Finite-difference modeling of Maxwell viscoelastic media developed from perfectly matched layer

In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.However,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in FDTD.To incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation costs.By modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the parameters.The proposed viscoelastic model is essentially equivalent to a Maxwell model.Compared with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much easier.The attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than 10.The numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity.

A Fast Multi-Pattern Matching Algorithm for Mining Big Network Data

The rapid development of mobile network brings opportunities for researchers to analyze user behaviors based on largescale network traffic data. It is important for Internet Service Providers(ISP) to optimize resource allocation and provide customized services to users. The first step of analyzing user behaviors is to extract information of user actions from HTTP traffic data by multi-pattern URL matching. However, the efficiency is a huge problem when performing this work on massive network traffic data. To solve this problem, we propose a novel and accurate algorithm named Multi-Pattern Parallel Matching(MPPM) that takes advantage of HashMap in data searching for extracting user behaviors from big network data more effectively. Extensive experiments based on real-world traffic data prove the ability of MPPM algorithm to deal with massive HTTP traffic with better performance on accuracy, concurrency and efficiency. We expect the proposed algorithm and it parallelized implementation would be a solid base to build a high-performance analysis engine of user behavior based on massive HTTP traffic data processing.

Stability of Perfectly Matched Layers for Time Fractional Schrödinger Equation

It is an important issue to numerically solve the time fractional Schrödinger equation on unbounded domains, which models the dynamics of optical solitons propagating via optical fibers. The perfectly matched layer approach is applied to truncate the unbounded physical domain, and obtain an initial boundary value problem on a bounded computational domain, which can be efficiently solved by the finite difference method. The stability of the reduced initial boundary value problem is rigorously analyzed. Some numerical results are presented to illustrate the accuracy and feasibility of the perfectly matched layer approach. According to these examples, the absorption parameters and the width of the absorption layer will affect the absorption effect. The larger the absorption width, the better the absorption effect. There is an optimal absorption parameter, the absorption effect is the best.

Perfect matchings on a type of lattices with toroidal boundary

Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obtain some Pfaffan orientations and enumerating their Pfaffans.

Robust key point descriptor for multi-spectral image matching

Histogram of collinear gradient-enhanced coding （HCGEC）, a robust key point descriptor for multi-spectral image matching, is proposed. The HCGEC mainly encodes rough structures within an image and suppresses detailed textural information, which is desirable in multi-spectral image matching. Experiments on two multi-spectral data sets demonstrate that the proposed descriptor can yield significantly better results than some state-of- the-art descriptors.

Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd＋1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd＋1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] ＋ 1 q2d 33 1.

Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.

Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.

A Multi-stage Heuristic Algorithm for Matching Problem in the Modified Miniload Automated Storage and Retrieval System of E-commerce

E-commerce, as an emerging marketing mode, has attracted more and more attention and gradually changed the way of our life. However, the existing layout of distribution centers can＇t fulfill the storage and picking demands of e-commerce sufficiently. In this paper, a modified miniload automated storage/retrieval system is designed to fit these new characteristics of e-commerce in logistics. Meanwhile, a matching problem, concerning with the improvement of picking efficiency in new system, is studied in this paper. The problem is how to reduce the travelling distance of totes between aisles and picking stations. A multi-stage heuristic algorithm is proposed based on statement and model of this problem. The main idea of this algorithm is, with some heuristic strategies based on similarity coefficients, minimizing the transportations of items which can not arrive in the destination picking stations just through direct conveyors. The experimental results based on the cases generated by computers show that the average reduced rate of indirect transport times can reach 14.36% with the application of multi-stage heuristic algorithm. For the cases from a real e-commerce distribution center, the order processing time can be reduced from 11.20 h to 10.06 h with the help of the modified system and the proposed algorithm. In summary, this research proposed a modified system and a multi-stage heuristic algorithm that can reduce the travelling distance of totes effectively and improve the whole performance of e-commerce distribution center.

MULTI-EPIPOLAR LINES MATCHING-BASED RAY-SPACE INTERPOLATION FOR FREE VIEWPOINT VIDEO SYSTEM

Ray-space based arbitrary viewpoint rendering without complex object segmentation or model construction is the main technology to realize Free Viewpoint Video(FVV) system for complex scenes. Ray-space interpolation and compression are two key techniques for the solution. In this paper,correlation among multiple epipolar lines in ray-space data is analyzed,and a new method of ray-space interpolation with multi-epipolar lines matching is proposed. Comparing with the pixel-based matching interpolation method and the block-based matching interpolation method,the proposed method can achieve higher Peak Signal to Noise Ratio(PSNR) in interpolating rayspace data and rendering arbitrary viewpoint images.

PARAMETRIC MATCHING SELECTION OF MULTI-MEDIUM COUPLING SHOCK ABSORBER

To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of multi-medium coupling shock absorber is presented. The coupling of quadratic damping, linear damping, Coulomb damping and nonlinear spring are considered in the model. The approximate theoretical calculating formulae are deduced by introducing transformation-tactics. The contrasts between the analytical results and numerical integration results are developed. The resisting impact characteristics of the model are also analyzed in progress. In the meantime, the optimum model of the parameters matching selection for design of the shock absorber is built. The example design is illustrated to confirm the validity of the modeling method and the theoretical solution.

Template Matching using Statistical Model and Parametric Template for Multi-Template

This paper represents a template matching using statistical model and parametric template for multi-template. This algorithm consists of two phases: training and matching phases. In the training phase, the statistical model created by principal component analysis method (PCA) can be used to synthesize multi-template. The advantage of PCA is to reduce the variances of multi-template. In the matching phase, the normalized cross correlation (NCC) is employed to find the candidates in inspection images. The relationship between image block and multi-template is built to use parametric template method. Results show that the proposed method is more efficient than the conventional template matching and parametric template. Furthermore, the proposed method is more robust than conventional template method.

Perfectly Matched Layer for an Elastic Parabolic Equation Model in Ocean Acoustics

The perfectly matched layer(PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation(PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide(Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer(ABL) both in acoustic and seismo-acoustic sound propagation modeling.

A Uniaxial Optimal Perfectly Matched Layer Method for Time-harmonic Scattering Problems

We develop a uniaxial optimal perfectly matched layer （opt PML） method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter ε0. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method.

Perfectly matched layer implementation for ADI-FDTD in dispersive media

Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.

An improved convolution perfectly matched layer for elastic second-order wave equation

A convolution perfectly matched layer(CPML)can efficiently absorb boundary reflection in numerical simulation.However,the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly to the second-order elastic wave equation.In view of this,based on the first-order CPML absorbing boundary condition,we propose a new CPML(NCPML)boundary which can be directly applied to the second-order wave equation.We first systematically extend the first-order CPML technique into second-order wave equations,neglecting the space-varying characteristics of the partial damping coefficient in the complex-frequency domain,avoiding the generation of convolution in the time domain.We then transform the technique back to the time domain through the inverse Fourier transform.Numerical simulation indicates that the space-varying characteristics of the attenuation factor have little influence on the absorption effect and increase the memory at the same time.A number of numerical examples show that the NCPML proposed in this study is effective in simulating elastic wave propagation,and this algorithm is more efficient and requires less memory allocation than the conventional PML absorbing boundary.

Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary

The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.