well with those of the analytical solution obtained by G.D. Maliuzhinets(1958).

Electrical Impedance Tomography Based on Direct Search Method

Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.

Low-velocity Impact Damage Analysis of Composite Laminates Using Self-adapting Delamination Element Method

On the basis ofa 2D 4-node Mindlin shell element method, a novel self-adapting delamination finite element method is presented, which is developed to model the delamination damage of composite laminates. In the method, the sublaminate elements are generated automatically when the delamination damage occurs or extends. Thus, the complex process and state of delamination damage can be simulated practically with high efficiency for both analysis and modeling. Based on the self-adapting delamination method, linear dynamic finite element damage analysis is performed to simulate the low-velocity impact damage process of three types of mixed woven composite laminates. Taking the frictional force among sublaminations during delaminating and the transverse normal stress into account, the analytical results are consistent with those of the experimental data.

Transient Hydroelastic Response of VLFS by FEM with Impedance Boundary Conditions in Time Domain

A time-dependent finite element method (FEM) is developed to analyze the transient hydroelastic responses of very large floating structures (VLFS) subjected to dynamic loads. The hydrodynamic problem is formulated based on the linear theory of fluid and the structural response is analyzed based on the thin plate theory. The FEM truncates the unbounded fluid domain by introducing an artificial boundary surface, thus defining a finite computational domain. At this boundary surface an impedance boundary conditions are applied so that no wave reflections occur. In the proposed scheme, all of the procedures are processed directly in time domain, which is efficient for nonlinear analyses of structure floating on unbounded fluid. Numerical results indicate acceptable accuracy of the proposed method.

Acoustic impedance inversion of zero-offset VSP data

Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoing and upgoing waves can be accurately separated, we propose a method of predicting the impedance below the borehole in front of the bit using VSP data. First, the method of nonlinear iterative inversion is adopted to invert for impedance using the VSP corridor stack. Then, by modifying the damping factor in the iteration and using the preconditioned conjugate gradient method to solve the equations, the stability and convergence of the inversion results can be enhanced. The results of theoretical models and actual data demonstrate that the method is effective for pre-drilling prediction using VSP data.

Electrochemical impedance spectra of V_2O_5 xerogel films with intercalation of lithium ion

Vanadium pentoxide xerogel films used for lithium rechargeable batteries were prepared from crystalline c-V2O5 by melt quenching method,then the electrochemical process of lithium intercalation into vanadium pentoxide xerogel films was simulated with an equivalent circuit model, which was derived from the mechanism of electrode reactions. Measured electrochemical impedance spectra at various electrode potentials were analyzed by using the complex non-linear least-squares fitting method. The results show that impedance spectra consist of 2 high-to- medium frequency depressed arcs and a low frequency straight line. The high frequency arc is attributed to the absorption reaction of lithium ions into the oxide film, the medium frequency arc is attributed to the charge transfer reaction at the vanadium oxide/electrolyte interface and the low frequency is characterized by a straight line with a phase angle of 45° corresponding to the diffusion of lithium ion through vanadium oxide phase. The experimental and calculated results are compared and discussed focusing on the electrochemical performance and the state of charge of the electrode. Moreover, the high consistence of the fitted values of the model to the experimental data indicates that this mathematical model does give a satisfying description of the intercalation process of vanadium pentoxide xerogel films.

AN ANALYSIS ON INPUT IMPEDANCE OF A SINGLE MICROSTRIP PATCH IN THE QUASI-OPTICAL CAVITY

The electromagnetic field integral equation in the quasi-optical cavity is obtained using the dyadic Green’s function. An expression is derived for the input impedance of a single microstrip patch cavity excited by a coaxial probe using moment method. The input impedance of a rectangular microstrip patch is discussed with this method. The result of this paper is similar to that of the microstrip antenna. This paper is of very important value for designing microstrip quasi-optical oscillator.

Improve Spatial Resolution of Electrical Impedance Tomography Image Based on Non-uniformity Fine Mesh

In electrical impedance tomography (EIT) an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. Several difficulties have been identified in EIT, where the main problem is the low spatial resolution. This paper presents a fining mesh method based on finite element method (FEM), by fining the sensitive element, the most actual signal is obtained in certain electrode number. Newton-Raphson reconstruction algorithm improves the spatial solution of image. The advantages of this method are the improvement of spatial resolution and ease of implementation.

Closed-form internal impedance model and characterization of mixed carbon nanotube bundles for three-dimensional integrated circuits

Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube （CNT） bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.

Efficient Computation of Scattering from Targets with Negative Impedance Surface

Current surface integral equations used for computing scattering from targets with negative impedance boundary condition（IBC）are not efficient.A modified surface dual integral equation（M-SDIE）for targets with negative IBC is presented.A pure imaginary number is used to balance the formulations.It is proved that the M-SDIE is accurate and efficient with three numerical examples.The first numerical example shows that the M-SDIE is accurate compared with Mie.The second example shows that the presented SIE is efficient.In the third example,a missile head is selected to present the computing power of the M-SDIE.All the examples show that the M-SDIE is an efficient algorithm for negative IBC.

Longitudinal impedance measurements and simulations of a three-metal-strip kicker

A kicker is a critical component for beam injection and accumulation in circular particle accelerators. A ceramic slat kicker plated with a TiN conductive coating was applied in the Beijing Electron Positron Collider (BEPCII). However, the ceramic slat kicker has experienced several sudden malfunctions during the operation of the BEPCII in the past. With a reliable kicker structure, a three-metal-strip kicker can substitute the original ceramic slat kicker to maintain the operational stability of the BEPCII. A comparison of the numerical simulation was conducted for three kicker models, demonstrating the comprehensive advantage of the three-metal-strip kicker. Furthermore, impedance bench measurements were conducted on a prototype of a three-metal-strip kicker. The longitudinal beam-coupling impedance was measured using a vector network analyzer via the coaxial wire method. A satisfactory agreement was obtained between the numerical simulations and measurements. Based on the numerical simulation data, the loss factor was 0.01721 V/pC, and the effective impedance was 3.59 mΩ(σ=10 mm).The simulation of the heat deposition on each part of the kicker demonstrated that 84.4%of the parasitic loss of the beam was deposited on the metal strips, and the total heat deposition power on the kicker was between 113.3 and 131.5 W. The obtained heat deposition powers can be considered as a reference for establishing the cooling system.

Boundary Estimation in Annular Two-Phase Flow Using Electrical Impedance Tomography with Particle Swarm Optimization

In this study we consider the boundary estimation of annular two-phase flow in a pipe with the potential distribution on the electrodes mounted on the outer boundary of the pipe, by taking use of electrical impedance tomography (EIT) technique with the numerical solution obtained from an improved boundary distributed source (IBDS) method. The particle swarm optimization (PSO) is used to iteratively seek the boundary configuration. The simulation results showed that PSO and EIT technique with numerical solution obtained from IBDS has been successfully applied to the monitoring of an annular two-phase flow.

Control of Virtual Synchronous Generator for Frequency Regulation Using a Coordinated Self-adaptive Method

Power inverter adopting virtual synchronous generator(VSG)control can provide inertia support for distributed generation systems.However,it cannot take into account the dynamic regulation characteristics of frequency.Thus,when the system encounters a sudden change in load or disturbance,the dynamic process of frequency regulation will be greatly influenced.In view of this issue,an improved VSG control strategy based on a coordinated self-adaptive(CSA)method is proposed.The time domain analysis method is used to study the influences of virtual inertia and damping parameter perturbation on the system steady and dynamic performances.Furthermore,in order to make the control strategy suitable for large load changes and suppress frequency variations beyond the limit,the secondary frequency modulation is introduced into the control loop.Through the coordinated adaptive control of virtual inertia,virtual damping and frequency modulation,the dynamic performance of vSG frequency regulation can be obviously improved.Simulation and experiment results have verified the effectiveness of the proposed CSA control strategy.

MoM-based topology optimization method for planar metallic antenna design

The metallic antenna design problem can be treated as a problem to find the optimal distribution of conductive material in a certain domain. Although this problem is well suited for topology optimization method, the volumetric distribution of conductive material based on 3D finite element method (FEM) has been known to cause numerical bottlenecks such as the skin depth issue, meshed 'air regions' and other numerical problems. In this paper a topology optimization method based on the method of moments (MoM) for configuration design of planar metallic antenna was proposed. The candidate structure of the planar metallic antenna was approximately considered as a resistance sheet with position-dependent impedance. In this way, the electromagnetic property of the antenna can be analyzed easily by using the MoM to solve the radiation problem of the resistance sheet in a finite domain. The topology of the antenna was depicted with the distribution of the impedance related to the design parameters or relative densities. The conductive material (metal) was assumed to have zero impedance, whereas the non-conductive material was simulated as a material with a finite but large enough impedance. The interpolation function of the impedance between conductive material and non-conductive material was taken as a tangential function. The design of planar metallic antenna was optimized for maximizing the efficiency at the target frequency. The results illustrated the effectiveness of the method.

On-line Measurement for Ohmic Resistance in Direct Methanol Fuel Cell by Current Interruption Method

Electrochemical impedance spectroscopy (EIS) is widely used in fuel cell impedance analysis. However, for ohmic resistance (R Ω), EIS has some disadvantages such as long test period and complex data analysis with equivalent circuits. Therefore, the current interruption method is explored to measure the value of RΩ in direct methanol fuel cells (DMFC) at different temperatures and current densities. It is found that RΩ decreases as temperature increase, and decreases initially and then increases as current density increases. These results are consistent with those measured by the EIS technique. In most cases, the ohmic resistances with current interruption (R iR ) are larger than those with EIS (R EIS ), but the difference is small, in the range from –0.848% to 5.337%. The errors of R iR at high current densities are less than those of R EIS . Our results show that the R iR data are reliable and easy to obtain in the measurement of ohmic resistance in DMFC.