Subdivision-stabilised immersed b-spline finite elements for moving boundary flows

An immersed finite element method is presented to compute flows with complex moving boundaries on a fixed Cartesian grid. The viscous, incompressible fluid flow equations are discretized with b-spline basis functions. The two-scale relation for b-splines is used to implement an elegant and efficient technique to satisfy the LBB condition. On non-grid-aligned fluid domains and at moving boundaries, the boundary conditions are enforced with a consistent penalty method as originally proposed by Nitsche. In addition, a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut-cells. The versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations.

A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

A fixed-grid b-spline finite element technique for fluid-structure interaction

We present a fixed-grid finite element technique for fluid-structure interaction problems involving incompressible viscous flows and thin structures. The flow equations are discretised with isoparametric b-spline basis functions defined on a logically Cartesian grid. In addition, the previously proposed subdivision-stabilisation technique is used to ensure inf-sup stability. The beam equations are discretised with b-splines and the shell equations with subdivision basis functions, both leading to a rotation-free formulation. The interface conditions between the fluid and the structure are enforced with the Nitsche technique. The resulting coupled system of equations is solved with a Dirichlet-Robin partitioning scheme, and the fluid equations are solved with a pressure-correction method. Auxiliary techniques employed for improving numerical robustness include the level-set based implicit representation of the structure interface on the fluid grid, a cut-cell integration algorithm based on marching tetrahedra and the conservative data transfer between the fluid and structure discretisations. A number of verification and validation examples, primarily motivated by animal locomotion in air or water, demonstrate the robustness and efficiency of our approach. © 2013 John Wiley & Sons, Ltd.

B-spline methods in R-matrix theory for scattering in two-electron systems

The use of B-spline basis sets in R-matrix theory for scattering processes has been investigated. In the present approach a B-spline basis is used for the description of the inner region, which is matched to the physical outgoing wavefunctions by the R-matrix. Using B-splines, continuum basis functions can be determined easily, while pseudostates can be included naturally. The accuracy for low-energy scattering processes is demonstrated by calculating inelastic scattering cross sections for e colliding on H. Very good agreement with other calculations has been obtained. Further extensions of the codes to quasi two-electron systems and general atoms are discussed as well as the application to (multi) photoionization.

Partial and total multiphoton detachment rates for H- in a perturbative B-spline-based approach

An ab initio approach has been applied to study multiphoton detachment rates for the negative hydrogen ion in the lowest nonvanishing order of perturbation theory. The approach is based on the use of B splines allowing an accurate treatment of the electronic repulsion. Total detachment rates have been determined for two- to six-photon processes as well as partial rates for detachment into the different final symmetries. It is shown that B-spline expansions can yield accurate continuum and bound-state wave functions in a very simple manner. The calculated total rates for two- and three-photon detachment are in good agreement with other perturbative calculations. For more than three-photon detachment little information has been available before now. While the total cross sections show little structure, a fair amount of structure is predicted in the partial cross sections. In the two-photon process, it is shown that the detached electrons mainly have s character. For four- and six-photon processes, the contribution from the d channel is the most important. For three- and five-photon processes p electrons dominate the electron emission spectrum. Detachment rates for s and p electrons show minima as a function of photon energy. © 1994 The American Physical Society.

Genetic and bacterial programming for B-Spline neural networks design

The design phase of B-spline neural networks is a highly computationally complex task. Existent heuristics have been found to be highly dependent on the initial conditions employed. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this paper, the Bacterial Programming approach is presented, which is based on the replication of the microbial evolution phenomenon. This technique produces an efficient topology search, obtaining additionally more consistent solutions.

A hybrid training method for B-spline neural networks

Current and past research has brought up new views related to the optimization of neural networks. For a fixed structure, second order methods are seen as the most promising. From previous works we have shown how second order methods are of easy applicability to a neural network. Namely, we have proved how the Levenberg-Marquard possesses not only better convergence but how it can assure the convergence to a local minima. However, as any gradient-based method, the results obtained depend on the startup point. In this work, a reformulated Evolutionary algorithm - the Bacterial Programming for Levenberg-Marquardt is proposed, as an heuristic which can be used to determine the most suitable starting points, therefore achieving, in most cases, the global optimum.

B-spline and neuro-fuzzy models design with function and derivative equalities

The design of neuro-fuzzy models is still a complex problem, as it involves not only the determination of the model parameters, but also its structure. Of special importance is the incorporation of a priori information in the design process. In this paper two known design algorithms for B-spline models will be updated to account for function and derivatives equality restrictions, which are important when the neural model is used for performing single or multi-objective optimization on-line.

Design of B-spline neural networks using a bacterial programming approach

The design phase of B-spline neural networks represents a very high computational task. For this purpose, heuristics have been developed, but have been shown to be dependent on the initial conditions employed. In this paper a new technique, Bacterial Programming, is proposed, whose principles are based on the replication of the microbial evolution phenomenon. The performance of this approach is illustrated and compared with existing alternatives.

Completely supervised training algorithms for B-spline neural networks and neuro-fuzzy systems

Complete supervised training algorithms for B-spline neural networks and fuzzy rule-based systems are discussed. By interducing the relationship between B-spline neural networks and certain types of fuzzy models, training algorithms developed initially for neural networks can be adapted by fuzzy systems.

Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.

Otimização de pré-formas e matrizes em problemas bidimensionais de forjamento

Este trabalho apresenta uma sistemática para realizar a otimização numérica de pré-formas e de matrizes em problemas de forjamento axissimétricos e em estado plano de deformações. Para este fim, desenvolveu-se um código computacional composto basicamente de três módulos: módulo de pré-processamento, módulo de análise e módulo de otimização. Cada um destes foi elaborado acrescentando rotinas em programas comerciais ou acadêmicos disponíveis no GMAp e no CEMACOM. Um programa gerenciador foi desenvolvido para controlar os módulos citados no processo de otimização. A abordagem proposta apresenta uma nova função objetivo a minimizar, a qual está baseada em uma operação booleana XOR (exclusive or) sobre os dois polígonos planos que representam a geometria desejada para o componente e a obtida na simulação, respectivamente. Esta abordagem visa eliminar possíveis problemas geométricos associados com as funções objetivo comumente utilizadas em pesquisas correlatas. O trabalho emprega análise de sensibilidade numérica, via método das diferenças finitas. As dificuldades associadas a esta técnica são estudadas e dois pontos são identificados como limitadores da abordagem para problemas de conformação mecânica (grandes deformações elastoplásticas com contato friccional): baixa eficiência e contaminação dos gradientes na presença de remalhamentos. Um novo procedimento de diferenças finitas é desenvolvido, o qual elimina as dificuldades citadas, possibilitando a sua aplicação em problemas quaisquer, com características competitivas com as da abordagem analítica Malhas não estruturadas são tratadas mediante suavizações Laplacianas, mantendo as suas topologias. No caso de otimização de pré-formas, o contorno do componente a otimizar é parametrizado por B-Splines cujos pontos de controle são adotados como variáveis de projeto. Por outro lado, no caso de otimização de matrizes, a parametrização é realizada em termos de segmentos de reta e arcos de circunferências. As variáveis de projeto adotadas são, então, as coordenadas das extremidades das retas, os raios e centros dos arcos, etc. A sistemática é fechada pela aplicação dos algoritmos de programação matemática de Krister Svanberg (Método das Assíntotas Móveis Globalmente Convergente) e de Klaus Schittkowski (Programação Quadrática Sequencial – NLPQLP). Resultados numéricos são apresentados mostrando a evolução das implementações adotadas e o ganho de eficiência obtido.

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Modelos para estimação de componentes de (co)variância para produção de leite no dia do controle de vacas da raça Holandesa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.