The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
R. S. Chen - One of the best experts on this subject based on the ideXlab platform.
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mixed inner Outer Iteration technique based surface integral equations for fast solving em scattering from penetrable objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
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Mixed Inner–Outer Iteration Technique-Based Surface Integral Equations for Fast Solving EM Scattering From Penetrable Objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
Lei Zhang - One of the best experts on this subject based on the ideXlab platform.
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mixed inner Outer Iteration technique based surface integral equations for fast solving em scattering from penetrable objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
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Mixed Inner–Outer Iteration Technique-Based Surface Integral Equations for Fast Solving EM Scattering From Penetrable Objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
Zhongxiao Jia - One of the best experts on this subject based on the ideXlab platform.
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on convergence of the inexact rayleigh quotient Iteration with the lanczos method used for solving linear systems
Science China-mathematics, 2013Co-Authors: Zhongxiao JiaAbstract:For the Hermitian inexact Rayleigh quotient Iteration (RQI), we consider the local convergence of the inexact RQI with the Lanczos method for the linear systems involved. Some attractive properties are derived for the residual, whose norm is ξ k , of the linear system obtained by the Lanczos method at Outer Iteration k+1. Based on them, we make a refined analysis and establish new local convergence results. It is proved that (i) the inexact RQI with Lanczos converges quadratically provided that ξ k ⩽ ξ with a constant ξ ⩾ 1 and (ii) the method converges linearly provided that ξ k is bounded by some multiple of \(\tfrac{1} {{\left\| {r_k } \right\|}} \) with ‖r k ‖ the residual norm of the approximate eigenpair at Outer Iteration k. The results are fundamentally different from the existing ones that always require ξ k < 1, and they have implications on effective implementations of the method. Based on the new theory, we can design practical criteria to control ξ k to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory and demonstrate that the inexact RQI with Lanczos is competitive to the inexact RQI with MINRES.
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on convergence of the inexact rayleigh quotient Iteration with minres
Journal of Computational and Applied Mathematics, 2012Co-Authors: Zhongxiao JiaAbstract:For the Hermitian inexact Rayleigh quotient Iteration (RQI), we present a new general theory, independent of iterative solvers for shifted inner linear systems. The theory shows that the method converges at least quadratically under a new condition, called the uniform positiveness condition, that may allow the residual norm @x"k>=1 of the inner linear system at Outer Iteration k+1 and can be considerably weaker than the condition @x"[email protected][email protected]<1 with @x a constant not near one commonly used in the literature. We consider the convergence of the inexact RQI with the unpreconditioned and tuned preconditioned MINRES methods for the linear systems. Some attractive properties are derived for the residuals obtained by MINRES. Based on them and the new general theory, we make a refined analysis and establish a number of new convergence results. Let @?r"[email protected]? be the residual norm of approximating eigenpair at Outer Iteration k. Then all the available cubic and quadratic convergence results require @x"k=O(@?r"[email protected]?) and @x"[email protected][email protected] with a fixed @x not near one, respectively. Fundamentally different from these, we prove that the inexact RQI with MINRES generally converges cubically, quadratically and linearly provided that @x"[email protected][email protected] with a constant @x<1 not near one, @x"k=1-O(@?r"[email protected]?) and @x"k=1-O(@?r"[email protected]?^2), respectively. The new convergence conditions are much more relaxed than ever before. The theory can be used to design practical stopping criteria to implement the method more effectively. Numerical experiments confirm our results.
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on convergence of the inexact rayleigh quotient Iteration with minres
arXiv: Numerical Analysis, 2009Co-Authors: Zhongxiao JiaAbstract:For the Hermitian inexact Rayleigh quotient Iteration (RQI), we present a new general theory, independent of iterative solvers for shifted inner linear systems. The theory shows that the method converges at least quadratically under a new condition, called the uniform positiveness condition, that may allow inner tolerance $\xi_k\geq 1$ at Outer Iteration $k$ and can be considerably weaker than the condition $\xi_k\leq\xi<1$ with $\xi$ a constant not near one commonly used in literature. We consider the convergence of the inexact RQI with the unpreconditioned and tuned preconditioned MINRES method for the linear systems. Some attractive properties are derived for the residuals obtained by MINRES. Based on them and the new general theory, we make a more refined analysis and establish a number of new convergence results. Let $\|r_k\|$ be the residual norm of approximating eigenpair at Outer Iteration $k$. Then all the available cubic and quadratic convergence results require $\xi_k=O(\|r_k\|)$ and $\xi_k\leq\xi$ with a fixed $\xi$ not near one, respectively. Fundamentally different from these, we prove that the inexact RQI with MINRES generally converges cubically, quadratically and linearly provided that $\xi_k\leq\xi$ with a constant $\xi<1$ not near one, $\xi_k=1-O(\|r_k\|)$ and $\xi_k=1-O(\|r_k\|^2)$, respectively. Therefore, the new convergence conditions are much more relaxed than ever before. The theory can be used to design practical stopping criteria to implement the method more effectively. Numerical experiments confirm our results.
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on convergence of the inexact rayleigh quotient Iteration without and with minres
2009Co-Authors: Zhongxiao JiaAbstract:For the Hermitian inexact Rayleigh quotient Iteration (RQI), we present general convergence results, independent of iterative solvers for inner linear systems. We prove that the method converges quadratically at least under a new condition, called the uniform positiveness condition. This condition can be much weaker than the commonly used one that at Outer Iteration k, requires the relative residual norm ξk (inner tolerance) of the inner linear system to be smaller than one considerably and may allow ξk ≥ 1. Our focus is on the inexact RQI with MINRES used for solving the linear systems. We derive some subtle and attractive properties of the residuals obtained by MINRES. Based on these properties and the new general convergence results, we establish a number of insightful convergence results. Let ‖rk‖ be the residual norm of approximating eigenpair at Outer Iteration k. Fundamentally different from the existing results that cubic and quadratic convergence requires ξk = O(‖rk‖) and ξk ≤ ξ ≪ 1 with ξ fixed, respectively, our new results remarkably show that the inexact RQI with MINRES generally converges cubically, quadratically and linearly provided that ξk ≤ ξ with ξ fixed not near one, ξk = 1−O(‖rk‖) and ξk = 1−O(‖rk‖), respectively. Since we always have ξk ≤ 1 in MINRES for any inner Iteration steps, the results mean that the inexact RQI with MINRES can achieve cubic, quadratic and linear convergence by solving the linear systems only with very low accuracy and very little accuracy, respectively. New theory can be used to design much more effective implementations of the method than ever before. The results also suggest that we implement the method with fixed small inner Iteration steps. Numerical experiments confirm our results and demonstrate much higher effectiveness of the new implementations.
Zhenhong Fan - One of the best experts on this subject based on the ideXlab platform.
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mixed inner Outer Iteration technique based surface integral equations for fast solving em scattering from penetrable objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
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Mixed Inner–Outer Iteration Technique-Based Surface Integral Equations for Fast Solving EM Scattering From Penetrable Objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
Shifei Tao - One of the best experts on this subject based on the ideXlab platform.
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mixed inner Outer Iteration technique based surface integral equations for fast solving em scattering from penetrable objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
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Mixed Inner–Outer Iteration Technique-Based Surface Integral Equations for Fast Solving EM Scattering From Penetrable Objects
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Lei Zhang, Shifei Tao, Zhenhong Fan, R. S. ChenAbstract:In this paper, a mixed inner–Outer Iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as Outer Iteration and the electric-magnetic current combined-field integral equation as inner Iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method.
