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The goal of this paper is to solve the complex symmetric linear systems generated from the discretization of the space fractional coupled nonlinear Schrödinger (CNLS) equations, whose coefficient matrix is equal to the sum of a symmetric positive definite Toeplitz matrix and a Hermitian positive definite complex diagonal matrix. In order to make the best use of the full Toeplitz structure of the coefficient matrix, a new Toeplitz and diagonal splitting (TDS) is given and the corresponding TDS iteration method is proposed to solve the discretized linear systems, then two circulant preconditioners based on Strang’s and T. Chan’s circulant approximation, are proposed to accelerate the convergence of the preconditioned conjugated gradient (PCG) method for solving the first linear sub-system in the TDS method. Theoretical analysis and numerical experiments demonstrate that the TDS method is unconditional convergence and the TDS-PCG inner-outer iteration method with two circulant preconditioners to solve the discretization linear systems of the space fractional CNLS equations is feasible and efficient. [ABSTRACT FROM AUTHOR]

The complicated geological conditions will bring great challenges to the drillstring of horizontal wells for the reason that the increase of the well depth in Sichuan- Chongqing region. Since drillstring failure and friction during drilling are generally caused by drillstring vibration, great importance must be attached to computer simulation methods for the prediction of drillstring vibration. A finite element model considering axial, lateral and torsional vibration is established. In order to verify the established numerical model, an indoor experimental device based on the similarity principle was established. The vibration characteristics of three shale gas horizontal wells drillstrings are described. The reasons for the large difference in vibration characteristics between the three wells were discussed by changing the well structure, BHA(bottom hole assembly) and drilling parameters. The simulation results show that the depth of ultra-deep well 3 is only 1.27 times of that of medium-deep well 2, but the fluctuation of WOB (weight on bit) is 2.8 times. The primary factor for the great difference of WOB fluctuation is the change of vertical section depth, the secondary factor is the change of the horizontal section length. Additionally, the reasonable range of speeds has been proposed and applied in the field. The advantage of this numerical analysis method is that it can judge the vibration and friction torque of drillstring in horizontal wells with arbitrary structure, drilling parameters and BHA. This method has certain guiding significance to the field practice. [ABSTRACT FROM AUTHOR]

A meshless local Petrov–Galerkin (MLPG) approach based on the streamline upwind (SU) idea and the variational multiscale (VMS) concept, called as VMS-SUMLPG method, is herein proposed to solve the convection-dominated problems. In the present VMS-SUMLPG method, the streamline upwind is constructed in the test function to solve the non-self-adjoint matrix. Meanwhile, the VMS concept as a stability term is adopted to alleviate the numerical instability such as spurious oscillations, overshoots, and undershoots. Its numerical accuracy and stability are validated by comparing with the streamline upwind Petrov–Galerkin (SUMLPG) method and the finite volume method with high-order difference schemes for two classical convection-dominated problems at the Peclet number ranging from 106to 108. It is shown that the numerical solutions of the present VMS-SUMLPG method are accuracy, smoothness, and stability. [ABSTRACT FROM PUBLISHER]

In a recent publication (Ritschel et al., J. Chem. Phys. 2015, 142, 034115) we have derived a hierarchy of coupled differential equations in time domain to calculate the linear optical properties of molecular aggregates. Here, we provide details about issues concerning the numerical implementation. In addition we present the corresponding hierarchy in frequency domain. [ABSTRACT FROM AUTHOR]

A physically consistent difference scheme is proposed to discretize the convection–diffusion equation in this paper. The interface variables of control volume are calculated by the interpolation of the discretized convection–diffusion equation rather than the direct interpolation with neighbor nodes in the direction perpendicular to the interface. In the new scheme, all the nodes of parallel and normal to the interface are involved, which means that the influence of cross-stream fluxes is considered. Obviously, the proposed interpolation scheme is full of physical meaning and better than the traditional convective interpolation schemes. Two simulations of typical benchmark problems, lid-driven cavity flow in square cavity and flow over a backward-facing step, are carried out with this scheme and some traditional schemes to prove the advantages of the proposed scheme. [ABSTRACT FROM AUTHOR]

Based on the Hermitian and skew-Hermitian (HS) splitting for non-Hermitian matrices, a nonalternating preconditioned Hermitian and skew-Hermitian splitting-Krylov plus inverted Krylov subspace (NPHSS-KPIK) iteration method for solving a class of large and low-rank complex Sylvester equations arising from the two-dimensional time- periodic fractional diffusion problem is established. The local convergence condition is proposed and the optimal parameter is given. Numerical experiments are used to show the efficiency of the NPHSS-KPIK iteration method for solving the Sylvester equations arising from the time-periodic fractional diffusion equations. [ABSTRACT FROM AUTHOR]

Passive cooling schemes, such as natural convection, are the most reliable heat dissipation apprpaches for electronic equipment. Some times, the highest temperature of the printed circuit board (PCB), rather than the highest of chips, is very much concern because of some technological reasons. In order to reduce the maximum PCB temperature, this article analyze the PCB temperature distribution by multiscale simulation. A top-to-down approach is adopted in order to reveal the details of temperature distribution of some interested local position. In the top-to-down approach, the system level simulation by a not-too-fine grid system is the key to obtain a reliable solution. In order to reach such a goal each component of the PCB should be reasonably simplified. The thermal analysis method is proposed to simplify the components, and the implementation details are provided for three types of components. In the companion article, the settlement of boundary conditions from the data of system level simulation and several improvements in heat transfer by numerical simulation will be presented. [ABSTRACT FROM PUBLISHER]

In the companion article (Part I), simplified compact model of components in a system level model was established based on heat transfer path and thermal resistance network analysis. In this article, component level simulation and lead level simulation was conducted by assiging the boundary conditions from the data of the higher level simulation, and effects of different boundary conditions on numerical accuracy and stability are studied. Comparison shows that multiscale thermal modeling methodology can save 87% of the total computation time compared with full simulation with a fine grid system, and can greatly improve the resolution of the calculation result. Mainly based on the multiscale simulation five improvements for the reduction of the maximum PCB temperature are proposed. This article also provides an example that by a careful numerical thermal design, a passive cooling mode can sometimes meet the cooling requirement of a PCB with high power input in some extent. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the performance of an amplify-and-forward (AF) two-way relaying system, where two sources exchange information via the aid of an intermediate relay that is selected among multiple relays according to max-min criterion. We consider a practical scenario, where one source-relay link undergoes Rician fading, and the other source-relay link is subject to Rayleigh fading. To be specific, we derive a tight lower bound for the outage probability. From this lower bound, the asymptotic outage probability and average symbol error rate (SER) expressions are derived to gain insight into the system performance at high signal-to-noise ratio (SNR) region. Furthermore, we investigate the optimal power allocation (PA) with fixed relay location (RL), optimal RL with fixed PA and joint optimization of PA and RL to minimize the outage probability and average SER. The analytical expressions are verified through Monte Carlo simulations, where the positive impact of Rician factor on the system performance is also illustrated. Simulation results also validate the effectiveness of the proposed PA and relay positioning schemes. [ABSTRACT FROM AUTHOR]

Passive cooling schemes, such as natural convection, are the most safe heat dissipation mode of electronic equipment. Some times the highest temperature of the PCB, rather than the highest of chips, is very much a concern due to technological reasons. In order to reduce the maximum PCB temperature, this article discusses various improvement methods via numerical simulation. These include optimization of fin number of heat sink, structure improvement of sun shield, and creation of insulation cavity in the base plate of heat sink. Taking the PCB of an RBS as an example, numerical simulation results show that by integrating these methods the maximum PCB temperature can be appreciably reduced. This article provides an example that by using a careful numerical thermal design, a passive cooling mode can sometimes meet the cooling requirement of a PCB with high power input in some extent. [ABSTRACT FROM AUTHOR]

Linear scan cone-beam Computed Tomography (CT) is useful to fixed pipeline inspection. We extend Simultaneous Algebraic Reconstruction Technique (SART) to linear scan cone-beam CT and focus on reducing its reconstruction time through cluster computing. In order to reduce communication overhead, we investigate a trapeziform image space decomposition scheme and a subsets-reduce communication technique. The performance of proposed parallel algorithm is analyzed theoretically and verified through experiment. The results show that the proposed parallel algorithm can generate approving CT images and its performance is mainly influenced by load imbalance and network bandwidth. [ABSTRACT FROM AUTHOR]

This paper numerically investigated the coupled flow and heat transfer of a parabolic trough collector (PTC), with the non-uniform heat flux boundary condition on the absorber wall and the rarefied gas effects in the annular vacuum gap being taken into consideration. A fully coupled cross-sectional heat transfer model is established with Direct Simulation Monte Carlo (DSMC) method for the rarefied gas flow and heat transfer in the vacuum annual gap. The PTC tube efficiency can be obtained from the above simulation for a given HTF temperature. Such simulation is conducted for several specified HTF temperature and different efficiency data are obtained. These data are fitted by an equation. This equation is then used to advance the HTF temperature in the axial direction. In such a way a simplified 3D model for the design of a PTC receiver is obtained. Cross-sectional simulation results show that when the gas pressure is less than 0.1 Pa further decrease in pressure makes no further contribution to reduce the heat loss. The effects of periphery non-uniform distribution of heat flux, coating material emissivity, envelope diameter and HTF inlet velocity on the PTC efficiency are discussed. An operation variant is proposed by using the 3D model by which the total PTC tube length can be reduced for a given thermal load. [ABSTRACT FROM AUTHOR]