The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Tetsuya Sakurai - One of the best experts on this subject based on the ideXlab platform.
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efficient Contour Integral based eigenvalue computation using an iterative linear solver with shift invert preconditioning
IEEE International Conference on High Performance Computing Data and Analytics, 2021Co-Authors: Yasunori Futamura, Tetsuya SakuraiAbstract:Contour Integral-based (CI) eigenvalue solvers are one of the efficient and robust approaches for sparse eigenvalue problems. They have attracted attention owing to their inherent parallelism. For implementing a CI eigensolver, the inner linear systems arising in the algorithm need to be solved using an efficient method. One widely-used method is to use a sparse direct linear solver provided by a well-established numerical library; it is numerically robust and presents good load balancing of parallel execution of the CI eigensolver. However, owing to high total computational and memory cost, the performance of the direct solver approach is suboptimal. In this study, we propose an alternative method that utilizes a block Krylov iterative linear solver and shift-invert preconditioning that can take advantage of the shift-invariance of the block Krylov subspace. Our approach adaptively sets a preconditioning parameter according to the number of parallel processes to reduce the iteration counts. Several numerical examples confirm that our method outperforms the direct solver approach.
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Contour Integral method for obtaining the self energy matrices of electrodes in electron transport calculations
Physical Review B, 2018Co-Authors: Shigeru Iwase, Akira Imakura, Tetsuya Sakurai, Yasunori Futamura, Shigeru Tsukamoto, Tomoya OnoAbstract:We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a Contour Integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the free-standing silicene with the line defect originating from the reversed buckled phases.
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Relationships among Contour Integral-based methods for solving generalized eigenvalue problems
Japan Journal of Industrial and Applied Mathematics, 2016Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:Recently, Contour Integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical Contour Integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all Contour Integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.
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error bounds of rayleigh ritz type Contour Integral based eigensolver for solving generalized eigenvalue problems
Numerical Algorithms, 2016Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:We investigate Contour Integral-based eigensolvers for computing all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we focus on a Rayleigh---Ritz type method and analyze its error bounds. From the results of our analysis, we conclude that the Rayleigh---Ritz type Contour Integral-based eigensolver with sufficient subspace size can achieve high accuracy for target eigenpairs even if some eigenvalues exist outside but near the region.
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a map of Contour Integral based eigensolvers for solving generalized eigenvalue problems
arXiv: Numerical Analysis, 2015Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:Recently, Contour Integral-based eigensolvers have been actively studied for solving interior eigenvalue problems that find all eigenvalues loca ted in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical Contour Integral-based eigensolvers from the view point of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all Contour Integral-based eigensolvers can be regarded as projection methods and can be categorized on their subspace, an orthogonal condition and a problem to be applied implicitly.
Quanyuan Jiang - One of the best experts on this subject based on the ideXlab platform.
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a parallelized Contour Integral rayleigh ritz method for computing critical eigenvalues of large scale power systems
IEEE Transactions on Smart Grid, 2018Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A Contour Integral based spectrum transform (CIST) is first introduced for computing critical eigenvalues of power systems. Different from commonly-used shift-invert and Cayley transforms, CIST is able to give equal dominance to the eigenvalue set in a customizable complex plane area, which is defined by a given Integral curve. The spectral property of CIST brings high distinctiveness of eigenvalues enclosed by the Integral curve in transformed spectrum, along with well convergence of these eigenvalues in subspace methods. With CIST, Rayleigh–Ritz process is used to build subspace and extract eigenvalues. An iterative scheme is proposed for subspace refinement. The iterative Contour Integral Rayleigh–Ritz method is implemented with full utilization of parallel potentiality in Contour Integral numerical evaluation. Experiments on three test systems of different scales are performed to validate the reliability, computational efficiency, and parallel scalability of the proposed method.
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A Parallelized Contour Integral Rayleigh–Ritz Method for Computing Critical Eigenvalues of Large-Scale Power Systems
IEEE Transactions on Smart Grid, 2018Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A Contour Integral based spectrum transform (CIST) is first introduced for computing critical eigenvalues of power systems. Different from commonly-used shift-invert and Cayley transforms, CIST is able to give equal dominance to the eigenvalue set in a customizable complex plane area, which is defined by a given Integral curve. The spectral property of CIST brings high distinctiveness of eigenvalues enclosed by the Integral curve in transformed spectrum, along with well convergence of these eigenvalues in subspace methods. With CIST, Rayleigh–Ritz process is used to build subspace and extract eigenvalues. An iterative scheme is proposed for subspace refinement. The iterative Contour Integral Rayleigh–Ritz method is implemented with full utilization of parallel potentiality in Contour Integral numerical evaluation. Experiments on three test systems of different scales are performed to validate the reliability, computational efficiency, and parallel scalability of the proposed method.
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A Parallel Contour Integral Method for Eigenvalue Analysis of Power Systems
IEEE Transactions on Power Systems, 2017Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A parallelized numerical Contour Integral based method is proposed for counting interior eigenvalues in a given region on the complex plane. The proposed method is derived from descriptor system of power system linearized model and complex analysis theory, based on which the computation of eigenvalue number is converted to a set of matrix trace problems. The Contour Integral results are able to be utilized to detect missing target eigenvalues in partial eigenvalue methods and provide an approximate eigenvalue distribution along the Integral curve. Efficient evaluation of Integral function is implemented by exploiting the sparsity of descriptor systems. An adaptive Integral point collocation strategy is proposed for numerically evaluating Contour Integral with moderate number of discretized points. As the computation of Integral function is decoupled at each Integral point, the proposed method features well parallel computing capability.
Akira Imakura - One of the best experts on this subject based on the ideXlab platform.
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Contour Integral method for obtaining the self energy matrices of electrodes in electron transport calculations
Physical Review B, 2018Co-Authors: Shigeru Iwase, Akira Imakura, Tetsuya Sakurai, Yasunori Futamura, Shigeru Tsukamoto, Tomoya OnoAbstract:We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a Contour Integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the free-standing silicene with the line defect originating from the reversed buckled phases.
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Relationships among Contour Integral-based methods for solving generalized eigenvalue problems
Japan Journal of Industrial and Applied Mathematics, 2016Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:Recently, Contour Integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical Contour Integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all Contour Integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.
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error bounds of rayleigh ritz type Contour Integral based eigensolver for solving generalized eigenvalue problems
Numerical Algorithms, 2016Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:We investigate Contour Integral-based eigensolvers for computing all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we focus on a Rayleigh---Ritz type method and analyze its error bounds. From the results of our analysis, we conclude that the Rayleigh---Ritz type Contour Integral-based eigensolver with sufficient subspace size can achieve high accuracy for target eigenpairs even if some eigenvalues exist outside but near the region.
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a map of Contour Integral based eigensolvers for solving generalized eigenvalue problems
arXiv: Numerical Analysis, 2015Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:Recently, Contour Integral-based eigensolvers have been actively studied for solving interior eigenvalue problems that find all eigenvalues loca ted in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical Contour Integral-based eigensolvers from the view point of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all Contour Integral-based eigensolvers can be regarded as projection methods and can be categorized on their subspace, an orthogonal condition and a problem to be applied implicitly.
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a block arnoldi type Contour Integral spectral projection method for solving generalized eigenvalue problems
Applied Mathematics Letters, 2014Co-Authors: Akira Imakura, Tetsuya SakuraiAbstract:Abstract For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, Contour Integral spectral projection methods have been proposed for solving such problems. In this study, from the analysis of the relationship between the Contour Integral spectral projection and the Krylov subspace, we conclude that the Rayleigh–Ritz-type of the Contour Integral spectral projection method is mathematically equivalent to the Arnoldi method with the projected vectors obtained from the Contour integration. By this Arnoldi-based interpretation, we then propose a block Arnoldi-type Contour Integral spectral projection method for solving the eigenvalue problem.
Guangchao Geng - One of the best experts on this subject based on the ideXlab platform.
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a parallelized Contour Integral rayleigh ritz method for computing critical eigenvalues of large scale power systems
IEEE Transactions on Smart Grid, 2018Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A Contour Integral based spectrum transform (CIST) is first introduced for computing critical eigenvalues of power systems. Different from commonly-used shift-invert and Cayley transforms, CIST is able to give equal dominance to the eigenvalue set in a customizable complex plane area, which is defined by a given Integral curve. The spectral property of CIST brings high distinctiveness of eigenvalues enclosed by the Integral curve in transformed spectrum, along with well convergence of these eigenvalues in subspace methods. With CIST, Rayleigh–Ritz process is used to build subspace and extract eigenvalues. An iterative scheme is proposed for subspace refinement. The iterative Contour Integral Rayleigh–Ritz method is implemented with full utilization of parallel potentiality in Contour Integral numerical evaluation. Experiments on three test systems of different scales are performed to validate the reliability, computational efficiency, and parallel scalability of the proposed method.
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A Parallelized Contour Integral Rayleigh–Ritz Method for Computing Critical Eigenvalues of Large-Scale Power Systems
IEEE Transactions on Smart Grid, 2018Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A Contour Integral based spectrum transform (CIST) is first introduced for computing critical eigenvalues of power systems. Different from commonly-used shift-invert and Cayley transforms, CIST is able to give equal dominance to the eigenvalue set in a customizable complex plane area, which is defined by a given Integral curve. The spectral property of CIST brings high distinctiveness of eigenvalues enclosed by the Integral curve in transformed spectrum, along with well convergence of these eigenvalues in subspace methods. With CIST, Rayleigh–Ritz process is used to build subspace and extract eigenvalues. An iterative scheme is proposed for subspace refinement. The iterative Contour Integral Rayleigh–Ritz method is implemented with full utilization of parallel potentiality in Contour Integral numerical evaluation. Experiments on three test systems of different scales are performed to validate the reliability, computational efficiency, and parallel scalability of the proposed method.
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A Parallel Contour Integral Method for Eigenvalue Analysis of Power Systems
IEEE Transactions on Power Systems, 2017Co-Authors: Guangchao Geng, Quanyuan JiangAbstract:A parallelized numerical Contour Integral based method is proposed for counting interior eigenvalues in a given region on the complex plane. The proposed method is derived from descriptor system of power system linearized model and complex analysis theory, based on which the computation of eigenvalue number is converted to a set of matrix trace problems. The Contour Integral results are able to be utilized to detect missing target eigenvalues in partial eigenvalue methods and provide an approximate eigenvalue distribution along the Integral curve. Efficient evaluation of Integral function is implemented by exploiting the sparsity of descriptor systems. An adaptive Integral point collocation strategy is proposed for numerically evaluating Contour Integral with moderate number of discretized points. As the computation of Integral function is decoupled at each Integral point, the proposed method features well parallel computing capability.
D P Rooke - One of the best experts on this subject based on the ideXlab platform.
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A Contour Integral for three-dimensional crack elastostatic analysis☆
Engineering Analysis with Boundary Elements, 1997Co-Authors: Pihua Wen, M.h. Aliabadi, D P RookeAbstract:A Contour Integral method for calculating stress intensity factors has been successfully applied to two-dimensional crack problems for both static and dynamic cases. In this paper the method is extended to three-dimensional static problems. By means of the displacement discontinuity method and the technique of variation of crack area, the required derivatives of traction and displacement for a reference problem are determined. The stress intensity factors are calculated by a Contour Integral with a non-singular integrand. The only absolute values of traction and displacement that are required for the real problem are on Contours away from the crack-tip; they are determined by the dual boundary element method. For mixed-mode problems, the ratios of stress intensity factors are determined by the ratios of the mixed-mode discontinuity displacements near the crack front, all stress intensity factors can be calculated from only one reference solution.
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A Contour Integral method for dynamic stress intensity factors
Theoretical and Applied Fracture Mechanics, 1997Co-Authors: P. H. Wen, M.h. Aliabadi, D P RookeAbstract:Abstract The Contour Integral method previously used to determine static stress intensity factors is applied to dynamic crack problems. The required derivatives of the traction in the reference problem are obtained numerically by the displacement discontinuity method. Stress intensity factors are determined by an Integral around a Contour which contains a crack tip. If the Contour is chosen as the outer boundary of the body, the stress intensity factor is obtained from the boundary values of traction and displacement. The advantage of this path-independent Integral is that it yields directly both the opening-mode and sliding-mode stress intensity factors for a straight crack. For dynamic problems, Laplace transforms are used and the dynamic stress intensity factors in the time domain are determined by Durbin's inversion method. An indirect boundary element method, incorporating both displacement discontinuity and fictitious load techniques, is used to determine the boundary or Contour values of traction and displacement numerically.
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A Contour Integral for the evaluation of stress intensity factors
Applied Mathematical Modelling, 1995Co-Authors: P. H. Wen, M.h. Aliabadi, D P RookeAbstract:A Contour Integral is proposed for the evaluation of stress intensity factors. The Integral utilizes the exact solution of a loaded crack in an infinite sheet as an auxiliary solution. The advantage of this new path-independent Integral is that it yields directly the opening mode and sliding mode stress intensity factors. This Integral in used together with an indirect boundary element method to calculate stress intensity factors for several cracked configurations.
