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Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly nonlinear Problems

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Computer Modeling in Engineering & Sciences 2024年第5期139卷 1263-1294页

作者： Xuechuan Wang Wei He Haoyang Feng satya n.atluri School of Astronautics Northwestern Polytechnical UniversityXi’an710072China Department of Mechanical Engineering Texas Tech UniversityLubbock79409USA

Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.

关键词： Predictor-corrector method feedback-accelerated Picard iteration nonlinear dynamical system real-time computation

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Harmonic Balance Methods:A Review and Recent Developments

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Computer Modeling in Engineering & Sciences 2023年第11期137卷 1419-1459页

作者： Zipu Yan Honghua Dai Qisi Wang satya n.atluri School of Astronautics Northwestern Polytechnical UniversityXi’an710072China national Key Laboratory of Aerospace Flight Dynamics Northwestern Polytechnical UniversityXi’an710072China Department of Mechanical Engineering Texas Tech UniversityLubbock79401USA

The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.

关键词： Harmonic balance frequency domain HB-like method time domain HB-like method dealiasing technique HB algebraic equation

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A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods;and a Local Variational Iteration Method

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Computer Modeling in Engineering & Sciences 2016年第6期111卷 567-585页

作者： Xuechuan Wang satya n.atluri Texas Tech University Center for Advanced Research in the Engineering Sciences northwestern Polytechnical University China

This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.

关键词： Variational iteration method Adomian decomposition method Picard iteration method asymptotic technique nonlinear dynamical system

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Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large noise

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Computer Modeling in Engineering & Sciences 2015年第1期104卷 1-39页

作者： Chein-Shan Liu satya n.atluri Department of Civil Engineering National Taiwan UniversityTaipeiTaiwan Center for Aerospace Research&Education University of CaliforniaIrvine

A double optimal solution of an n-dimensional system of linear equations Ax=b has been derived in an affine m-dimensional Krylov subspace with m <<n.We further develop a double optimal iterative algorithm(DOIA),with t... 详细信息

A double optimal solution of an n-dimensional system of linear equations Ax=b has been derived in an affine m-dimensional Krylov subspace with m n.We further develop a double optimal iterative algorithm(DOIA),with the descent direction z being solved from the residual equation Az=r0 by using its double optimal solution,to solve ill-posed linear problem under large noise.The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||^2=||b-Ax||^2 being reduced by a positive quantity ||Azk||^2 at each iteration step,which is found to be better than those algorithms based on the minimization of the square residual error in an m-dimensional Krylov subspace.In order to tackle the ill-posed linear problem under a large noise,we also propose a novel double optimal regularization algorithm(DORA)to solve it,which is an improvement of the Tikhonov regularization method.Some numerical tests reveal the high performance of DOIA and DORA against large noise.These methods are of use in the ill-posed problems of structural health-monitoring.

关键词： Ill-posed linear equations system Double optimal solution Affine Krylov subspace Double optimal iterative algorithm Double optimal regularization algorithm

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Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces

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Computer Modeling in Engineering & Sciences 2022年第6期131卷 1857-1882页

作者： Shuangxin He Chaoyang Wang Xuan Zhou Leiting Dong satya n.atluri School of Aeronautic Science and Engineering Beihang UniversityBeijingChina Department of Mechanical Engineering Texas Tech UniversityLubbockUSA

The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.

关键词： Symmetric Galerkin boundary element method rotational inertia gravitational force weak singularity stress intensity factor

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The Use of High-Performance Fatigue Mechanics and the Extended Kalman/Particle Filters,for Diagnostics and Prognostics of Aircraft Structures

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Computer Modeling in Engineering & Sciences 2015年第5期105卷 1-24页

作者： Hai-Kun Wang Robert Haynes Hong-Zhong Huang Leiting Dong satya n.atluri School of Mechanical Electronicand Industrial EngineeringUniversity of Electronic Science and Technology of China Center for Aerospace Research&Education University of CaliforniaIrvine Vehicle Technology Directorate US Army Research Laboratory Department of Hohai University China

In this paper,we propose an approach for diagnostics and prognostics of damaged aircraft structures,by combing high-performance fatigue mechanics with filtering theories.Fast&accurate deterministic analyses of fatigue crack propagations are carried out,by using the Finite Element Alternating Method(FEAM)for computing SIFs,and by using the newly developed Moving Least Squares(MLS)law for computing fatigue crack growth rates.Such algorithms for simulating fatigue crack propagations are embedded in the computer program Safe-Flaw,which is called upon as a subroutine within the probabilistic framework of filter theories.Both the extended Kalman as well as particle filters are applied in this study,to obtain the statistically optimal and semi-optimal estimates of crack lengths,from a series of noisy measurements of crack-lengths over time.For the specific problem,a simple modification to the particle filter,which can drastically reduce the computational burden,is also proposed.Based on the results of such diagnostic analyses,the prognostics of aerospace structures are thereafter achieved,to estimate the probabilistic distribution of the remaining useful life.By using a simple example of a single-crack near a fastener hole,we demonstrate the concept and effectiveness of the proposed framework.This paper thus forms the scientific foundation for the recently proposed concepts of VRAMS(Virtual Risk-Informed Agile Maneuver Sustainment)and Digital Twins of aerospace vehicles.

关键词： Diagnostics and prognostics fatigue mechanics extended Kalmanfilter particle filter

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基于三维纤维计算晶粒的纤维复合材料直接细观力学建模

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Acta Mechanica Sinica 2023年第11期39卷 54-69页

作者：黄业增王俊博李明净王冠楠董雷霆 satya n.atluri Tianmushan Laboratory Hangzhou 310023China School of Aeronautic Science and Engineering Beihang UniversityBejing 100191China Shenyang Aircrafi Design Institute Yangzhou Collaborative Innovation Institute Co LidYangzhou 225000China Department of Civil Engineering Zhejiang UniversityHangzhou 310058China Department of Mechanical Engineering Texas Tech UniversityLubbock 79409USA

面向纤维复合材料与结构的优化设计需要,建立高效准确的纤维复材细观力学仿真工具具有重要意义.本文首次提出了包含内嵌纤维的三维计算晶粒(computational grains),用于纤维增强复合材料的直接细观力学建模,基于所开发的纤维计算晶粒方... 详细信息

面向纤维复合材料与结构的优化设计需要,建立高效准确的纤维复材细观力学仿真工具具有重要意义.本文首次提出了包含内嵌纤维的三维计算晶粒(computational grains),用于纤维增强复合材料的直接细观力学建模,基于所开发的纤维计算晶粒方法,可以直接构造含有多根随机分布纤维的代表性体积单元(RVE).此外,本文提出了一种基于缩放柱调和函数的Papkovich-neuber解来表征纤维和基体中独立的Trefftz试函数位移场,并且开发了一种新的多场边界变分原理来计算纤维计算晶粒的刚度矩阵.数值算例表明,对于内嵌大量随机分布纤维的RVE,纤维计算晶粒不需要构造复杂的网格,即可快速计算RVE的精确应力场,并预测其有效力学性能.此外,这也是内嵌纤维的三维有限元单元的首次提出.

关键词：细观力学纤维增强复合材料纤维复合材料代表性体积单元调和函数随机分布变分原理试函数

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Insights into the interface of niCo_(2)O_(4) spinel/LaCoO_(3) perovskite nano-composite for CO and soot oxidation

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Journal of Environmental Sciences 2024年第4期138卷 339-349页

作者： neha Harshita Singh satya Vir Singh Department of Chemical Engineering Indian Institute of Technology(BHU)Varanasi221005India Department of Botany Institute of ScienceBanaras Hindu UniversityVaranasi221005India

In the quest for the development of thermally stable,highly active and low-cost catalysts for use in catalyzed diesel particulate filter,nano-composites are new areas of research.Therefore,we reported the easy synthesis of spinel niCo_(2)O_(4)/perovskite LaCoO_(3) nano-composite,and its individual oxides niCo_(2)O_(4)and LaCoO_(3) for comparison.The detailed insights into the physio-chemical characteristics of formed niCo_(2)O_(4)/LaCoO_(3) nano-composite were done based on various characterization analysis such as X-ray diffraction(XRD),Fourier transform infrared(FT-IR),n_(2) physiosorption,scanning electron microscopy-energy dispersive spectroscopy(SEM-EDX),transmission electron microscopy(TEM),and X-ray photoelectron spectroscopy(XPS).The characterization analysis of niCo_(2)O_(4)/LaCoO_(3) revealed the successful formation of a chemical interface possessing strong interfacial interaction,resulting in desirable physicochemical characteristics such as small crystallite size,abundant mesoporosity,high specific surface area and activation of surface lattice oxygen.Owing to the desirable characteristics,the activity results over niCo_(2)O_(4)/LaCoO_(3) nano-composite showed the excellent CO oxidation performance and high soot oxidation activity,recyclability and thermal stability.This work mainly attempts to emphasize the effectiveness of the facile,inexpensive and conventionally used precipitation method for the successful formation of highly efficient nano-composites.

关键词： LaCoO_(3) niCo_(2)O_(4) Spinel/perovskite CO oxidation Soot oxidation Chemical interface

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Topological transverse thermoelectrics:A new way forward?

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The Innovation 2023年第6期4卷 23-24页

作者： Shubham Yadav B.M.Anil Kumar satya n.Guin Department of Chemistry Birla Institute of Technology and SciencePilani-Hyderabad CampusHyderabad 500078India

Electronic structure is one of the most fundamental factors that decide the physical properties of a material.In the past 18 years,a deeper fundamental understanding of the electronic band structure of material has resulted in the development of topological band theory,which has reclassified solid-state materials into two different classes:topologically trivial and topologically nontrivial.Topologically nontrivial systems provide a new opportunity for material design for fundamental and functional applications from experimental and theoretical viewpoints.

关键词： material. topological nontrivial

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Pathway-selective suppression of chemokine receptor signaling in B cells by LPS through downregulation of PLC-b2

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Cellular & Molecular Immunology 2010年第6期7卷 428-439页

作者： Aiko-Konno Shirakawa Fang Liao Hongwei H Zhang Michael n Hedrick satya P Singh Dianqing Wu Joshua M Farber Inflammation Biology Section Laboratory of Molecular ImmunologyNational Institute of Allergy and Infectious DiseasesNational Institutes of HealthBethesdaMDUSA Department of Pharmacology Yale University School of MedicineNew HavenCTUSA

Lymphocyte activation leads to changes in chemokine receptor expression.There are limited data,however,on how lymphocyte activators can alter chemokine signaling by affecting downstream pathways.We hypothesized that B cell-activating agents might alter chemokine responses by affecting downstream signal transducers,and that such effects might differ depending on the activator.We found that activating mouse B cells using either anti-IgM or lipopolysaccharide(LPS)increased the surface expression of CCR6 and CCR7 with large increases in chemotaxis to their cognate ligands.By contrast,while anti-IgM also led to enhanced calcium responses,LPS-treated cells showed only small changes in calcium signaling as compared with cells that were freshly isolated.Of particular interest,we found that LPS caused a reduction in the level of B-cell phospholipase C(PLC)-b2 mRnA and protein.Data obtained using PLC-b22/2 mice showed that the b2 isoform mediates close to one-half the chemokine-induced calcium signal in resting and anti-IgM-activated B cells,and we found that calcium signals in the LPS-treated cells were boosted by increasing the level of PLC-b2 using transfection,consistent with a functional effect of downregulating PLC-b2.Together,our results show activator-specific effects on responses through B-cell chemokine receptors that are mediated by quantitative changes in a downstream signal-transducing protein,revealing an activity for LPS as a downregulator of PLC-b2,and a novel mechanism for controlling chemokine-induced signals in lymphocytes.

关键词： B cells calcium chemokine chemotaxis GPCR

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