The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Yinnian He - One of the best experts on this subject based on the ideXlab platform.
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Some iterative finite element methods for steady Navier-Stokes equations with different viscosities
Journal of Computational Physics, 2020Co-Authors: Hui Xu, Yinnian HeAbstract:Two-level iterative finite element methods are designed to solve numerically the steady 2D/3D Navier-Stokes equations for a large viscosity @n such that a strong Uniqueness Condition holds. Moreover, the one-level Oseen iterative finite element method based on a fine mesh with small mesh size h is designed to solve numerically the steady 2D/3D Navier-Stokes equations for small viscosity @n such that a weak Uniqueness Condition holds. Meanwhile, the numerical investigations are provided to show that the proposed methods are efficient for solving the 2D/3D steady Navier-Stokes equations for different viscosities.
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Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics
Science China-mathematics, 2015Co-Authors: Xiaojing Dong, Yinnian HeAbstract:Based on finite element method (FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics (MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong Uniqueness Condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak Uniqueness Condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters Re,Rm, Sc, mesh sizes h,H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.
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Stability and convergence of iterative methods related to viscosities for the 2D/3D steady Navier–Stokes equations☆
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Yinnian HeAbstract:Abstract Some finite element iterative methods related to viscosities are designed to solve numerically the steady 2D/3D Navier–Stokes equations. The two-level finite element iterative methods are designed to solve numerically the steady 2D/3D Navier–Stokes equations for a large viscosity ν such that a strong Uniqueness Condition holds. The two-level finite element iterative methods consist of using the Stokes, Newton and Oseen iterations of m times on a coarse mesh with mesh size H and computing the Stokes, Newton and Oseen correction of one time on a fine grid with mesh size h ≪ H . Moreover, the one-level Oseen finite element iterative method based on a fine mesh with a small mesh size is designed to solve numerically the steady 2D/3D Navier–Stokes equations for small viscosity ν such that a weak Uniqueness Condition holds. The uniform stability and convergence of these methods with respect to ν and mesh sizes h and H and iterative times m are provided.
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convergence analysis of three finite element iterative methods for the 2d 3d stationary incompressible magnetohydrodynamics
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Xiaojing Dong, Yinnian He, Yan ZhangAbstract:Three finite element iterative methods are designed and analyzed for solving 2D/3D stationary incompressible magnetohydrodynamics (MHD). By a new technique, strong Uniqueness Conditions for both Stokes type iterative method (Iterative method I) and Newton iterative method (Iterative method II) are obtained, which are weaker than the ones reported in open literature. Stability and optimal convergence rates for the above two methods are derived, where the Iterative method II has an exponential convergent part with respect to iterative step m. Moreover, Oseen type iterative method (Iterative method III) is unConditionally stable and convergent under a Uniqueness Condition. Finally, performance of the three proposed methods is investigated by numerical experiments.
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convergence of three iterative methods based on the finite element discretization for the stationary navier stokes equations
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: Yinnian He, Jian LiAbstract:Abstract This paper considers three iterative methods for solving the stationary Navier–Stokes equations. Iterative method I consists in solving the stationary Stokes equations, iterative method II consists in solving the stationary linearized Navier–Stokes equations and iterative method III consists in solving the stationary Oseen equations under the finite element discretization, respectively, at each iterative step. Also, we discuss the stability and convergence of three iterative methods. The iterative methods I and II are stability and convergence under the strong Uniqueness Conditions, where the iterative method II is the second order convergence. Furthermore, the iterative method III is unCondition stability and convergence under the Uniqueness Condition. Finally, some numerical tests show that the efficiency of the theoretical analysis.
Lieven De Lathauwer - One of the best experts on this subject based on the ideXlab platform.
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Tensor Decompositions With Several Block-Hankel Factors and Application in Blind System Identification
IEEE Transactions on Signal Processing, 2017Co-Authors: Frederik Van Eeghem, Mikael Sorensen, Lieven De LathauwerAbstract:Several applications in biomedical data processing, telecommunications, or chemometrics can be tackled by computing a structured tensor decomposition. In this paper, we focus on tensor decompositions with two or more block-Hankel factors, which arise in blind multiple-input-multiple-output (MIMO) convolutive system identification. By assuming statistically independent inputs, the blind system identification problem can be reformulated as a Hankel structured tensor decomposition. By capitalizing on the available block-Hankel and tensorial structure, a relaxed Uniqueness Condition for this structured decomposition is obtained. This Condition is easy to check, yet very powerful. The Uniqueness Condition also forms the basis for two subspace-based algorithms, able to blindly identify linear underdetermined MIMO systems with finite impulse response.
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Generic Uniqueness of a Structured Matrix Factorization and Applications in Blind Source Separation
IEEE Journal of Selected Topics in Signal Processing, 2016Co-Authors: Ignat Domanov, Lieven De LathauwerAbstract:Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold “almost everywhere.” We present a set of Conditions that are sufficient for demonstrating the generic Uniqueness of a certain structured matrix factorization. This set of Conditions may be used as a checklist for generic Uniqueness in different settings. We discuss two particular applications in detail. We provide a relaxed generic Uniqueness Condition for joint matrix diagonalization that is relevant for independent component analysis in the underdetermined case. We present generic Uniqueness Conditions for a recently proposed class of deterministic blind source separation methods that rely on mild source models. For the interested reader, we provide some intuition on how the results are connected to their algebraic geometric roots.
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Multiple Invariance ESPRIT for Nonuniform Linear Arrays: A Coupled Canonical Polyadic Decomposition Approach
IEEE Transactions on Signal Processing, 2016Co-Authors: Mikael Sorensen, Lieven De LathauwerAbstract:The Canonical Polyadic Decomposition (CPD) of higher-order tensors has proven to be an important tool for array processing. CPD approaches have so far assumed regular array geometries such as uniform linear arrays. However, in the case of sparse arrays such as nonuniform linear arrays (NLAs), the CPD approach is not suitable anymore. Using the coupled CPD we propose in this paper a multiple invariance ESPRIT method for both one- and multi-dimensional NLA processing. We obtain a multiresolution ESPRIT method for sparse arrays with multiple baselines. The coupled CPD framework also yields a new Uniqueness Condition that is relaxed compared with the CPD approach. It also leads to an eigenvalue decomposition based algorithm that is guaranteed to reduce the multi-source NLA problem into decoupled single-source NLA problems in the noiseless case. Finally, we present a new polynomial rooting procedure for the latter problem, which again is guaranteed to find the solution in the noiseless case. In the presence of noise, the algebraic algorithm provides an inexpensive initialization for optimization-based methods.
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New Uniqueness Conditions for the Canonical Polyadic Decomposition of Third-Order Tensors
SIAM Journal on Matrix Analysis and Applications, 2015Co-Authors: Mikael Sorensen, Lieven De LathauwerAbstract:The Uniqueness properties of the canonical polyadic decomposition (CPD) of higher-order tensors make it an attractive tool for signal separation. However, CPD Uniqueness is not yet fully understood. In this paper, we first present a new Uniqueness Condition for a polyadic decomposition (PD) where one of the factor matrices is assumed to be known. We also show that this result can be used to obtain a new overall Uniqueness Condition for the CPD. In signal processing the CPD factor matrices are often constrained. Building on the preceding results, we provide a new Uniqueness Condition for a CPD with a columnwise orthonormal factor matrix, representing uncorrelated signals. We also obtain a new Uniqueness Condition for a CPD with a partial Hermitian symmetry, useful for tensors in which covariance matrices are stacked, which are common in statistical signal processing. We explain that such constraints can lead to more relaxed Uniqueness Conditions. Finally, we provide an inexpensive algorithm for computing a...
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Multidimensional ESPRIT: A coupled canonical polyadic decomposition approach
2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014Co-Authors: Mikael Sorensen, Lieven De LathauwerAbstract:The ESPRIT method is a classical method for one-dimensional harmonic retrieval. During the past two decades it has become apparent that several applications in signal processing correspond to the less studied Multi-dimensional Harmonic Retrieval (MHR) problem. In order to accommodate this demand, we propose an extension of ESPRIT to MHR based on the coupled canonical polyadic decomposition. This leads to a dedicated Uniqueness Condition and an algebraic framework for MHR.
Jian Li - One of the best experts on this subject based on the ideXlab platform.
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convergence of three iterative methods based on the finite element discretization for the stationary navier stokes equations
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: Yinnian He, Jian LiAbstract:Abstract This paper considers three iterative methods for solving the stationary Navier–Stokes equations. Iterative method I consists in solving the stationary Stokes equations, iterative method II consists in solving the stationary linearized Navier–Stokes equations and iterative method III consists in solving the stationary Oseen equations under the finite element discretization, respectively, at each iterative step. Also, we discuss the stability and convergence of three iterative methods. The iterative methods I and II are stability and convergence under the strong Uniqueness Conditions, where the iterative method II is the second order convergence. Furthermore, the iterative method III is unCondition stability and convergence under the Uniqueness Condition. Finally, some numerical tests show that the efficiency of the theoretical analysis.
Christian Jutten - One of the best experts on this subject based on the ideXlab platform.
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A generalization of weighted sparse decomposition to negative weights
2017 25th European Signal Processing Conference (EUSIPCO), 2017Co-Authors: Ghazaleh Delfi, Shayan Aziznejad, Sana Amani, Massoud Babaie-zadeh, Christian JuttenAbstract:Sparse solutions of underdetermined linear systems of equations are widely used in different fields of signal processing. This problem can also be seen as a sparse decomposition problem. Traditional sparse decomposition gives the same priority to all atoms for being included in the decomposition or not. However, in some applications, one may want to assign different priorities to different atoms for being included in the decomposition. This results to the so called "weighted sparse decomposition" problem [Babaie-Zadeh et al. 2012]. However, Babaie-Zadeh et al. studied this problem only for positive weights; but in some applications (e.g. classification) better performance can be obtained if some weights become negative. In this paper, we consider "weighted sparse decomposition" problem in its general form (positive and negative weights). A tight Uniqueness Condition and some applications for the general case will be presented.
Yan Zhang - One of the best experts on this subject based on the ideXlab platform.
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convergence analysis of three finite element iterative methods for the 2d 3d stationary incompressible magnetohydrodynamics
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Xiaojing Dong, Yinnian He, Yan ZhangAbstract:Three finite element iterative methods are designed and analyzed for solving 2D/3D stationary incompressible magnetohydrodynamics (MHD). By a new technique, strong Uniqueness Conditions for both Stokes type iterative method (Iterative method I) and Newton iterative method (Iterative method II) are obtained, which are weaker than the ones reported in open literature. Stability and optimal convergence rates for the above two methods are derived, where the Iterative method II has an exponential convergent part with respect to iterative step m. Moreover, Oseen type iterative method (Iterative method III) is unConditionally stable and convergent under a Uniqueness Condition. Finally, performance of the three proposed methods is investigated by numerical experiments.
