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gradient coefficient</title> <meta name="description" content="Search results for: conjugate gradient coefficient"> <meta name="keywords" content="conjugate gradient coefficient"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="conjugate gradient coefficient"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3033</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: conjugate gradient coefficient</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3033</span> A New Modification of Nonlinear Conjugate Gradient Coefficients with Global Convergence Properties</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Alhawarat">Ahmad Alhawarat</a>, <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20Mamat"> Mustafa Mamat</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Rivaie"> Mohd Rivaie</a>, <a href="https://publications.waset.org/abstracts/search?q=Ismail%20Mohd"> Ismail Mohd</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title="conjugate gradient method">conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20coefficient" title=" conjugate gradient coefficient"> conjugate gradient coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20convergence" title=" global convergence"> global convergence</a> </p> <a href="https://publications.waset.org/abstracts/1392/a-new-modification-of-nonlinear-conjugate-gradient-coefficients-with-global-convergence-properties" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1392.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">463</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3032</span> Global Convergence of a Modified Three-Term Conjugate Gradient Algorithms</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Belloufi%20Mohammed">Belloufi Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Sellami%20Badreddine"> Sellami Badreddine</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=unconstrained%20optimization" title="unconstrained optimization">unconstrained optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=three-term%20conjugate%20gradient" title=" three-term conjugate gradient"> three-term conjugate gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=sufficient%20descent%20property" title=" sufficient descent property"> sufficient descent property</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20search" title=" line search"> line search</a> </p> <a href="https://publications.waset.org/abstracts/41727/global-convergence-of-a-modified-three-term-conjugate-gradient-algorithms" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41727.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">375</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3031</span> A New Family of Globally Convergent Conjugate Gradient Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20Sellami">B. Sellami</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Laskri"> Y. Laskri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Belloufi"> M. Belloufi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, a new family of conjugate gradient method is proposed for unconstrained optimization. This method includes the already existing two practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which implies the new method is promising. In addition the methods related to this family are uniformly discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title="conjugate gradient method">conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20convergence" title=" global convergence"> global convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20search" title=" line search"> line search</a>, <a href="https://publications.waset.org/abstracts/search?q=unconstrained%20optimization" title=" unconstrained optimization"> unconstrained optimization</a> </p> <a href="https://publications.waset.org/abstracts/40381/a-new-family-of-globally-convergent-conjugate-gradient-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40381.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">410</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3030</span> A New Conjugate Gradient Method with Guaranteed Descent</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20Sellami">B. Sellami</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Belloufi"> M. Belloufi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but also has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=unconstrained%20optimization" title="unconstrained optimization">unconstrained optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20search" title=" line search"> line search</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20convergence" title=" global convergence"> global convergence</a> </p> <a href="https://publications.waset.org/abstracts/41734/a-new-conjugate-gradient-method-with-guaranteed-descent" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41734.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">452</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3029</span> A New Class of Conjugate Gradient Methods Based on a Modified Search Direction for Unconstrained Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Belloufi%20Mohammed">Belloufi Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Sellami%20Badreddine"> Sellami Badreddine</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of conjugate gradient methods which ensures sufficient descent. Moreover, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=unconstrained%20optimization" title="unconstrained optimization">unconstrained optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=sufficient%20descent%20property" title=" sufficient descent property"> sufficient descent property</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20comparisons" title=" numerical comparisons"> numerical comparisons</a> </p> <a href="https://publications.waset.org/abstracts/41725/a-new-class-of-conjugate-gradient-methods-based-on-a-modified-search-direction-for-unconstrained-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41725.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">403</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3028</span> On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hussaini%20Doko%20Ibrahim">Hussaini Doko Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%20Cyprian%20Chinwenyi"> Hamilton Cyprian Chinwenyi</a>, <a href="https://publications.waset.org/abstracts/search?q=Henrietta%20Nkem%20Ude"> Henrietta Nkem Ude</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient" title="conjugate gradient">conjugate gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20equations" title=" linear equations"> linear equations</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20and%20positive%20definite%20matrix" title=" symmetric and positive definite matrix"> symmetric and positive definite matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=gauss-seidel" title=" gauss-seidel"> gauss-seidel</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacobi" title=" Jacobi"> Jacobi</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithm" title=" algorithm"> algorithm</a> </p> <a href="https://publications.waset.org/abstracts/138341/on-the-algorithmic-iterative-solutions-of-conjugate-gradient-gauss-seidel-and-jacobi-methods-for-solving-systems-of-linear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138341.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">149</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3027</span> A Conjugate Gradient Method for Large Scale Unconstrained Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Belloufi">Mohammed Belloufi</a>, <a href="https://publications.waset.org/abstracts/search?q=Rachid%20Benzine"> Rachid Benzine</a>, <a href="https://publications.waset.org/abstracts/search?q=Badreddine%20Sellami"> Badreddine Sellami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=unconstrained%20optimization" title="unconstrained optimization">unconstrained optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20Wolfe%20line%20search" title=" strong Wolfe line search"> strong Wolfe line search</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20convergence" title=" global convergence"> global convergence</a> </p> <a href="https://publications.waset.org/abstracts/40028/a-conjugate-gradient-method-for-large-scale-unconstrained-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40028.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">421</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3026</span> A Modified Nonlinear Conjugate Gradient Algorithm for Large Scale Unconstrained Optimization Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tsegay%20Giday%20Woldu">Tsegay Giday Woldu</a>, <a href="https://publications.waset.org/abstracts/search?q=Haibin%20Zhang"> Haibin Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Xin%20Zhang"> Xin Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yemane%20Hailu%20Fissuh"> Yemane Hailu Fissuh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well known that nonlinear conjugate gradient method is one of the widely used first order methods to solve large scale unconstrained smooth optimization problems. Because of the low memory requirement, attractive theoretical features, practical computational efficiency and nice convergence properties, nonlinear conjugate gradient methods have a special role for solving large scale unconstrained optimization problems. Large scale optimization problems are with important applications in practical and scientific world. However, nonlinear conjugate gradient methods have restricted information about the curvature of the objective function and they are likely less efficient and robust compared to some second order algorithms. To overcome these drawbacks, the new modified nonlinear conjugate gradient method is presented. The noticeable features of our work are that the new search direction possesses the sufficient descent property independent of any line search and it belongs to a trust region. Under mild assumptions and standard Wolfe line search technique, the global convergence property of the proposed algorithm is established. Furthermore, to test the practical computational performance of our new algorithm, numerical experiments are provided and implemented on the set of some large dimensional unconstrained problems. The numerical results show that the proposed algorithm is an efficient and robust compared with other similar algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title="conjugate gradient method">conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20convergence" title=" global convergence"> global convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20scale%20optimization" title=" large scale optimization"> large scale optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=sufficient%20descent%20property" title=" sufficient descent property"> sufficient descent property</a> </p> <a href="https://publications.waset.org/abstracts/102625/a-modified-nonlinear-conjugate-gradient-algorithm-for-large-scale-unconstrained-optimization-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102625.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">205</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3025</span> Parallel Pipelined Conjugate Gradient Algorithm on Heterogeneous Platforms</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sergey%20Kopysov">Sergey Kopysov</a>, <a href="https://publications.waset.org/abstracts/search?q=Nikita%20Nedozhogin"> Nikita Nedozhogin</a>, <a href="https://publications.waset.org/abstracts/search?q=Leonid%20Tonkov"> Leonid Tonkov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems does not scale well on multi-CPU/multi-GPUs clusters. For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration instead of two for standard CG. The standard and pipelined CG methods need the vector entries generated by the current GPU and other GPUs for matrix-vector products. So the communication between GPUs becomes a major performance bottleneck on multi GPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using the pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP, and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient" title="conjugate gradient">conjugate gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=GPU" title=" GPU"> GPU</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20programming" title=" parallel programming"> parallel programming</a>, <a href="https://publications.waset.org/abstracts/search?q=pipelined%20algorithm" title=" pipelined algorithm"> pipelined algorithm</a> </p> <a href="https://publications.waset.org/abstracts/141808/parallel-pipelined-conjugate-gradient-algorithm-on-heterogeneous-platforms" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/141808.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">165</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3024</span> Numerical Studies for Standard Bi-Conjugate Gradient Stabilized Method and the Parallel Variants for Solving Linear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kuniyoshi%20Abe">Kuniyoshi Abe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bi-conjugate%20gradient%20stabilized%20method" title="bi-conjugate gradient stabilized method">bi-conjugate gradient stabilized method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20speed" title=" convergence speed"> convergence speed</a>, <a href="https://publications.waset.org/abstracts/search?q=Krylov%20subspace%20methods" title=" Krylov subspace methods"> Krylov subspace methods</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20equations" title=" linear equations"> linear equations</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20variant" title=" parallel variant"> parallel variant</a> </p> <a href="https://publications.waset.org/abstracts/96373/numerical-studies-for-standard-bi-conjugate-gradient-stabilized-method-and-the-parallel-variants-for-solving-linear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96373.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">164</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3023</span> Parameter Estimation for the Mixture of Generalized Gamma Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wikanda%20Phaphan">Wikanda Phaphan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title="conjugate gradient method">conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-Newton%20method" title=" quasi-Newton method"> quasi-Newton method</a>, <a href="https://publications.waset.org/abstracts/search?q=EM-algorithm" title=" EM-algorithm"> EM-algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20gamma%20distribution" title=" generalized gamma distribution"> generalized gamma distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=length%20biased%20generalized%20gamma%20distribution" title=" length biased generalized gamma distribution"> length biased generalized gamma distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20method" title=" maximum likelihood method"> maximum likelihood method</a> </p> <a href="https://publications.waset.org/abstracts/81404/parameter-estimation-for-the-mixture-of-generalized-gamma-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81404.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">219</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3022</span> Degree of Approximation of Functions Conjugate to Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=signals" title="signals">signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20fourier%20approximation" title=" trigonometric fourier approximation"> trigonometric fourier approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=class%20W%28L%5Er" title=" class W(L^r"> class W(L^r</a>, <a href="https://publications.waset.org/abstracts/search?q=%5Cxi%28t%29" title="\xi(t)">\xi(t)</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fourier%20series" title=" conjugate fourier series"> conjugate fourier series</a> </p> <a href="https://publications.waset.org/abstracts/20996/degree-of-approximation-of-functions-conjugate-to-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20996.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3021</span> Loudspeaker Parameters Inverse Problem for Improving Sound Frequency Response Simulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20T.%20Tsai">Y. T. Tsai</a>, <a href="https://publications.waset.org/abstracts/search?q=Jin%20H.%20Huang"> Jin H. Huang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20problem" title="inverse problem">inverse problem</a>, <a href="https://publications.waset.org/abstracts/search?q=cone%20effective%20area" title=" cone effective area"> cone effective area</a>, <a href="https://publications.waset.org/abstracts/search?q=loudspeaker" title=" loudspeaker"> loudspeaker</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20conjugate%20gradient%20method" title=" nonlinear conjugate gradient method"> nonlinear conjugate gradient method</a> </p> <a href="https://publications.waset.org/abstracts/7816/loudspeaker-parameters-inverse-problem-for-improving-sound-frequency-response-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7816.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">303</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3020</span> A Stokes Optimal Control Model of Determining Cellular Interaction Forces during Gastrulation </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuanhao%20Gao">Yuanhao Gao</a>, <a href="https://publications.waset.org/abstracts/search?q=Ping%20%20Lin"> Ping Lin</a>, <a href="https://publications.waset.org/abstracts/search?q=Kees%20Weijer"> Kees Weijer</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An optimal control system model is proposed for the cell flow in the process of chick embryo gastrulation in this paper. The target is to determine the cellular interaction forces which are hard to measure. This paper will take an approach to investigate the forces with the idea of the inverse problem. By choosing the forces as the control variable and regarding the cell flow as Stokes fluid, an objective functional will be established to match the numerical result of cell velocity with the experimental data. So that the forces could be determined by minimizing the objective functional. The Lagrange multiplier method is utilized to derive the state and adjoint equations consisting the optimal control system, which specifies the first-order necessary conditions. Finite element method is used to discretize and approximate equations. A conjugate gradient algorithm is given for solving the minimum solution of the system and determine the forces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal%20control%20model" title="optimal control model">optimal control model</a>, <a href="https://publications.waset.org/abstracts/search?q=Stokes%20equation" title=" Stokes equation"> Stokes equation</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=chick%20embryo%20gastrulation" title=" chick embryo gastrulation"> chick embryo gastrulation</a> </p> <a href="https://publications.waset.org/abstracts/52434/a-stokes-optimal-control-model-of-determining-cellular-interaction-forces-during-gastrulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52434.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">259</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3019</span> An Optimal Control Model to Determine Body Forces of Stokes Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuanhao%20Gao">Yuanhao Gao</a>, <a href="https://publications.waset.org/abstracts/search?q=Pin%20Lin"> Pin Lin</a>, <a href="https://publications.waset.org/abstracts/search?q=Kees%20Weijer"> Kees Weijer</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal%20control%20model" title="optimal control model">optimal control model</a>, <a href="https://publications.waset.org/abstracts/search?q=Stokes%20equation" title=" Stokes equation"> Stokes equation</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a> </p> <a href="https://publications.waset.org/abstracts/54716/an-optimal-control-model-to-determine-body-forces-of-stokes-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54716.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3018</span> Degree of Approximation by the (T.E^1) Means of Conjugate Fourier Series in the Hölder Metric</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kejal%20Khatri">Kejal Khatri</a>, <a href="https://publications.waset.org/abstracts/search?q=Vishnu%20Narayan%20Mishra"> Vishnu Narayan Mishra</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20Fourier%20series" title="conjugate Fourier series">conjugate Fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20of%20approximation" title=" degree of approximation"> degree of approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%B6lder%20metric" title=" Hölder metric"> Hölder metric</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20summability" title=" matrix summability"> matrix summability</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20summability" title=" product summability"> product summability</a> </p> <a href="https://publications.waset.org/abstracts/2123/degree-of-approximation-by-the-te1-means-of-conjugate-fourier-series-in-the-holder-metric" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2123.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">419</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3017</span> Optimization of Double-Layered Microchannel Heat Sinks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tu-Chieh%20Hung">Tu-Chieh Hung</a>, <a href="https://publications.waset.org/abstracts/search?q=Wei-Mon%20Yan"> Wei-Mon Yan</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiao-Dong%20Wang"> Xiao-Dong Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yu-Xian%20Huang"> Yu-Xian Huang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work employs a combined optimization procedure including a simplified conjugate-gradient method and a three-dimensional fluid flow and heat transfer model to study the optimal geometric parameter design of double-layered microchannel heat sinks. The overall thermal resistance RT is the objective function to be minimized with number of channels, N, the channel width ratio, β, the bottom channel aspect ratio, αb, and upper channel aspect ratio, αu, as the search variables. It is shown that, for the given bottom area (10 mm×10 mm) and heat flux (100 W cm-2), the optimal (minimum) thermal resistance of double-layered microchannel heat sinks is about RT=0.12 ℃/m2W with the corresponding optimal geometric parameters N=73, β=0.50, αb=3.52, and, αu= 7.21 under a constant pumping power of 0.05 W. The optimization process produces a maximum reduction by 52.8% in the overall thermal resistance compared with an initial guess (N=112, β=0.37, αb=10.32 and, αu=10.93). The results also show that the optimal thermal resistance decreases rapidly with the pumping power and tends to be a saturated value afterward. The corresponding optimal values of parameters N, αb, and αu increase while that of β decrease as the pumping power increases. However, further increasing pumping power is not always cost-effective for the application of heat sink designs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimization" title="optimization">optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=double-layered%20microchannel%20heat%20sink" title=" double-layered microchannel heat sink"> double-layered microchannel heat sink</a>, <a href="https://publications.waset.org/abstracts/search?q=simplified%20conjugate-gradient%20method" title=" simplified conjugate-gradient method"> simplified conjugate-gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20resistance" title=" thermal resistance"> thermal resistance</a> </p> <a href="https://publications.waset.org/abstracts/15975/optimization-of-double-layered-microchannel-heat-sinks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15975.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">490</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3016</span> Coefficients of Some Double Trigonometric Cosine and Sine Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jatinderdeep%20Kaur">Jatinderdeep Kaur</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20dirichlet%20kernel" title="conjugate dirichlet kernel">conjugate dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fejer%20kernel" title=" conjugate fejer kernel"> conjugate fejer kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20series" title=" fourier series"> fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=semi-convexity" title=" semi-convexity"> semi-convexity</a> </p> <a href="https://publications.waset.org/abstracts/32156/coefficients-of-some-double-trigonometric-cosine-and-sine-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32156.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3015</span> Numerical Investigation of Al2O3/Water Nanofluid Heat Transfer in a Microtube with Viscous Dissipation Effect</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Misagh%20Irandoost%20Shahrestani">Misagh Irandoost Shahrestani</a>, <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Shokouhmand"> Hossein Shokouhmand</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Kalteh"> Mohammad Kalteh</a>, <a href="https://publications.waset.org/abstracts/search?q=Behrang%20Hasanpour"> Behrang Hasanpour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, nanofluid conjugate heat transfer through a microtube with viscous dissipation effect is investigated numerically. The fluid flow is considered as a laminar regime. A constant heat flux is applied on the microtube outer wall and the two ends of its wall are considered adiabatic. Conjugate heat transfer problem is solved and investigated for this geometry. It is shown that viscous dissipation effect which is induced by shear stresses can not be neglected in microtubes. Viscous heating behaves as an energy source in the fluid and affects the temperature distribution. The effect of Reynolds number, particle volume fraction and the nanoparticles diameter on the energy source are investigated and an attempt on establishing suitable equations for assessing the value of the energy source based on Re, Dp and Φ is performed and they are depicted as 3D diagrams. Finally, the significance of viscous dissipation and the influence of these parameters on convective heat transfer coefficient are studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convective%20heat%20transfer%20coefficient" title="convective heat transfer coefficient">convective heat transfer coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=microtube" title=" microtube"> microtube</a>, <a href="https://publications.waset.org/abstracts/search?q=nanofluid" title=" nanofluid"> nanofluid</a>, <a href="https://publications.waset.org/abstracts/search?q=viscous%20dissipation" title=" viscous dissipation"> viscous dissipation</a> </p> <a href="https://publications.waset.org/abstracts/15475/numerical-investigation-of-al2o3water-nanofluid-heat-transfer-in-a-microtube-with-viscous-dissipation-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15475.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">512</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3014</span> Novel Technique for calculating Surface Potential Gradient of Overhead Line Conductors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sudip%20Sudhir%20Godbole">Sudip Sudhir Godbole</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In transmission line surface potential gradient is a critical design parameter for planning overhead line, as it determines the level of corona loss (CL), radio interference (RI) and audible noise (AN).With increase of transmission line voltage level bulk power transfer is possible, using bundle conductor configuration used, it is more complex to find accurate surface stress in bundle configuration. The majority of existing models for surface gradient calculations are based on analytical methods which restrict their application in simulating complex surface geometry. This paper proposes a novel technique which utilizes both analytical and numerical procedure to predict the surface gradient. One of 400 kV transmission line configurations has been selected as an example to compare the results for different methods. The different strand shapes are a key variable in determining. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=surface%20gradient" title="surface gradient">surface gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20potential%20coefficient%20method" title=" Maxwell potential coefficient method"> Maxwell potential coefficient method</a>, <a href="https://publications.waset.org/abstracts/search?q=market%20and%20Mengele%E2%80%99s%20method" title=" market and Mengele’s method"> market and Mengele’s method</a>, <a href="https://publications.waset.org/abstracts/search?q=successive%20images%20method" title=" successive images method"> successive images method</a>, <a href="https://publications.waset.org/abstracts/search?q=charge%20simulation%20method" title=" charge simulation method"> charge simulation method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method "> finite element method </a> </p> <a href="https://publications.waset.org/abstracts/15407/novel-technique-for-calculating-surface-potential-gradient-of-overhead-line-conductors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15407.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">538</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3013</span> Review on Quaternion Gradient Operator with Marginal and Vector Approaches for Colour Edge Detection</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nadia%20Ben%20Youssef">Nadia Ben Youssef</a>, <a href="https://publications.waset.org/abstracts/search?q=Aicha%20Bouzid"> Aicha Bouzid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Gradient estimation is one of the most fundamental tasks in the field of image processing in general, and more particularly for color images since that the research in color image gradient remains limited. The widely used gradient method is Di Zenzo’s gradient operator, which is based on the measure of squared local contrast of color images. The proposed gradient mechanism, presented in this paper, is based on the principle of the Di Zenzo’s approach using quaternion representation. This edge detector is compared to a marginal approach based on multiscale product of wavelet transform and another vector approach based on quaternion convolution and vector gradient approach. The experimental results indicate that the proposed color gradient operator outperforms marginal approach, however, it is less efficient then the second vector approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=gradient" title="gradient">gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=edge%20detection" title=" edge detection"> edge detection</a>, <a href="https://publications.waset.org/abstracts/search?q=color%20image" title=" color image"> color image</a>, <a href="https://publications.waset.org/abstracts/search?q=quaternion" title=" quaternion"> quaternion</a> </p> <a href="https://publications.waset.org/abstracts/141138/review-on-quaternion-gradient-operator-with-marginal-and-vector-approaches-for-colour-edge-detection" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/141138.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">234</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3012</span> Mathematical Modeling of the Working Principle of Gravity Gradient Instrument</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Danni%20Cong">Danni Cong</a>, <a href="https://publications.waset.org/abstracts/search?q=Meiping%20Wu"> Meiping Wu</a>, <a href="https://publications.waset.org/abstracts/search?q=Hua%20Mu"> Hua Mu</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaofeng%20He"> Xiaofeng He</a>, <a href="https://publications.waset.org/abstracts/search?q=Junxiang%20Lian"> Junxiang Lian</a>, <a href="https://publications.waset.org/abstracts/search?q=Juliang%20Cao"> Juliang Cao</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaokun%20Cai"> Shaokun Cai</a>, <a href="https://publications.waset.org/abstracts/search?q=Hao%20Qin"> Hao Qin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=gravity%20gradient" title="gravity gradient">gravity gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=gravity%20gradient%20sensor" title=" gravity gradient sensor"> gravity gradient sensor</a>, <a href="https://publications.waset.org/abstracts/search?q=accelerometer" title=" accelerometer"> accelerometer</a>, <a href="https://publications.waset.org/abstracts/search?q=single-axis%20rotation%20modulation" title=" single-axis rotation modulation"> single-axis rotation modulation</a> </p> <a href="https://publications.waset.org/abstracts/74776/mathematical-modeling-of-the-working-principle-of-gravity-gradient-instrument" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74776.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">326</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3011</span> An Analytical Approach of Computational Complexity for the Method of Multifluid Modelling </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20K.%20Borah">A. K. Borah</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20K.%20Singh"> A. K. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we deal building blocks of the computer simulation of the multiphase flows. Whole simulation procedure can be viewed as two super procedures; The implementation of VOF method and the solution of Navier Stoke’s Equation. Moreover, a sequential code for a Navier Stoke’s solver has been studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bi-conjugate%20gradient%20stabilized%20%28Bi-CGSTAB%29" title="Bi-conjugate gradient stabilized (Bi-CGSTAB)">Bi-conjugate gradient stabilized (Bi-CGSTAB)</a>, <a href="https://publications.waset.org/abstracts/search?q=ILUT%20function" title=" ILUT function"> ILUT function</a>, <a href="https://publications.waset.org/abstracts/search?q=krylov%20subspace" title=" krylov subspace"> krylov subspace</a>, <a href="https://publications.waset.org/abstracts/search?q=multifluid%20flows%20preconditioner" title=" multifluid flows preconditioner"> multifluid flows preconditioner</a>, <a href="https://publications.waset.org/abstracts/search?q=simple%20algorithm" title=" simple algorithm "> simple algorithm </a> </p> <a href="https://publications.waset.org/abstracts/23043/an-analytical-approach-of-computational-complexity-for-the-method-of-multifluid-modelling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23043.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">528</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3010</span> Improving the Efficiency of a High Pressure Turbine by Using Non-Axisymmetric Endwall: A Comparison of Two Optimization Algorithms</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Rehman">Abdul Rehman</a>, <a href="https://publications.waset.org/abstracts/search?q=Bo%20Liu"> Bo Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Axial flow turbines are commonly designed with high loads that generate strong secondary flows and result in high secondary losses. These losses contribute to almost 30% to 50% of the total losses. Non-axisymmetric endwall profiling is one of the passive control technique to reduce the secondary flow loss. In this paper, the non-axisymmetric endwall profile construction and optimization for the stator endwalls are presented to improve the efficiency of a high pressure turbine. The commercial code NUMECA Fine/ Design3D coupled with Fine/Turbo was used for the numerical investigation, design of experiments and the optimization. All the flow simulations were conducted by using steady RANS and Spalart-Allmaras as a turbulence model. The non-axisymmetric endwalls of stator hub and shroud were created by using the perturbation law based on Bezier Curves. Each cut having multiple control points was supposed to be created along the virtual streamlines in the blade channel. For the design of experiments, each sample was arbitrarily generated based on values automatically chosen for the control points defined during parameterization. The Optimization was achieved by using two algorithms i.e. the stochastic algorithm and gradient-based algorithm. For the stochastic algorithm, a genetic algorithm based on the artificial neural network was used as an optimization method in order to achieve the global optimum. The evaluation of the successive design iterations was performed using artificial neural network prior to the flow solver. For the second case, the conjugate gradient algorithm with a three dimensional CFD flow solver was used to systematically vary a free-form parameterization of the endwall. This method is efficient and less time to consume as it requires derivative information of the objective function. The objective function was to maximize the isentropic efficiency of the turbine by keeping the mass flow rate as constant. The performance was quantified by using a multi-objective function. Other than these two classifications of the optimization methods, there were four optimizations cases i.e. the hub only, the shroud only, and the combination of hub and shroud. For the fourth case, the shroud endwall was optimized by using the optimized hub endwall geometry. The hub optimization resulted in an increase in the efficiency due to more homogenous inlet conditions for the rotor. The adverse pressure gradient was reduced but the total pressure loss in the vicinity of the hub was increased. The shroud optimization resulted in an increase in efficiency, total pressure loss and entropy were reduced. The combination of hub and shroud did not show overwhelming results which were achieved for the individual cases of the hub and the shroud. This may be caused by fact that there were too many control variables. The fourth case of optimization showed the best result because optimized hub was used as an initial geometry to optimize the shroud. The efficiency was increased more than the individual cases of optimization with a mass flow rate equal to the baseline design of the turbine. The results of artificial neural network and conjugate gradient method were compared. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=artificial%20neural%20network" title="artificial neural network">artificial neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=axial%20turbine" title=" axial turbine"> axial turbine</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title=" conjugate gradient method"> conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=non-axisymmetric%20endwall" title=" non-axisymmetric endwall"> non-axisymmetric endwall</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a> </p> <a href="https://publications.waset.org/abstracts/91090/improving-the-efficiency-of-a-high-pressure-turbine-by-using-non-axisymmetric-endwall-a-comparison-of-two-optimization-algorithms" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91090.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">225</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3009</span> Numerical Investigation of Aerodynamic Analysis on Passenger Vehicle</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cafer%20G%C3%B6rkem%20P%C4%B1nar">Cafer Görkem Pınar</a>, <a href="https://publications.waset.org/abstracts/search?q=I%CC%87lker%20Co%C5%9Far"> İlker Coşar</a>, <a href="https://publications.waset.org/abstracts/search?q=Serkan%20Uzun"> Serkan Uzun</a>, <a href="https://publications.waset.org/abstracts/search?q=Atahan%20%C3%87elebi"> Atahan Çelebi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20Ali%20Ersoy"> Mehmet Ali Ersoy</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20P%C4%B1narba%C5%9F%C4%B1"> Ali Pınarbaşı</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, it was numerically investigated that a 1:1 scale model of the Renault Clio MK4 SW brand vehicle aerodynamic analysis was performed in the commercial computational fluid dynamics (CFD) package program of ANSYS CFX 2021 R1 under steady, subsonic, and 3-D conditions. The model of vehicle used for the analysis was made independent of the number of mesh elements, and the k-epsilon turbulence model was applied during the analysis. Results were interpreted as streamlines, pressure gradient, and turbulent kinetic energy contours around the vehicle at 50 km/h and 100 km/h speeds. In addition, the validity of the analysis was decided by comparing the drag coefficient of the vehicle with the values in the literature. As a result, the pressure gradient contours of the taillight of the Renault Clio MK4 SW vehicle were examined, and the behavior of the total force at speeds of 50 km/h and 100 km/h was interpreted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CFD" title="CFD">CFD</a>, <a href="https://publications.waset.org/abstracts/search?q=k-epsilon" title=" k-epsilon"> k-epsilon</a>, <a href="https://publications.waset.org/abstracts/search?q=aerodynamics" title=" aerodynamics"> aerodynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=drag%20coefficient" title=" drag coefficient"> drag coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=taillight" title=" taillight"> taillight</a> </p> <a href="https://publications.waset.org/abstracts/150772/numerical-investigation-of-aerodynamic-analysis-on-passenger-vehicle" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150772.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">143</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3008</span> Steady Conjugate Heat Transfer of Two Connected Thermal Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20El-Sayed%20Mosaad">Mohamed El-Sayed Mosaad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An analytic approach is obtained for the steady heat transfer problem of two fluid systems, in thermal communication via heat conduction across a solid wall separating them. The two free convection layers created on wall sides are assumed to be in parallel flow. Fluid-solid interface temperature on wall sides is not prescribed in analysis in advance; rather, determined from conjugate solution among other unknown parameters. The analysis highlights the main conjugation parameters controlling thermal interaction process of involved heat transfer modes. Heat transfer results of engineering importance are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20heat%20transfer" title="conjugate heat transfer">conjugate heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20layer" title=" boundary layer"> boundary layer</a>, <a href="https://publications.waset.org/abstracts/search?q=convection" title=" convection"> convection</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20systems" title=" thermal systems"> thermal systems</a> </p> <a href="https://publications.waset.org/abstracts/23261/steady-conjugate-heat-transfer-of-two-connected-thermal-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23261.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">379</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3007</span> Conjugate Free Convection in a Square Cavity Filled with Nanofluid and Heated from Below by Spatial Wall Temperature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ishak%20Hashim">Ishak Hashim</a>, <a href="https://publications.waset.org/abstracts/search?q=Ammar%20Alsabery"> Ammar Alsabery</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20free%20convection" title="conjugate free convection">conjugate free convection</a>, <a href="https://publications.waset.org/abstracts/search?q=square%20cavity" title=" square cavity"> square cavity</a>, <a href="https://publications.waset.org/abstracts/search?q=nanofluid" title=" nanofluid"> nanofluid</a>, <a href="https://publications.waset.org/abstracts/search?q=spatial%20temperature" title=" spatial temperature"> spatial temperature</a> </p> <a href="https://publications.waset.org/abstracts/46696/conjugate-free-convection-in-a-square-cavity-filled-with-nanofluid-and-heated-from-below-by-spatial-wall-temperature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46696.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">359</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3006</span> Linear Study of Electrostatic Ion Temperature Gradient Mode with Entropy Gradient Drift and Sheared Ion Flows</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Yaqub%20Khan">M. Yaqub Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Usman%20Shabbir"> Usman Shabbir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> History of plasma reveals that continuous struggle of experimentalists and theorists are not fruitful for confinement up to now. It needs a change to bring the research through entropy. Approximately, all the quantities like number density, temperature, electrostatic potential, etc. are connected to entropy. Therefore, it is better to change the way of research. In ion temperature gradient mode with the help of Braginskii model, Boltzmannian electrons, effect of velocity shear is studied inculcating entropy in the magnetoplasma. New dispersion relation is derived for ion temperature gradient mode, and dependence on entropy gradient drift is seen. It is also seen velocity shear enhances the instability but in anomalous transport, its role is not seen significantly but entropy. This work will be helpful to the next step of tokamak and space plasmas. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=entropy" title="entropy">entropy</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity%20shear" title=" velocity shear"> velocity shear</a>, <a href="https://publications.waset.org/abstracts/search?q=ion%20temperature%20gradient%20mode" title=" ion temperature gradient mode"> ion temperature gradient mode</a>, <a href="https://publications.waset.org/abstracts/search?q=drift" title=" drift"> drift</a> </p> <a href="https://publications.waset.org/abstracts/70221/linear-study-of-electrostatic-ion-temperature-gradient-mode-with-entropy-gradient-drift-and-sheared-ion-flows" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70221.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">386</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3005</span> Torsional Vibration of Carbon Nanotubes via Nonlocal Gradient Theories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20Arda">Mustafa Arda</a>, <a href="https://publications.waset.org/abstracts/search?q=Metin%20Aydogdu"> Metin Aydogdu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Carbon nanotubes (CNTs) have many possible application areas because of their superior physical properties. Nonlocal Theory, which unlike the classical theories, includes the size dependency. Nonlocal Stress and Strain Gradient approaches can be used in nanoscale static and dynamic analysis. In the present study, torsional vibration of CNTs was investigated according to nonlocal stress and strain gradient theories. Effects of the small scale parameters to the non-dimensional frequency were obtained. Results were compared with the Molecular Dynamics Simulation and Lattice Dynamics. Strain Gradient Theory has shown more weakening effect on CNT according to the Stress Gradient Theory. Combination of both theories gives more acceptable results rather than the classical and stress or strain gradient theory according to Lattice Dynamics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=torsional%20vibration" title="torsional vibration">torsional vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=carbon%20nanotubes" title=" carbon nanotubes"> carbon nanotubes</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20gradient%20theory" title=" nonlocal gradient theory"> nonlocal gradient theory</a>, <a href="https://publications.waset.org/abstracts/search?q=stress" title=" stress"> stress</a>, <a href="https://publications.waset.org/abstracts/search?q=strain" title=" strain"> strain</a> </p> <a href="https://publications.waset.org/abstracts/48828/torsional-vibration-of-carbon-nanotubes-via-nonlocal-gradient-theories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48828.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">389</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3004</span> Methodology of Geometry Simplification for Conjugate Heat Transfer of Electrical Rotating Machines Using Computational Fluid Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Aggarwal">Sachin Aggarwal</a>, <a href="https://publications.waset.org/abstracts/search?q=Sarah%20Kassinger"> Sarah Kassinger</a>, <a href="https://publications.waset.org/abstracts/search?q=Nicholas%20Hoffman"> Nicholas Hoffman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Geometry simplification is a key step in performing conjugate heat transfer analysis using CFD. This paper proposes a standard methodology for the geometry simplification of rotating machines, such as electrical generators and electrical motors (both air and liquid-cooled). These machines are extensively deployed throughout the aerospace and automotive industries, where optimization of weight, volume, and performance is paramount -especially given the current global transition to renewable energy sources and vehicle hybridization and electrification. Conjugate heat transfer analysis is an essential step in optimizing their complex design. This methodology will help in reducing convergence issues due to poor mesh quality, thus decreasing computational cost and overall analysis time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CFD" title="CFD">CFD</a>, <a href="https://publications.waset.org/abstracts/search?q=electrical%20machines" title=" electrical machines"> electrical machines</a>, <a href="https://publications.waset.org/abstracts/search?q=Geometry%20simplification" title=" Geometry simplification"> Geometry simplification</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a> </p> <a href="https://publications.waset.org/abstracts/150058/methodology-of-geometry-simplification-for-conjugate-heat-transfer-of-electrical-rotating-machines-using-computational-fluid-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150058.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">132</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20coefficient&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20coefficient&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20coefficient&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20coefficient&page=5">5</a></li> <li class="page-item"><a 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