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An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites

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INTERNATIONAL JOURNAL OF PLASTICITY 2006年第1期22卷 131-157页

作者： Pierard, O Doghri, I Catholic Univ Louvain CESAME B-1348 Louvain Belgium

This paper deals with the prediction of the overall behavior of a class of two-phase elasto-viscoplastic composites, based on mean-field homogenization. For this, important improvements are made to the recently-proposed affine formulation. The latter theory linearizes the rate-dependent inelastic constitutive equations of each phase's material and transforms them into fictitious linear thermo-elastic relations in the Laplace-Carson domain. The main contributions of the present work are threefold. Firstly, complete mathematical developments including a full treatment of internal variables are carried out, enabling the modeling of the response under unloading and cyclic histories. Secondly, robust and accurate computational algorithms are proposed. Thirdly, an extensive validation of the predictions against reference unit cell finite element results is conducted for a variety of materials and loadings. A good agreement between predictions and reference results is observed. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： particulate reinforced material elasto-viscoplastic material cyclic loading numerical algorithms homogenization

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Unsaturated soils: From constitutive modelling to numerical algorithms

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COMPUTERS AND GEOTECHNICS 2008年第6期35卷 810-824页

作者： Sheng, Daichao Gens, Antonio Fredlund, Delwyn G. Sloan, Scott W. Univ Newcastle Ctr Geotech & Mat Modelling Callaghan NSW 2308 Australia Tech Univ Catalonia Dept Geotech Engn & Geosci Barcelona Spain Golder Associates Saskatoon SK Canada

This paper presents an overview of constitutive modelling of unsaturated soils and the numerical algorithms for solving the associated boundary value problems. It first discusses alternative stress and strain variables that can be used in constitutive models for unsaturated soils. The paper then discusses the key issues in unsaturated soil modelling and how these issues can be incorporated into an existing model for saturated soils. These key issues include (1) volumetric behaviour associated with saturation or suction changes;(2) strength behaviour associated with saturation and suction changes, and (3) hydraulic behaviour associated with saturation or suction changes. The paper also shows how hysteresis in soil-water characteristics can be incorporated into the elasto-plastic framework, leading to coupled hydro-mechanical models. Finally, the paper demonstrates the derivation of the incremental stress-strain relations for unsaturated soils and discusses briefly the new challenges in implementing these relations into the finite element method. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Unsaturated soils Constitutive modelling numerical algorithms

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MEASURING RATES OF CONVERGENCE OF numerical algorithms

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1993年第1期78卷 109-125页

作者： BARZILAI, J DEMPSTER, MAH UNIV ESSEX DEPT MATHCOLCHESTER CO4 3SQESSEXENGLAND

We analyze the behavior of common indices used in numerical linear algebra, analysis, and optimization to measure rates of convergence of an algorithm. A simple consistent axiomatic structure is used to uniquely define convergence rate measures on the basic linear, superlinear, and sublinear scales in terms of standard comparison sequences. Agreement with previously utilized indices and related measures is discussed.

关键词： numerical algorithms CONVERGENCE RATES COMPARISON SEQUENCES

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Homogenization of two-phase elasto-plastic composite materials and structures - Study of tangent operators, cyclic plasticity and numerical algorithms

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2003年第7期40卷 1681-1712页

作者： Doghri, I Ouaar, A Univ Catholique Louvain CESAME B-1348 Louvain Belgium

We develop homogenization schemes and numerical algorithms for two-phase elasto-plastic composite materials and structures. A Hill-type incremental formulation enables the simulation of unloading and cyclic loadings. It also allows to handle any rate-independent model for each phase. We study the crucial issue of tangent operators: elasto-plastic (or "continuum") versus algorithmic (or "consistent"), and anisotropic versus isotropic. We apply two methods of extraction of isotropic tangent moduli. We compare mathematically the stiffnesses of various tangent operators. All rate equations are discretized in time using implicit integration. We implemented two homogenization schemes: Mori-Tanaka and a double inclusion model, and two plasticity models: classical J(2) plasticity and Chaboche's model with non-linear kinematic and isotropic hardenings. We consider composites with different properties and present several discriminating numerical simulations. In many cases, the results are validated against finite element (FE) or experimental data. We integrated our homogenization code into the FE program ABAQUS using a user material interface UMAT. A two-scale procedure allows to compute realistic structures made of non-linear composite materials within reasonable CPU time and memory usage;examples are shown. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： composites micro-mechanics homogenization plasticity numerical algorithms finite elements

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Connections Between numerical algorithms for PDEs and Neural Networks

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2023年第1期65卷 185-208页

作者： Alt, Tobias Schrader, Karl Augustin, Matthias Peter, Pascal Weickert, Joachim Saarland Univ Fac Math & Comp Sci Math Image Anal Grp Campus E1-7 D-66041 Saarbrucken Germany

We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to neural networks. Besides structural insights, we provide concrete examples and experimental evaluations of the resulting architectures. Using the example of generalised nonlinear diffusion in 1D, we consider explicit schemes, acceleration strategies thereof, implicit schemes, and multigrid approaches. We connect these concepts to residual networks, recurrent neural networks, and U-net architectures. Our findings inspire a symmetric residual network design with provable stability guarantees and justify the effectiveness of skip connections in neural networks from a numerical perspective. Moreover, we present U-net architectures that implement multigrid techniques for learning efficient solutions of partial differential equation models, and motivate uncommon design choices such as trainable nonmonotone activation functions. Experimental evaluations show that the proposed architectures save half of the trainable parameters and can thus outperform standard ones with the same model complexity. Our considerations serve as a basis for explaining the success of popular neural architectures and provide a blueprint for developing new mathematically well-founded neural building blocks.

关键词： numerical algorithms Partial differential equations Neural networks Nonlinear diffusion Stability

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Comparison of numerical algorithms for bivariate sequential tests based on marginal criteria

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2005年第3期49卷 631-641页

作者： Zhao, YL Grambsch, PM Neaton, JD Univ Minnesota Sch Publ Hlth Div Biostat Minneapolis MN 55455 USA

Group sequential tests are widely used for interim analyses in randomized clinical trials. These tests have been extended to bivariate outcomes, but calculation of boundary values is computationally intensive. In this paper, we compare 3 algorithms: (1) quasi-Monte Carlo;(2) Schervish's MULNOR;and (3) a bivariate version of Armitage's recursive formula proposed by Jennison and Turnbull, for calculating boundary values for the L-region bivariate design which takes account of the correlation between the outcomes. Up to 5 interim analyses (stages) and a range of values for the correlation between the two endpoints were considered. The three algorithms produced very similar boundary values, but the quasi-Monte Carlo approach was much faster than the other two. The quasi-Monte Carlo method is an attractive approach for studying higher dimensions-designs with more stages and designs with more than two outcomes. The increased speed of this algorithm may permit the development of more flexible monitoring guidelines for multiple endpoints for clinical trials. (c) 2004 Elsevier B.V. All rights reserved.

关键词： group sequential monitoring bivariate responses numerical algorithms

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Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some numerical algorithms

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numerical ANALYSIS AND APPLICATIONS 2019年第3期12卷 234-250页

作者： Matskevich, N. A. Chubarov, L. B. Novosibirsk State Univ Ul Pirogova 2 Novosibirsk 630090 Russia Russian Acad Sci Inst Computat Technol Siberian Branch Pr Akad Lavrenteva 6 Novosibirsk 630090 Russia

We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth's rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

关键词： wave run-up free surface Coriolis force bottom friction mathematical modeling shallow water equations exact solutions ordinary differential equations numerical algorithms large-particle method verification

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Evaluation of numerical algorithms used in extracting the parameters of a single-diode photovoltaic model

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SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS 2016年 13卷 51-59页

作者： Ayodele, T. R. Ogunjuyigbe, A. S. O. Ekoh, E. E. Univ Ibadan Fac Technol Elect & Elect Engn Dept Power Energy Machines & Drives PEMD Res Grp Ibadan Nigeria

The current-voltage relationship of the single-diode photovoltaic (PV) cell/panel equivalent circuit model is defined by its implicit nonlinear transcendental equation, which is difficult to solve using analytical methods. This difficulty has led to the development of several algorithms for solving this equation using numerical techniques. This paper investigates and compares three different algorithms commonly employed in solving current-voltage equation of a 5-parameter single-diode solar PV model using manufacturer's data sheet. The comparison is performed based on accuracy (i.e. closeness of the obtained results to experimental values), required computer memory, speed of computation, robustness of the algorithm, and ease of implementation of algorithm. The results reveal that no single algorithm performs best in all the metrics and there will always be a trade-off in the choice of the algorithms based on the user's focus. Villalva algorithm is preferable in terms of robustness whilst T. Esram performs better in the area of computational speed, memory space and ease of implementation. No generic conclusion could be easily made in terms of accuracy as it varies with the PV technology and parameter of interest. The present work can be a potential tool for researchers and designers working in the area of photovoltaic systems, to make decisions related to the selection of the best possible algorithm for the extraction of the characteristic parameters of single-diode 5-parameter PV models. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Comparison numerical algorithms Single-diode model Solar PV Datasheet values

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Automation and Decision Support in the Area of Nephrology Using numerical algorithms, Artificial Intelligence, and Expert Approach: Review of the Current State of Knowledge

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IEEE ACCESS 2024年 12卷 86043-86066页

作者： Pawus, Dawid Porazko, Tomasz Paszkiel, Szczepan Opole Univ Technol Fac Elect Engn Automat Control & Informat PL-45758 Opole Poland Univ Opole Inst Med Sci Dept Internal Med & Nephrol PL-45052 Opole Poland Opole Univ Hosp Dept Nephrol Dialysis Unit PL-46020 Opole Poland

This study explores the contemporary landscape of integrating numerical algorithms, artificial intelligence (AI), and expert methodologies within the domain of nephrology. Focusing on automation and decision support, we scrutinize the impact of numerical algorithms on the precise evaluation of kidney function. Furthermore, we delve into the transformative potential of artificial intelligence, particularly in the realms of machine learning and deep learning applications, elucidating its role in early disease detection and the formulation of personalized treatment strategies. The synergy between computer-based tools and expert-driven approaches is examined, underscoring their collaborative role in enhancing the accuracy and dependability of diagnoses. Additionally, we address the ethical considerations and challenges associated with the incorporation of automation in nephrology. The paper provides a concise overview of in-depth analysis while illustrating the promising prospects of these innovative methodologies for reshaping nephrology research and patient care.

关键词： Kidney Diseases Nephrology Artificial intelligence Blood Proteins Medical services Expert systems Neural networks Automation Expert system artificial intelligence neural networks classification numerical algorithms automation system machine learning algorithms in nephrology kidney disease AI in medicine

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STOCHASTIC-MODELS, numerical algorithms AND OPTIMAL COMPUTERIZED-GRAPHICS AND DECISION-MAKING PROCESSES FOR NUCLEAR-PLANT SURVEILLANCE AND ANOMALY DETECTION

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PROGRESS IN NUCLEAR ENERGY 1985年第1-3期15卷 77-83页

作者： KEMENY, LG School of Nuclear Engineering University of New South Wales P.O. Box 1 Kensington N.S.W. 2033 Australia

The identification, on-line and in near to real-time, of the resonant frequencies, modes and amplitudes of selected key reactor components and the visual monitoring of these phenomena by nuclear power plant operating staff will serve to further the safety and control philosophy of nuclear systems and lead to design optimisation. The rapid recognition of the onset of unusual or accidental conditions in reactor sub-channels by means of the optimal filtering of noise-like sources will lead to the development of new safety systems. In this paper a computer based nuclear power plant surveillance system utilising pattern recognition techniques is described and the results of preliminary tests and experiments carried out with it are discussed. Computer based algorithms utilising correlation and spectral analysis and linear and non-linear auto-regression techniques are assessed and their optimal utilisation described.

关键词： anomaly detection Noise analysis nuclear power plant numerical algorithms pattern recognition regression analysis spectral analysis stochastic processes surveillance and control

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