Kind Of Numerical Method Research Articles

A hierarchical parallel implementation for heterogeneous computing. Application to algebra-based CFD simulations on hybrid supercomputers

The quest for new portable implementations of simulation algorithms is motivated by the increasing variety of computing architectures. Moreover, the hybridization of high-performance computing systems imposes additional constraints, since heterogeneous computations are needed to efficiently engage processors and massively-parallel accelerators. This, in turn, involves different parallel paradigms and computing frameworks and requires complex data exchanges between computing units. Typically, simulation codes rely on sophisticated data structures and computing subroutines, so-called kernels, which makes portability terribly cumbersome. Thus, a natural way to achieve portability is to dramatically reduce the complexity of both data structures and computing kernels. In our algebra-based approach, the scale-resolving simulation of incompressible turbulent flows on unstructured meshes relies on three fundamental kernels: the sparse matrix-vector product, the linear combination of vectors and the dot product. It is noteworthy that this approach is not limited to a particular kind of numerical method or a set of governing equations. In our code, an auto-balanced multilevel partitioning distributes workload among computing devices of various architectures. The overlap of computations and multistage communications efficiently hides the data exchanges overhead in large-scale supercomputer simulations. In addition to computing on accelerators, special attention is paid at efficiency on manycore processors in multiprocessor nodes with significant non-uniform memory access factor. Parallel efficiency and performance are studied in detail for different execution modes on various supercomputers using up to 9,600 processor cores and up to 256 graphics processor units. The heterogeneous implementation model described in this work is a general-purpose approach that is well suited for various subroutines in numerical simulation codes.

IHP: a dynamic heterogeneous parallel scheme for iterative or time-step methods—image denoising as case study

Iterative and time-step methods are spread far and wide in several mathematics and physics domains. At the same time, modern computers include multicore CPUs along with GPUs, so it is important to use all their computing capabilities for their efficient use. Aiming to improve performance of this kind of numerical methods, we introduce in this work a new heterogeneous parallelism CPU + GPU scheme which we call IHP. This new scheme has the advantage of being self-balanced and able to dynamically distribute the workload between CPU and GPU according to their performance on the fly. Also, it can be used with several contending technologies, like CUDA and OpenCL for GPUs or OpenMP and Intel TBB for CPUs. As a case in point, we analyse an image denoising problem based on time-step diffusion methods for brightness and chromaticity. Results show execution significant improvements in execution time using this scheme, with a minimal overhead.

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Although many kinds of numerical methods have been announced for the predator-prey system, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, in this paper, a new interpolation collocation method is proposed for a class of predator-prey systems with complex dynamics characters. Some complex dynamics characters and pattern formations are shown by using this new approach, and the results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

GPU acceleration of splitting schemes applied to differential matrix equations

We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.

Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

Hyperchaotic system, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, hyperchaotic system between nonlinear systems has been extensively studied. Although many kinds of numerical methods of the system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. Barycentric Lagrange interpolation collocation method is given and illustrated with hyperchaotic system () as examples. Numerical simulations are used to verify the effectiveness of the present method.

Determination of Weibull Parameters by Different Numerical Methods and Analysis of Wind Power Density in Osmaniye, Turkey

In this study the potential of wind energy in Osmaniye Region has been analysed statistically in the basis of information that has been measured hourly between the years of 2009-2013. The two parameter Weibull Distribution Function is generally applied to evaluate potential of wind energy at any region. This study introduced the evaluation of Weibull Distribution Function parameters which are obtained by different kinds of numerical methods, namely Graphical Method (GM), Moment Method (MM), Energy Pattern Method (EPM), Energy Trend Method (ETM) and Maximum Likelihood Method (MLM). The Relative Percentage Error (RPE) statistical test is used to compare the efficiency of all used methods. The calculated power density of all used numerical methods is a major key issue for suitability use of wind energy. The evaluation of Weibull parameters and wind power distribution play a crucial role in producing electricity from wind power. The results of the used methods are compared and the obtained pre-research results show that the wind energy potential in Osmaniye Region is statistically suitable for electricity production.

Research on vibro-acoustic characteristics of the aluminum motor shell based on GA-BP neural network and boundary element method

Firstly, the paper established a finite element model for a steel motor shell and computed related modals, vibration velocities, stress and strain respectively. Computational results show that the flange and end shield of the motor shell had the maximum vibration velocities and strain because these locations lacked the reinforcing ribs, while the maximum stress was mainly at joints between different structures. Secondly, the steel material was replaced by the aluminum alloy. Mechanical parameters of the motor shell were recomputed and compared with those of the steel structure. Results show that modal frequency on each order increased, which is good for avoiding the structural resonance. In addition, the maximum stress of the structure decreased by 4.4 MPa, and the maximum strain decreased by 0.27 mm, which could effectively improve the fatigue characteristics of the motor shell under long-term excitation. Then, the boundary element method was used to compute radiation noises of the motor shell in far field, where the radiation noise presented an obvious directivity. Finally, the paper proposed a GA-BP neural network model to predict the radiation noise of the motor and compared the prediction results with the boundary element. In the whole analyzed frequency band, the maximum difference between the neural network prediction and the real values did not exceed 5 dB, indicating that it is feasible to predict radiation noises of the motor by the neural network. Additionally, experiments were also conducted and compared with two kinds of numerical methods. Methods proposed in this paper provide some references for realizing the rapid noise reduction and light weight of motors.

The Finite Difference Method Of Discontinuous Constraint Slabs

With the improvement of building standard, structural form becomes more and more complicated. The utility rate of special-shaped column, corner window and cantilever structure is higher and higher, which often makes reinforced concrete floor slabs in a discontinuous constraint state. To make the design of discontinuous constraint slabs more scientific, the author puts forward a kind of numerical method that can solve the problem of low calculation precision. On this basis, the numerical method is applied to solve the problem of rectangular slabs with two simply supported and the other with part of simply supported and part of clamped ,having a theoretical analysis of the result to verify that the calculation method is correct. The result shows : 1. For discontinuous constraint slabs, the displacement difference is large and the average is 10%~20% when it comes to whether the method is adopted or not. 2. For discontinuous constraint slabs, higher precision is obtained by using the numerical method proposed in this paper. And it is necessary to consider the influence of boundary constraints when we design discontinuous Constraint slabs.

Spectral and pseudospectral methods for unbounded domains

In this paper, we review the current trends and progresses in spectral and pseudospectral methods for unbounded domains and exterior problems. The rst kind of numerical methods are based on the orthogonal approximations and interpolations by using the Hermite polynomials and functions, and the Laguerre polynomi-fials and functions. The second kind of numerical methods are based on the Jacobi orthogonal approximations and interpolations with suitable variable transformations. The third kind of numerical methods are induced by the various combinations of the previous orthogonal approximations and interpolations coupled with domain decomposition and other techniques. We also present the main results on the Hermite, Laguerre, Jacobi irra-fitional orthogonal approximations and interpolations, which serve as the mathematical foundation of the related numerical algorithms.

A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data

Bimodal mixture Weibull distribution being a special case of mixture Weibull distribution has been used recently as a suitable model for heterogeneous data sets in many practical applications. The bimodal mixture Weibull term represents a mixture of two Weibull distributions. Although many estimation methods have been proposed for the bimodal mixture Weibull distribution, there is not a comprehensive comparison. This paper presents a detailed comparison of five kinds of numerical methods, such as maximum likelihood estimation, least-squares method, method of moments, method of logarithmic moments and percentile method (PM) in terms of several criteria by simulation study. Also parameter estimation methods are applied to real data.

Model and Algorithm for Wood Moisture Content Detection by Capacitance Sensor

In this article, a model which was used to measure wood moisture content(MC) was presented. It was founded under non-uniform and asymmetric conditions and there was no any need for wood shape. It can work out the relationship between capacitance value( ) and dielectric constant( ). Compared with previous methods, it not only can greatly lessened measuring work, but also avoided the waste of media resources, such as wood. At the same time, a new kind of numerical method was given for this problem. The number of unknown variables significantly are reduced by doing this.

Numerical Simulation of Buried Structure Response to Strong Dynamic Load

Three kinds of numerical methods (Lagrange, ALE, SPH-FEM) were used to analyze the response of an fully buried underground structure under blast loading, the differences of these three methods and factors which affect calculation accuracy were analyzed and compared. The results show that the Lagrange method can give more accurate results, but it should be taken into account that the shape of the ammunition may influence the calculation of impact stress in soil.

Solution of Boundary Value Obstacle Problems Using MQ-RBF and IMQ-RBF

A kind of numerical method which is based on multiquadric RBF, inverse multiquadric RBF, and Wu-Schaback operators is presented for solving second-order and third-order boundary value problems associated with obstacle, unilateral, and contact problems. The algorithms are proved to be highly accurate and easy to implement. Some numerical tests are also presented to show the efficiency of the algorithms.

Numerical and analytical approaches to MHD Jeffery‐Hamel flow in a porous channel

PurposeThe main purpose of the work is to demonstrate the eligibility of the methods applied and to have the more reliable and user friendly approaches to find the solution of the applicable governing equations such as of the MHD flow.Design/methodology/approachThe numerical and semi analytical methods have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the results obtained and the results of the former studies performed using the other numerical approach.FindingsThe reliability of the methods are approved, so that the method could be used to discuss more in depth arguments on the different profiles of the solution.Originality/valueIt could be considered as a first endeavor to use the solution of the MHD Jeffery Hamel flow using this kind of numerical method along with the semi analytical approach.

Calculation for Equivalent Nodal Force of Prestress in 20 Nodes Isoparametric Element

When establishing the prestressed bridge model with the entity unit, the simulation of prestress bar has very big limitation. The paper takes 20 nodes isoparametric element as an example and puts forward a kind of numerical method combined with the Newton iterative algorithm and Gauss integral algorithm to calculate equivalent loads of prestress in body element. This method can be used to calculate the equivalent loads of prestress in the various complex steel in bundle shapes and suits the computer programming. Through the final regular inspection, this method has been proved to have very high precision.

Research on Stability Condition of Polar Winding on the Dished Head

The polar winding, as a kind of non-geodesic winding, is in a serious slippage trend. Based on the Theoretical Model of the filament winding, this paper outlines a kind of numerical methods for determining the stability condition of the polar winding on the composite pressure vessel with dished head. At last, through the providing some examples, this paper shows the stable trend on the dished dome during polar winding to optimize the design result.

Research on a Numerical Schemes for Capturing Free Front during Injection Molding

In order to capture the free front in injection molding filling precisely, the numerical method is studied for the H-J (Hamilton Jacobi) equations. The central WENO (Weighted Essentially Non-Oscillatory) scheme for the level set equations, the third-order central WENO scheme in space respectively and the third-order TVD R-K (Total Variation Diminishing Runge–Kutta) scheme in time, are used for capturing the melt flow front in injection molding filling. The numerical results show the high-order WENO scheme can capture discontinuity precisely and the melt flow front can be captured precisely using this kind of numerical method during the injection molding filling.

On collocation methods for delay differential and Volterra integral equations with proportional delay

To compute long term integrations for the pantograph differential equation with proportional delay qt, 0 < q ⩽ 1: y′(t) = ay(t) + by(qt) + f(t), y(0) = y0, we offer two kinds of numerical methods using special mesh distributions, that is, a rational approximant with ‘quasi-uniform meshes’ (see E. Ishiwata and Y. Muroya [Appl. Math. Comput., 2007, 187: 741-747]) and a Gauss collocation method with ‘quasi-constrained meshes’. If we apply these meshes to rational approximant and Gauss collocation method, respectively, then we obtain useful numerical methods of order p* = 2m for computing long term integrations. Numerical investigations for these methods are also presented.

Numerical analysis of strip edge drop for Sendzimir mill

A new kind of numerical method, Contact Element Method (CEM) with two relative coordinates, has been proposed. There are two main characteristics in this method. First, meshing is based on the contact length between the rolls or between the work roll and the strip; second, two relative coordinates are established for every element depending on the contact objects. A matrix for analyzing the rolling process of a Sendzimir mill has been established as well as a software SM4SM (Setup Models for Sendzimir Mill) by which the strip edge drop during rolling has been studied using the CEM. The calculated results show that the strip edge drop will decrease when increasing the 1st intermediate roll (IMR) taper slope and length, reducing the 1st IMR shifting, increasing the roll J and the work roll crown, or increasing the tension stress; by contraries, the strip edge drop will increase. Meanwhile, three methods (changing the work roll crown, changing the work roll edge rigidity, changing the pressure distribution on the work roll) for controlling the strip edge drop are discussed.

The condition of the integral representation of American Options

The pricing of an American option can be formulated as a free boundary problem for the Black–Scholes equation. If the free boundary is known, the option price can be evaluated by an integral representation involving the free boundary. Usually, the free boundary is approximated by some kind of numerical method, eg, as a solution of a suitable integral equation (Kim (1990); McKean (1965)) or a series expansion (Zhu (2006)). In this paper it is shown how the approximation error of the boundary influences the error in the option evaluation. A condition number κ depending only on the option parameters is introduced to measure this deviation.