A Parallel Computational Scheme on Hybrid Methods

Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.

Implicit 2-Step Hybrid Methods and Their Stability Analysis

In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order one is not, but still has a relatively large region of absolute stability. The implementation of the 5th order method is also discussed.

Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Research on the Generation Mechanism and Suppression Method of Aerodynamic Noise in Expansion Cavity Based on Hybrid Method

The expansion chamber serves as the primary silencing structure within the exhaust pipeline.However,it can also act as a sound-emitting structure when subjected to airflow.This article presents a hybrid method for numerically simulating and analyzing the unsteady flow and aerodynamic noise in an expansion chamber under the influence of airflow.A fluid simulation model is established,utilizing the Large Eddy Simulation(LES)method to calculate the unsteady flow within the expansion chamber.The simulation results effectively capture the development and changes of the unsteady flow and vorticity inside the cavity,exhibiting a high level of consistency with experimental observations.To calculate the aerodynamic noise sources within the cavity,the flow field results are integrated using the method of integral interpolation and inserted into the acoustic grid.The acoustic analogy method is then employed to determine the aerodynamic noise sources.An acoustic simulation model is established,and the flow noise source is imported into the sound field grid to calculate the sound pressure at the far-field response point.The calculated sound pressure levels and resonance frequencies show good agreement with the experimental results.To address the issue of airflow regeneration noise within the cavity,perforated tubes are selected as a means of noise suppression.An experimental platformfor airflow regeneration noise is constructed,and experimental samples are processed to analyze and verify the noise suppression effect of perforated tube expansion cavities under different airflow velocities.The research findings indicate that the perforated tube expansion cavity can effectively suppress low-frequency aerodynamic noise within the cavity by impeding the formation of strong shear layers.Moreover,the semi-perforated tube expansion cavity demonstrates the most effective suppression of aerodynamic noise.

QP-FREE,TRUNCATED HYBRID METHODS FOR LARGE-SCALE NONLINEAR CONSTRAINED OPTIMIZATION

In this paper, a truncated hybrid method is proposed and developed for solving sparse large-scale nonlinear programming problems. In the hybrid method, a symmetric system of linear equations, instead of the usual quadratic programming subproblems, is solved at iterative process. In order to ensure the global convergence, a method of multiplier is inserted in iterative process. A truncated solution is determined for the system of linear equations and the unconstrained subproblems are solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to the large-scale problems. The local convergence of the hybrid algorithm is proved and some numerical tests for medium-sized truss problem are given.

Three-step relaxed hybrid steepest-descent methods for variational inequalities

The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.

Hybrid High‑Order Methods for the Acoustic Wave Equation in the Time Domain

We devise hybrid high-order(HHO)methods for the acoustic wave equation in the time domain.We frst consider the second-order formulation in time.Using the Newmark scheme for the temporal discretization,we show that the resulting HHO-Newmark scheme is energy-conservative,and this scheme is also amenable to static condensation at each time step.We then consider the formulation of the acoustic wave equation as a frst-order system together with singly-diagonally implicit and explicit Runge-Kutta(SDIRK and ERK)schemes.HHO-SDIRK schemes are amenable to static condensation at each time step.For HHO-ERK schemes,the use of the mixed-order formulation,where the polynomial degree of the cell unknowns is one order higher than that of the face unknowns,is key to beneft from the explicit structure of the scheme.Numerical results on test cases with analytical solutions show that the methods can deliver optimal convergence rates for smooth solutions of order O(hk+1)in the H1-norm and of order O(h^(k+2))in the L^(2)-norm.Moreover,test cases on wave propagation in heterogeneous media indicate the benefts of using high-order methods.

Behavioral Decision-Making of Key Stakeholders in Public-Private Partnerships:A Hybrid Method and Benefit Distribution Study

Public-private partnerships(PPPs)have been used by governments around the world to procure and construct infrastructural amenities.It relies on private sector expertise and funding to achieve this lofty objective.However,given the uncertainties of project management,transparency,accountability,and expropriation,this phenomenon has gained tremendous attention in recent years due to the important role it plays in curbing infrastructural deficits globally.Interestingly,the reasonable benefit distribution scheme in a PPP project is related to the behavior decisionmaking of the government and social capital,aswell as the performance of the project.In this paper,the government and social capital which are the key stakeholders of PPP projects were selected as the research objects.Based on the fuzzy expected value model and game theory,a hybrid method was adopted in this research taking into account the different risk preferences of both public entities and private parties under the fuzzy demand environment.To alleviate the problem of insufficient utilization of social capital in a PPP project,this paper seeks to grasp the relationship that exists between the benefit distribution of stakeholders,their behavioral decision-making,and project performance,given that they impact the performance of both public entities and private parties,as well as assist in maximizing the overall utility of the project.Furthermore,four game models were constructed in this study,while the expected value and opportunity-constrained programming model for optimal decision-making were derived using alternate perspectives of both centralized decision-making and decentralized decision-making.Afterward,the optimal behavioral decision-making of public entities and private parties in four scenarios was discussed and thereafter compared,which led to an ensuing discussion on the benefit distribution system under centralized decision-making.Lastly,based on an example case,the influence of different confidence levels,price,and fuzzy uncertainties of PPP projects on the equilibrium strategy results of both parties were discussed,giving credence to the effectiveness of the hybrid method.The results indicate that adjusting different confidence levels yields different equilibriumpoints,and therefore signposts that social capital has a fair perception of opportunities,as well as identifies reciprocal preferences.Nevertheless,we find that an increase in the cost coefficient of the government and social capital does not inhibit the effort of both parties.Our results also indicate that a reasonable benefit distribution of PPP projects can assist them in realizing optimum Pareto improvements over time.The results provide us with very useful strategies and recommendations to improve the overall performance of PPP projects in China.

A Hybrid Approach to Neighbour Discovery in Wireless Sensor Networks

In the contemporary era of unprecedented innovations such as Internet of Things(IoT),modern applications cannot be imagined without the presence of Wireless Sensor Network(WSN).Nodes in WSN use neighbour discovery(ND)protocols to have necessary communication among the nodes.Neighbour discovery process is crucial as it is to be done with energy efficiency and minimize discovery latency and maximize percentage of neighbours discovered.The current ND approaches that are indirect in nature are categorized into methods of removal of active slots from wake-up schedules and intelligent addition of new slots.The two methods are found to have certain drawbacks.Thefirst category disturbs original integrity of wake-up schedules leading to reduced chances of discovering new nodes in WSN as neighbours.When second category is followed,it may have inefficient slots in the wake-up schedules leading to performance degradation.Therefore,the motivation behind the work in this paper is that by combining the two categories,it is possible to reap benefits of both and get rid of the limitations of the both.Making a hybrid is achieved by introducing virtual nodes that help maximize performance by ensuring original integrity of wake-up schedules and adding of efficient active slots.Thus a Hybrid Approach to Neighbour Discovery(HAND)protocol is realized in WSN.The simulation study revealed that HAND outperforms the existing indirect ND models.

Prediction of separation flows around a 6:1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier-Stokes （RANS） and large-eddy-simulation （LES） methods for the separated flows at high angles of attack around a 6：1 prolate spheroid. The RANS/LES hybrid meth- ods studied in this work include the detached eddy simulation （DES） based on Spalart-Allmaras （S-A）, Menter＇s k-ω shear-stress-transport （SST） and k-o9 with weakly nonlinear eddy viscosity formulation （Wilcox-Durbin＋, WD＋） models and the zonalANS/LES methods based on the SST and WD＋ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower-upper symmetric-Gauss-Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows.

Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface

A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinitely long conducting target with arbitrary cross section and a one-dimensional （1D） Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation （EFIE） in MOM region （target） is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.

HYBRID FINITE ANALYTIC SOLUTIONS OF SHALLOW WATER CIRCULATION

The hybrid finite analytic(HFA) method is a kind of numerical scheme in rectangular element. In order to simulate the shallow circulation in irregular bathymetry by HFA scheme, the model in sigma coordinate system was obtained. The model has been tested against three cases: 1) Wind induced circulation; 2) Density driven circulation and 3) Seiche oscillation. The results obtained in the present study compare well with those obtained from the corresponding analytical solutions under idealized for the above three cases. The hybrid finite analytic method and the circulation model in sigma coordinate system can be used calculate the flow and water quality in estuaries and coastal waters.

AN ANALYSIS OF THE MODELING OF STRESS AND STRAIN FIELDS IN A REAL MICROSTRUC-TURE USING AHYBRID METHOD

The distribution of stress and strain fields in a micro-structuralarea of a particle reinforced composite is studied by a combinationof experimental and numerical method (hybrid method). With the ex-perimental values of displacements in a micro-region as the boundaryloading condition, strain and stress fields inside the micro-regionare calculated by the finite element method under tow different kindsof model- ing, namely, as pale stress and plane strain condition. Thedifferences between the two kinds of modeling conditions as appliedto micro-structural areas are discussed.

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.

A constrained particle dynamics for continuum-particle hybrid method in micro- and nano-fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics （MD） in one domain and by the Navier-Stokes （NS） equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip bound- ary conditions.

High performance corrosion and wear resistant composite titanium nitride layers produced on the AZ91D magnesium alloy by a hybrid method

Composite,diffusive titanium nitride layers formed on a titanium and aluminum sub-layer were produced on the AZ91D magnesium alloy.The layers were obtained using a hybrid method which combined the PVD processes with the final sealing by a hydrothermal treatment.The microstructure,resistance to corrosion,mechanical damage,and frictional wear of the layers were examined.The properties of the AZ91D alloy covered with these layers were compared with those of the untreated alloy and of some engineering materials such as 316L stainless steel,100Cr6 bearing steel,and the AZ91D alloy subjected to commercial anodizing.It has been found that the composite diffusive nitride layer produced on the AZ91D alloy and then sealed by the hydrothermal treatment ensures the corrosion resistance comparable with that of 316L stainless steel.The layers are characterized by higher electrochemical durability which is due to the surface being overbuilt with the titanium oxides formed,as shown by the XPS examinations,from titanium nitride during the hydrothermal treatment.The composite titanium nitride layers exhibit high resistance to mechanical damage and wear,including frictional wear which is comparable with that of 100Cr6 bearing steel.The performance properties of the AZ91D magnesium alloy covered with the composite titanium nitride coating are substantially superior to those of the alloy subjected to commercial anodizing which is the dominant technique employed in industrial practice.

COARSE-MESH-ACCURACY IMPROVEMENT OF BILINEAR Q_4-PLANE ELEMENT BY THE COMBINED HYBRID FINITE ELEMENT METHOD

The combined hybrid finite element method is of an intrinsic mechanism of enhancing coarse-mesh-accuracy of lower order displacement schemes. It was confirmed that the combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes, and that the combination parameter plays an important role in the enhancement. As an improvement of conforming bilinear Q(4)-plane element, the combined hybrid method adopted the most convenient quadrilateral displacements-stress mode, i.e.,the mode of compatible isoparametric bilinear displacements and pure constant stresses. By adjusting the combined parameter, the optimized version of the combined hybrid element was obtained and numerical tests indicated that this parameter-adjusted version behaves much better than Q(4)-element and is of high accuracy at coarse meshes. Due to elimination of stress parameters at the elemental level, this combined hybrid version is of the same computational cost as that of Q(4)-element.

New hybridization of PO, SBR, and MoM for scattering by large complex conducting objects

As a marked extension of the traditional MoM-PO （method of moment-physical optics） hybrid method, a new hybridization of PO, SBR, and MoM （MoM-SBR/PO） is presented to calculate the multireflection contribution in the PO region efficiently by introducing the method of SBR based on RDN notion, which avoids the time-consuming iterative procedure and the choice of proper Green＇s function. As compared with the traditional MoM-PO hybrid method, the calculation efficiency of the proposed method is greatly improved, and its validity is verified by numerical results.

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

Global SH-wave propagation in a 2D whole Moon model using the parallel hybrid PSM/FDM method

We present numerical modeling of SH-wave propagation for the recently proposed whole Moon model and try to improve our understanding of lunar seismic wave propagation. We use a hybrid PSM/FDM method on staggered grids to solve the wave equations and implement the calculation on a parallel PC cluster to improve the computing efficiency. Features of global SH-wave propagation are firstly discussed for a 100-km shallow and900-km deep moonquakes, respectively. Effects of frequency range and lateral variation of crust thickness are then investigated with various models. Our synthetic waveforms are finally compared with observed Apollo data to show the features of wave propagation that were produced by our model and those not reproduced by our models. Our numerical modeling show that the low-velocity upper crust plays significant role in the development of reverberating wave trains. Increasing frequency enhances the strength and duration of the reverberations.Surface multiples dominate wavefields for shallow event.Core–mantle reflections can be clearly identified for deep event at low frequency. The layered whole Moon model and the low-velocity upper crust produce the reverberating wave trains following each phases consistent with observation. However, more realistic Moon model should be considered in order to explain the strong and slow decay scattering between various phases shown on observation data.