The Experts below are selected from a list of 1455 Experts worldwide ranked by ideXlab platform
Zhaoran Xiao - One of the best experts on this subject based on the ideXlab platform.
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The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method
International Journal of Engineering Science, 2010Co-Authors: Weixiang Zhang, Weihua Cui, Zhaoran XiaoAbstract:Abstract The symplectic system method is introduced into the quasi-static analysis for axial symmetric problems of the viscoelastic hollow circular cylinder, with the emphasis on the local effects. By employing the method of separation of variables, all the Fundamental Eigenvectors of the governing equations are obtained directly. The combinations of the Eigenvectors can describe the classical Saint-Venant problems and the local effects near the boundary. After constructing the adjoint symplectic relationships between the Eigenvectors, the symplectic system method can be applied to solve quasi-static viscoelastic problems by expanding the Eigenvectors to satisfy the given boundary conditions. Numerical results show the local effects due to the displacement constraints and the creep phenomenon of the time dependent material under certain boundary conditions. The results obtained by the approach are accurate, because all the given lateral boundary conditions and end conditions of the cylinder can be satisfied.
Weixiang Zhang - One of the best experts on this subject based on the ideXlab platform.
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The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method
International Journal of Engineering Science, 2010Co-Authors: Weixiang Zhang, Weihua Cui, Zhaoran XiaoAbstract:Abstract The symplectic system method is introduced into the quasi-static analysis for axial symmetric problems of the viscoelastic hollow circular cylinder, with the emphasis on the local effects. By employing the method of separation of variables, all the Fundamental Eigenvectors of the governing equations are obtained directly. The combinations of the Eigenvectors can describe the classical Saint-Venant problems and the local effects near the boundary. After constructing the adjoint symplectic relationships between the Eigenvectors, the symplectic system method can be applied to solve quasi-static viscoelastic problems by expanding the Eigenvectors to satisfy the given boundary conditions. Numerical results show the local effects due to the displacement constraints and the creep phenomenon of the time dependent material under certain boundary conditions. The results obtained by the approach are accurate, because all the given lateral boundary conditions and end conditions of the cylinder can be satisfied.
Richard Peng - One of the best experts on this subject based on the ideXlab platform.
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Faster spectral sparsification and numerical algorithms for SDD matrices
arXiv: Data Structures and Algorithms, 2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We study algorithms for spectral graph sparsification. The input is a graph $G$ with $n$ vertices and $m$ edges, and the output is a sparse graph $\tilde{G}$ that approximates $G$ in an algebraic sense. Concretely, for all vectors $x$ and any $\epsilon>0$, $\tilde{G}$ satisfies $$ (1-\epsilon) x^T L_G x \leq x^T L_{\tilde{G}} x \leq (1+\epsilon) x^T L_G x, $$ where $L_G$ and $L_{\tilde{G}}$ are the Laplacians of $G$ and $\tilde{G}$ respectively. We show that the fastest known algorithm for computing a sparsifier with $O(n\log n/\epsilon^2)$ edges can actually run in $\tilde{O}(m\log^2 n)$ time, an $O(\log n)$ factor faster than before. We also present faster sparsification algorithms for slightly dense graphs. Specifically, we give an algorithm that runs in $\tilde{O}(m\log n)$ time and generates a sparsifier with $\tilde{O}(n\log^3{n}/\epsilon^2)$ edges. This implies that a sparsifier with $O(n\log n/\epsilon^2)$ edges can be computed in $\tilde{O}(m\log n)$ time for graphs with more than $O(n\log^4 n)$ edges. We also give an $\tilde{O}(m)$ time algorithm for graphs with more than $n\log^5 n (\log \log n)^3$ edges of polynomially bounded weights, and an $O(m)$ algorithm for unweighted graphs with more than $n\log^8 n (\log \log n)^3 $ edges and $n\log^{10} n (\log \log n)^5$ edges in the weighted case. The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of slightly dense SDD matrices.
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Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices
2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/epsilon^2) edges that provides a strong approximation of G. Namely, for all vectors x and any epsilon>0, we have (1-epsilon) x^T L_G x n^{1+r} for some constant r this becomes softO(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of dense SDD matrices.
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STACS - Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices.
2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/epsilon^2) edges that provides a strong approximation of G. Namely, for all vectors x and any epsilon>0, we have (1-epsilon) x^T L_G x n log^5 n and runs in tilde{O}(m log_{m/ n log^5 n} n time. In the range where m>n^{1+r} for some constant r this becomes softO(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of dense SDD matrices.
Weihua Cui - One of the best experts on this subject based on the ideXlab platform.
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The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method
International Journal of Engineering Science, 2010Co-Authors: Weixiang Zhang, Weihua Cui, Zhaoran XiaoAbstract:Abstract The symplectic system method is introduced into the quasi-static analysis for axial symmetric problems of the viscoelastic hollow circular cylinder, with the emphasis on the local effects. By employing the method of separation of variables, all the Fundamental Eigenvectors of the governing equations are obtained directly. The combinations of the Eigenvectors can describe the classical Saint-Venant problems and the local effects near the boundary. After constructing the adjoint symplectic relationships between the Eigenvectors, the symplectic system method can be applied to solve quasi-static viscoelastic problems by expanding the Eigenvectors to satisfy the given boundary conditions. Numerical results show the local effects due to the displacement constraints and the creep phenomenon of the time dependent material under certain boundary conditions. The results obtained by the approach are accurate, because all the given lateral boundary conditions and end conditions of the cylinder can be satisfied.
Ioannis Koutis - One of the best experts on this subject based on the ideXlab platform.
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Faster spectral sparsification and numerical algorithms for SDD matrices
arXiv: Data Structures and Algorithms, 2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We study algorithms for spectral graph sparsification. The input is a graph $G$ with $n$ vertices and $m$ edges, and the output is a sparse graph $\tilde{G}$ that approximates $G$ in an algebraic sense. Concretely, for all vectors $x$ and any $\epsilon>0$, $\tilde{G}$ satisfies $$ (1-\epsilon) x^T L_G x \leq x^T L_{\tilde{G}} x \leq (1+\epsilon) x^T L_G x, $$ where $L_G$ and $L_{\tilde{G}}$ are the Laplacians of $G$ and $\tilde{G}$ respectively. We show that the fastest known algorithm for computing a sparsifier with $O(n\log n/\epsilon^2)$ edges can actually run in $\tilde{O}(m\log^2 n)$ time, an $O(\log n)$ factor faster than before. We also present faster sparsification algorithms for slightly dense graphs. Specifically, we give an algorithm that runs in $\tilde{O}(m\log n)$ time and generates a sparsifier with $\tilde{O}(n\log^3{n}/\epsilon^2)$ edges. This implies that a sparsifier with $O(n\log n/\epsilon^2)$ edges can be computed in $\tilde{O}(m\log n)$ time for graphs with more than $O(n\log^4 n)$ edges. We also give an $\tilde{O}(m)$ time algorithm for graphs with more than $n\log^5 n (\log \log n)^3$ edges of polynomially bounded weights, and an $O(m)$ algorithm for unweighted graphs with more than $n\log^8 n (\log \log n)^3 $ edges and $n\log^{10} n (\log \log n)^5$ edges in the weighted case. The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of slightly dense SDD matrices.
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Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices
2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/epsilon^2) edges that provides a strong approximation of G. Namely, for all vectors x and any epsilon>0, we have (1-epsilon) x^T L_G x n^{1+r} for some constant r this becomes softO(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of dense SDD matrices.
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STACS - Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices.
2012Co-Authors: Ioannis Koutis, Alex Levin, Richard PengAbstract:We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/epsilon^2) edges that provides a strong approximation of G. Namely, for all vectors x and any epsilon>0, we have (1-epsilon) x^T L_G x n log^5 n and runs in tilde{O}(m log_{m/ n log^5 n} n time. In the range where m>n^{1+r} for some constant r this becomes softO(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing Fundamental Eigenvectors of dense SDD matrices.
