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A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning

JOURNAL OF COMPUTATIONAL PHYSICS 2019年 383卷 72-93页

作者： Liu, Ju Marsden, Alison L. Stanford Univ Dept Pediat Cardiol Bioengn Clark Ctr E1-3 318 Campus Dr Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Clark Ctr E1-3 318 Campus Dr Stanford CA 94305 USA

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed in [1]. The numerical scheme is constructed based on the variational multiscale formulation and the generalized-alpha method. Within the nonlinear solution procedure, a block factorization is performed for the consistent tangent matrix to decouple the kinematics from the balance laws. Within the linear solution procedure, another block factorization is performed to decouple the mass balance equation from the linear momentum balance equations. A nested block preconditioning technique is proposed to combine the Schur complement reduction approach with the fully coupled approach. This preconditioning technique, together with the Krylov subspace method, constitutes a novel iterative method for solving hyper-elastodynamics. We demonstrate the efficacy of the proposed preconditioning technique by comparing with the SIMPLE preconditioner and the one-level domain decomposition preconditioner. Two representative examples are studied: the compression of an isotropic hyperelastic cube and the tensile test of a fully-incompressible anisotropic hyperelastic arterial wall model. The robustness with respect to material properties and the parallel performance of the preconditioner are examined. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Variational multiscale method Saddle-point problem nested iterative method Block preconditioner Anisotropic incompressible hyperelasticity Arterial wall model

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Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

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Applied Mathematics and Mechanics(English Edition) 2013年第8期34卷 931-944页

作者：罗志强陈志敏 Department of System Science and Applied Mathematics School of Science Kunming University of Science and Technology School of Engineering Sciences University of Southampton

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

关键词： three-dimensional (3D) nonlinear potential flow equation predictor-corrector finite difference method staggered grid nested iterative method 3D sloshing

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Numerical solution of potential flow equations with a predictor-corrector finite difference method

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Journal of Zhejiang University-Science C(Computers and Electronics) 2012年第5期13卷 393-402页

作者： Zhi-qiang LUO Department of System Science and Applied Mathematics School of ScienceKunming University of Science and TechnologyKunming 650083China

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) *** irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient *** finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary *** present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited *** beating period and the nonlinear phenomenon are very *** numerical solutions agree well with the analytical solutions and previously published results.

关键词： Predictor-corrector method Nonlinear potential flow equations Finite difference method Staggered grid nested iterative method

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Estimates for Convergence Rate of nested iterative methods

Estimates for Convergence Rate of Nested Iterative Methods

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2011 IEEE International Conference on Computer Science and Automation Engineering(CSAE 2011)

作者： FANG CAI,JIE XIAO,ZHAO-HONG XIANG Dept.of Information and computation science, Changsha University, Changsha,China

nested iterative methods were designed for parallel *** this article we consider the convergence rate of nested iterative *** for R-factor of stationary and non-stationary nested iterative methods are *** results we presented reveal the way that the numbers of inner iterations,together with the R-factors of inner and outer iterative methods influence on the convergence rate of nested iterative methods,and can be used to select the approximately optimal number of inner iterations.

关键词： Linear systems nested iterative method Convergence rate Parallel computation

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Base-age invariant cork growth model for Spanish cork oak (Quercus suber L.) forests

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EUROPEAN JOURNAL OF FOREST RESEARCH 2008年第3期127卷 173-182页

作者： Sanchez-Gonzalez, Mariola Canellas, Isabel Montero, Gregorio INIA Ctr Invest Forestal Madrid 28040 Spain

A cork growth model for Spanish cork oak forests was developed using data from 432 cork samples. Ten dynamic equations derived from the generalised algebraic difference approach (GADA) were considered for analysis, and both numerical and graphical methods were used to compare alternative models. All of the equations are base-age invariant and directly estimate accumulated cork thickness in complete years at any moment of the cork rotation. The fittings were done using the nested iterative method of the stochastic regression approach. The GADA formulation derived by Krumland and Eng (2005) from the Richards model by considering a (1) and a (3) as related to site productivity was finally selected. The cork growth model developed in this study allows the total accumulated cork thickness in complete years to be estimated in the fourth year of cork rotation with close to 80% reliability for any debarking period, increasing to nearly 90% from the eighth year onwards.

关键词： cork growth cork thickness dynamic equation generalised algebraic difference approach nested iterative method

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Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

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应用数学和力学 2013年第8期 931-944页

作者：罗志强陈志敏

A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa-tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa-tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

关键词： three-dimensional (3D) nonlinear potential flow equation predictor-corrector finite difference method staggered grid nested iterative method 3D sloshing

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Structured Sparse Approximation via Generalized Regularizers: With Application to V2V Channel Estimation

Structured Sparse Approximation via Generalized Regularizers...

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IEEE Global Communications Conference (GLOBECOM)

作者： Beygi, Sajjad Strom, Erik G. Mitra, Urbashi USC Sch Elect Engn Los Angeles CA 90089 USA Chalmers Univ Technol Dept Signals & Syst Gothenburg Sweden

ISBN: (纸本)9781479935123

In this paper, we consider the estimation of a signal that has both group-and element-wise sparsity (joint sparsity);motivated by channel estimation in vehicle-to-vehicle channels. A general approach for the design of separable regularizing functions is proposed to adaptively induce sparsity in the estimation. A joint sparse signal estimation problem is formulated via these regularizers and its optimal solution is computed based on proximity operations. Our optimization results are quite general and they can be applied in the context of hierarchical sparsity models as well. The proposed recovery algorithm is a nested iterative method based on the alternating direction method of multipliers (ADMM). Due to regularizer separability, key operations can be performed in parallel. V2V channels are estimated by exploiting the joint sparsity (group/element-wise) exhibited in the delay-Doppler domain. Simulation results reveal that the proposed method can achieve as much as a 1 0 dB gain over previously examined methods.

关键词： channel estimation iterative methods mobile radio optimisation signal processing ADMM V2V channel estimation alternating direction method of multipliers delay-Doppler domain element-wise sparsity hierarchical sparsity models nested iterative method recovery algorithm separable regularizing functions sparse signal estimation problem structured sparse approximation vehicle-to-vehicle channels Approximation methods Channel estimation Estimation Joints Optimization Signal processing Vectors

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An EKF-Based Fixed-Point iterative Filter for Nonlinear Systems

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SENSORS 2019年第8期19卷 1893.-1893.页

作者： Feng, Xiaoliang Feng, Yuxin Wen, Chenglin Henan Univ Technol Coll Elect Engn Zhengzhou 450001 Henan Peoples R China Hangzhou Dianzi Univ Sch Automat Hangzhou 310018 Zhejiang Peoples R China

In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filter to the linearized system by discarding the higher-order Taylor series items of the original nonlinear system. In order to reduce the influence of the discarded higher-order Taylor series items and improve the filtering accuracy of the obtained state estimate of the steady-state EKF, a fixed-point function was solved though a nested iterative method, which resulted in a fixed-point iterative filter. The convergence of the fixed-point function is also discussed, which provided the existing conditions of the fixed-point iterative filter. Then, Steffensen's iterative method is presented to accelerate the solution of the fixed-point function. The final simulation is provided to illustrate the feasibility and the effectiveness of the proposed nonlinear filtering method.

关键词： fixed-point filter extended Kalman filter nested iterative method Steffensen's iterative method convergence condition

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