A new generation 99 line Matlab code for compliance Topology Optimization and its extension to 3D

Compact and efficient Matlab implementations of compliance Topology Optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from $3\cdot 10^{4}$ to $4.8\cdot10^{5}$ elements, the 2D version, named top99neo, shows speedups from 2.55 to 5.5 times compared to the well-known top88 code (Andreassen-etal 2011). The 3D version, named top3D125, is the most compact and efficient Matlab implementation for 3D TO to date, showing a speedup of 1.9 times compared to the code of Amir-etal 2014, on a discretization with $2.2\cdot10^{5}$ elements. For both codes, improvements are due to much more efficient procedures for the assembly and implementation of filters and shortcuts in the design update step. The use of an acceleration strategy, yielding major cuts in the overall computational time, is also discussed, stressing its easy integration within the basic codes.Comment: 17 pages, 8 Figures, 4 Table

MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures

The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of non-linear equations, for which an efficient implementation is provided. The contributions include a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to non-admissible solutions, a blind non-uniform grid construction for effective distribution support detection and approximation, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.Comment: 17 pages, 6 figure

Iterative residual-based vector methods to accelerate fixed point iterations

International audienceFixed point iterations are still the most common approach to dealing with a variety of numerical problems such as coupled problems (multi-physics, domain decomposition,...) or nonlinear problems (electronic structure, heat transfer, nonlinear mechanics, ...). Methods to accelerate fixed point iteration convergence or more generally sequence convergence have been extensively studied since the 1960's. For scalar sequences, the most popular and efficient acceleration method remains the ∆ 2 of Aitken. Various vector acceleration algorithms are available in the literature, which often aim at being multi-dimensional generalizations of the ∆ 2 method. In this paper, we propose and analyze a generic residual-based formulation for accelerating vector sequences. The question of the dynamic use of this residual-based transformation during the fixed point iterations for obtaining a new accelerated fixed point method is then raised. We show that two main classes of such iterative algorithms can be derived and that this approach is generic in that various existing acceleration algorithms for vector sequences are thereby recovered. In order to illustrate the interest of such algorithms, we apply them in the field of nonlinear mechanics on a simplified "point-wise" solver used to perform mechanical behaviour unit testings. The proposed test cases clearly demonstrate that accelerated fixed point iterations based on the elastic operator (quasi-Newton method) are very useful when the mechanical behaviour does not provide the so-called consistent tangent operator. Moreover, such accelerated algorithms also prove to be competitive with respect to the standard Newton-Raphson algorithm when available

Anderson‐accelerated polarization schemes for fast Fourier transform‐based computational homogenization

Classical solution methods in fast Fourier transform‐based computational micromechanics operate on, either, compatible strain fields or equilibrated stress fields. By contrast, polarization schemes are primal‐dual methods whose iterates are neither compatible nor equilibrated. Recently, it was demonstrated that polarization schemes may outperform the classical methods. Unfortunately, their computational power critically depends on a judicious choice of numerical parameters. In this work, we investigate the extension of polarization methods by Anderson acceleration and demonstrate that this combination leads to robust and fast general‐purpose solvers for computational micromechanics. We discuss the (theoretically) optimum parameter choice for polarization methods, describe how Anderson acceleration fits into the picture, and exhibit the characteristics of the newly designed methods for problems of industrial scale and interest

Brezinski Inverse and Geometric Product-Based Steffensen's Methods for Image Reverse Filtering

This work develops extensions of Steffensen's method to provide new tools for solving the semi-blind image reverse filtering problem. Two extensions are presented: a parametric Steffensen's method for accelerating the Mann iteration, and a family of 12 Steffensen's methods for vector variables. The development is based on Brezinski inverse and geometric product vector inverse. Variants of these methods are presented with adaptive parameter setting and first-order method acceleration. Implementation details, complexity, and convergence are discussed, and the proposed methods are shown to generalize existing algorithms. A comprehensive study of 108 variants of the vector Steffensen's methods is presented in the Supplementary Material. Representative results and comparison with current state-of-the-art methods demonstrate that the vector Steffensen's methods are efficient and effective tools in reversing the effects of commonly used filters in image processing

Efficient flexible boundary conditions for long dislocations

We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix ($\mathscr{H}$-matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms. In addition, our implementation is supported by various other tools from numerical analysis, such as a residual-based transformation of the boundary conditions to accelerate the convergence. We assess the method for a comprehensive set of examples, relevant for predicting mechanical properties, such as yield strength or ductility, including dislocation bow-out, dislocation-precipitate interaction, and dislocation cross-slip. The main result of our analysis is that the FBC method is robust, easy-to-use, and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems, the periodic array of dislocations (PAD) method, in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for large-scale atomistic simulations - without having to worry about spurious image effects that plague classical boundary conditions.Comment: revised version; contains two additional examples compared with the first versio

Análise dinâmica de turbocompressores com mancais a lubrificação termo-hidrodinâmica

Orientador: Katia Lucchesi Cavalca DediniTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Recentemente, o uso de turbocompressores em motores downsized se tornou o novo padrão em aplicações automotivas, a fim de aumentar a economia de combustível, melhorar a eficiência do motor e reduzir emissões, sendo adotados em todas as categorias de veículos. Turbocompressores automotivos podem atingir velocidades de rotação extremamente elevadas e, tipicamente, quanto mais leve o rotor, maior a velocidade que pode atingir. Essa característica particular de um típico turbocompressor ¿ peso baixo e alta velocidade de rotação ¿ induz complexos fenômenos na dinâmica do rotor, principalmente devido à característica altamente não linear dos mancais de anel flutuante sustentando o eixo girante. Além disso, num turbocompressor, o uso de mancais axiais de dupla ação é imperativo, para sustentar a força axial desigual proveniente do fluxo de gás na turbina e do fluxo de ar no compressor. Nesse trabalho, desenvolveu-se um modelo rotordinâmico confiável de um turbocompressor, cujo eixo girante é suportado por mancais de anel flutuante e mancais axiais, incluindo variações de temperatura nos filmes de óleo. O modelo do mancal axial é composto por uma análise completa termo-hidrodinâmica, considerando efeitos de desalinhamento angular. Ambos os campos de pressão e temperatura são examinados e a capacidade de carga do mancal axial é avaliada. O modelo do mancal de anel flutuante é ligeiramente simplificado, a fim de reduzir os custos computacionais, mas inclui todo comportamento não linear e efeitos térmicos. As principais contribuições do trabalho são: a necessidade de incluir efeitos térmicos num modelo confiável dos mancais a fim de melhor estimar a carga suportada pelos mesmos; a inadequada aproximação do comportamento dinâmico dos mancais por coeficientes lineares equivalentes, devido ao comportamento altamente não linear dos mancais; e a inclusão obrigatória do mancal axial num modelo robusto e confiável do turbocompressor, devido à efeitos de acoplamento axial-radial que podem afetar as vibrações laterais típicas de um turbocompressorAbstract: In recent years, the use of turbochargers in downsized engines has become a new standard in automotive applications, in order to increase fuel economy, improve the engine efficiency and reduce emissions, being adopted in all vehicle categories. Automotive turbochargers can achieve extremely high rotational speeds and, typically, the lighter the rotor, the higher the rotational speed it can achieve. This particular characteristic of a typical turbocharger ¿ light weight and high rotational speed ¿ lead to complex rotordynamic phenomena, mainly due to the highly nonlinear characteristics of the floating ring bearings sustaining the rotating shaft. In addition, in a turbocharger, the use of a double-acting thrust bearing is imperative, to sustain the axial force imbalance of the gas flow in the turbine and the airflow in the compressor. In this work, we develop a reliable turbocharger rotordynamic model, whose rotating shaft is supported by both floating ring and thrust bearings, including temperature variations in the oil films. The thrust bearing model is composed of a full thermo-hydrodynamic analysis, considering angular misalignment effects. Both pressure and temperature fields are evaluated and the thrust bearing load-carrying capacity is examined. The floating ring bearing model is somewhat simplified, in order to ease computations, but it includes its full nonlinear behaviour and thermal effects. The main findings of the work are the necessity to include thermal effects in a reliable bearing model to better estimate the bearings supported load, the unsuitability of approximating the bearings dynamic behaviour by its equivalent linear coefficients, due to its high nonlinear characteristics, and the mandatory inclusion of the thrust bearing in a reliable and robust rotordynamic turbocharger model, due to axial-radial coupling effects that may affect lateral vibrations of a typical turbochagerDoutoradoMecânica dos Sólidos e Projeto MecânicoDoutor em Engenharia Mecânic