A hybrid method is presented for domain decomposition employing combinatorial and algebraic graph theoretical algorithms. The method uses combinatorial graph theory for partial decomposition, followed by a spectral bisection approach based on concepts from algebraic graph theory. Examples are presented to illustrate the efficiency of the mixed method. In this paper, the effects of nodal ordering on the performance of the spectral bisection and mixed method are investigated.

Newton's method is considered preferable due to its higher accuracy compared to first-order methods in approximating the target function; however, it requires the explicit computation of the Hessian matrix. On the other hand, quasi-Newton methods are popular among researchers because they don't require directly calculating the Hessian matrix.Here, we propose a quasi-Newton method designed to achieve high computational speed while accurately approximating the Hessian. Our approach views the Hessian matrix from an operational perspective.From the operational perspective, a matrix acts as an operator that transforms an input vector into an output vector. Following this approach, the Hessian matrix takes a gradient vector as input and generates an output vector accordingly. Our method is designed to perform calculations in parallel, enabling high execution speed. Moreover, our method is specifically designed to operate efficiently with limited memory, making it well-suited for large-scale problems. Our experimental results indicate that the proposed method is faster than the quasi-Newton L-BFGS method. For instance, in applications such as quadratic optimization problems, our method demonstrates a significant performance improvement, executing approximately ten times faster than L-BFGS. Furthermore, in problems involving a large number of variables, our method is more computationally efficient than BFGS.

A numerical methodology for two-phase gas-solid flow is developed, using parallel computing. The particles are assumed elliptic and their translation and rotation are both considered. The drag, weight, and hydrodynamic torques are taken into account. Due to high computational time, a parallel is used. The results are obtained for particles ranging from 2 to 30 microns with aspect ratios of 1-10. The effects of this ratio on particle deposition are examined. The results are compared with previous experimental and numerical benchmark data, which show acceptable agreements.

Multiple networking layers existing in the IoT network involve heterogeneity that must be addressed to facilitate proper communication such that the performance of an IoT network does not suffers. The performance of the IoT networks depends on networking topologies used in different layers, clustering algorithms, protocols used for handling heterogeneity communication speeds, and data packet sizes. In this Research, the performance of IoT networks is improved by adding device clustering via a multi-Stage network and using an efficient SOJK clustering algorithm in the device layer, which minimizes power depletion and increases the quantity of data and data packets; transmitted at zero power. A mechanism to handle heterogeneity that exists due to Wi-Fi, CDMA, and USB communication protocols is also presented while optimizing the communication speeds and data transmission size. It has also been shown that the use of 170Mbps cellular speed and the data size of 468 bytes gives the optimum response time of an IoT network. The time taken to transport information from the device to the storage layer is reduced by 57% compared to the time taken to transport the data using the prototype network.

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Performance of parallel-hole collimators may be evaluated by determining their response to a point radioactive source which for instance, the amount of collimator resolution is calculated by measuring the full width at half maximum (FWHM) of point spread function (PSF). The conventional method in calculating the response of the collimator to a point source by using Monte Carlo simulations is to map the signal values in each detector cell to the center of cell on the x or y axis. In this paper, a new computing algorithm has been proposed which optimally maps the signal values on these axes. The responses of LEUHR, LEHR, LEGP and LEHS collimators are simulated based on the conventional method and the optimized computing one by the MCNP5 code. The results have been indicated that the response based on the optimized method has a higher accuracy compared to that of the conventional one. The average relative differences between the amounts of resolution based on the optimized method and experimental data have been found to be considerably fewer than those of the conventional one. Therefore, one may obtain parallel hole collimators’ response with a higher accuracy by using the optimized computing method.