Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

Evaluation of bronchoscopic direct vision glottis anesthesia method in bronchoscopy

BACKGROUND Fibrobronchoscopy is a common adjunct tool that requires anesthesia and is widely used in the diagnosis and treatment of various respiratory diseases.However,current anesthesia methods,such as spray,nebulized inhalation,and cricothyroid membrane puncture,have their own advantages and disadvantages.Recently,studies have shown that bronchoscopic direct-view glottis anesthesia is a simple and inexpensive method that shortens the examination time and provides excellent anesthetic results.AIM To evaluate the effectiveness of bronchoscopic direct vision glottis anesthesia for bronchoscopy.METHODS The study included 100 patients who underwent bronchoscopy during thoracic surgery.A random number table method was used to divide the patients into control and observation groups(50 patients each).The control and observation groups were anesthetized using the nebulized inhalation and bronchoscopic direct vision glottis method,respectively.Hemodynamic indices[systolic blood pressure(SBP),diastolic blood pressure(DBP),heart rate(HR),and oxygen saturation(SpO_(2))before(T1),5 min after anesthesia(T2),and at the end of the operation(T3)]serum stress hormone indices[norepinephrine(NE),epinephrine(E),adrenocorticotropic hormone(ACTH),and cortisol(Cor)before and after treatment]were compared between the 2 groups.Adverse effects were also RESULTS At T2 and T3,SBP,DBP,and HR were lower in the observation group than the control group,whereas SpO_(2) was higher than the control group[(119.05±8.01)mmHg vs(127.05±7.83)mmHg,(119.35±6.66)mmHg vs(128.39±6.56)mmHg,(84.68±6.04)mmHg vs(92.42±5.57)mmHg,(84.53±4.97)mmHg compared to(92.57±6.02)mmHg,(74.25±5.18)beats/min compared to(88.32±5.72)beats/min,(74.38±5.31)beats/min compared to(88.42±5.69)beats/min,(97.36±2.21)%vs(94.35±2.16)%,(97.42±2.36)%vs(94.38±2.69%],with statistically significant differences(all P<0.05).After treatment,NE,E,ACTH,and Cor were significantly higher in both groups than before treatment,but were lower in the observation group than in the control group[(68.25±8.87)ng/mL vs(93.35±14.00)ng/mL,(53.59±5.89)ng/mL vs(82.32±10.70)ng/mL,(14.32±1.58)pg/mL vs(20.35±3.05)pg/mL,(227.35±25.01)nmol/L vs(322.28±45.12)nmol/L],with statistically significant differences(all P<0.05).The incidence of adverse reactions was higher in the control group than in the observation group[12.00%(12/50)vs 6.00%(3/50)](P<0.05).CONCLUSION The use of bronchoscopic direct vision glottis anesthesia method for bronchoscopy patients is beneficial for stabilizing hemodynamic indices during bronchoscopy and reducing the level of patient stress,with good safety and practicality.

Greedy Randomized Gauss-Seidel Method with Oblique Direction

For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.

A modified stochastic finite-fault method for estimating strong ground motion:Validation and application

We developed a modified stochastic finite-fault method for estimating strong ground motions.An adjustment to the dynamic corner frequency was introduced,which accounted for the effect of the location of the subfault relative to the hypocenter and rupture propagation direction,to account for the influence of the rupture propagation direction on the subfault dynamic corner frequency.By comparing the peak ground acceleration(PGA),pseudo-absolute response spectra acceleration(PSA,damping ratio of 5%),and duration,the results of the modified and existing methods were compared,demonstrating that our proposed adjustment to the dynamic corner frequency can accurately reflect the rupture directivity effect.We applied our modified method to simulate near-field strong motions within 150 km of the 2008 MW7.9 Wenchuan earthquake rupture.Our modified method performed well over a broad period range,particularly at 0.04-4 s.The total deviations of the stochastic finite-fault method(EXSIM)and the modified EXSIM were 0.1676 and 0.1494,respectively.The modified method can effectively account for the influence of the rupture propagation direction and provide more realistic ground motion estimations for earthquake disaster mitigation.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

Study on Measurement Methods of Multi-Directional Waves—Wave Gauge Array Method

Measuring multi-directional waves with the wave gauge array is one of the fundamental and easily realised methods. In this paper, the wave gauge array is described and the effects of the gauge spacing, the array orientations, etc. of the three array arrangements, i. e., linear array, T-type array and pentagon array, on the resolution of the directional spreading of waves, are investigated experimentally. This study can be used as a reference in the experimental study and the field measurement of directional waves.

Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation

In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.

A laboratory study of directional spectra with maximum likelihood method─I Developing wind wave

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.

Two-Order Approximate and Large Stepsize Numerical Direction Based on the Quadratic Hypothesis and Fitting Method

Many effective optimization algorithms require partial derivatives of objective functions, while some optimization problems' objective functions have no derivatives. According to former research studies, some search directions are obtained using the quadratic hypothesis of objective functions. Based on derivatives, quadratic function assumptions, and directional derivatives, the computational formulas of numerical first-order partial derivatives, second-order partial derivatives, and numerical second-order mixed partial derivatives were constructed. Based on the coordinate transformation relation, a set of orthogonal vectors in the fixed coordinate system was established according to the optimization direction. A numerical algorithm was proposed, taking the second order approximation direction as an example. A large stepsize numerical algorithm based on coordinate transformation was proposed. Several algorithms were validated by an unconstrained optimization of the two-dimensional Rosenbrock objective function. The numerical second order approximation direction with the numerical mixed partial derivatives showed good results. Its calculated amount is 0.2843% of that of without second-order mixed partial derivative. In the process of rotating the local coordinate system 360°, because the objective function is more complex than the quadratic function, if the numerical direction derivative is used instead of the analytic partial derivative, the optimization direction varies with a range of 103.05°. Because theoretical error is in the numerical negative gradient direction, the calculation with the coordinate transformation is 94.71% less than the calculation without coordinate transformation. If there is no theoretical error in the numerical negative gradient direction or in the large-stepsize numerical optimization algorithm based on the coordinate transformation, the sawtooth phenomenon occurs. When each numerical mixed partial derivative takes more than one point, the optimization results cannot be improved. The numerical direction based on the quadratic hypothesis only requires the objective function to be obtained, but does not require derivability and does not take into account truncation error and rounding error. Thus, the application scopes of many optimization methods are extended.

Synthesis of Hierarchically Porous FAU/γ-Al2O3 Composites with Different Morphologies via Directing Agent Induced Method

Zeolite FAU composites with a macro/meso-microporous hierarchical structure were hydrothermally synthesized using macro-mesoporous γ-Al_2O_3 monolith as the substrate by means of the liquid crystallization directing agent(LCDA) induced method. No template was needed throughout the synthesis processes. The structure and porosity of zeolite composites were analyzed by means of X-ray powder diffraction(XRD), scanning electron microscopy(SEM) and N_2adsorption-desorption isotherms. The results showed that the supported zeolite composites with varied zeolitic crystalline phases and different morphologies can be obtained by adjusting the crystallization parameters, such as the crystallization temperature, the composition and the alkalinity of the precursor solution. The presence of LCDA was defined as a determinant for synthesizing the zeolite composites. The mechanisms for formation of the hierarchically porous FAU zeolite composites in the LCDA induced synthesis process were discussed. The resulting monolithic zeolite with a trimodal-porous hierarchical structure shows potential applicability where facile diffusion is required.

Combined indirect and direct method for adaptive fuzzy output feedback control of nonlinear system

A novel control method for a general class of nonlinear systems using fuzzy logic systems （FLSs） is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Advances in traction methods for endoscopic submucosal dissection:What is the best traction method and traction direction?

Endoscopic submucosal dissection(ESD)has been developed as a treatment for superficial gastrointestinal neoplasms,which can achieve en bloc resection regardless of the lesion size.However,ESD is technically difficult because endoscopists cannot bring their hand into the gastrointestinal tract,unlike surgeons in regular surgery.It is difficult to obtain sufficient tension in the dissection plane and a good field of vision.Therefore,ESD is associated with a long procedure time and a high risk of adverse events in comparison with endoscopic mucosal resection.Traction methods have been developed to provide sufficient tension for the dissection plane and a good field of vision during the ESD procedure.However,traction direction is limited in most traction methods,resulting in insufficient effect in some cases.Although traction direction is considered important,there have been few investigations of its effect.In the first half of this review,important traction methods are discussed,including traction direction.In second half,appropriate traction methods for each organ are considered.Other important considerations for traction method,such as ability to adjust traction strength,interference between traction device and endoscope,and the need for specialized devices are also discussed.

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.

Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method

This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

The efficiency of direct integration methods in elastic contact-impact problems

A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.