EM - Escola de Minas

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Análise de problemas 3D no domínio da frequência via processo de acoplamento multidomínio.
(2000) Martins, Cláudio José; Araújo, Francisco Célio de
Neste trabalho é apresentado um algoritmo para a resolução de problemas elastodinâmicos tridimensionais no domínio da frequência via formulação direta do Método dos Elementos de Contorno(BEM), sendo enfatizados o desenvolvimento de uma técnica de acoplamento multidomínio e o estudo de procedimentos numéricos para a solução de sistemas algébricos de equações(diretos e iterativos). O algoritmo genérico de acoplamento BE/BE se baseia numa técnica de não-condensamento, ainda que apenas os blocos de matriz contendo coeficientes com valores complexos não nulos sejam armazenados e manipulados durante o processo de análise. Com o objetivo de aumentar a eficiência do algoritmo, solvers iterativos baseados nos processos de Lanczos e gradiente biconjugado, eventualmente precondicionados, que possuem excelente performance em análises via MEC envolvendo matrizes com coeficientes reais, serão implementados. Detalhes da formulação do algoritmo elastodinâmico desenvolvido e dos procedimentos iterativos serão discutidos. A performance do algoritmo é então verificada na resolução de vários problemas tridimensionais frequência e tempo-dependentes. Parâmetros importantes para a estimativa da eficiência do algoritmo, e que serão apresentadas nos resultados desta tese de mestrado são a precisão, número de iterações e tempo de processamento requerido.
An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics.
(2001) Araújo, Francisco Célio de; Martins, Cláudio José; Mansur, Webe João
This work is concerned with the development of an efficient and general algorithm to solve frequency-domain problems modelled by the boundary element method based on a sub-region technique. A specific feature of the algorithm discussed here is that the global sparse matrix of the coupled system is implicitly considered, i.e. problem quantities are not condensed into interface variables. The proposed algorithm requires that only the block matrices with non-zero complex-valued coefficients be stored and manipulated during the analysis process. In addition, the efficiency of the technique presented is improved by using iterative solvers. The good performance of pre-conditioned iterative solvers for systems of equations having real-valued coefficients, well demonstrated in the literature, is confirmed for the present case where the system matrix coefficients are complex. The efficiency of the algorithm described here is verified by analysing a soil–machine foundation interaction problem. CPU time and accuracy are the parameters used for estimating the computational efficiency.
New developments on BE/BE multi-zone algorithms based on krylov solvers - applications to 3D frequency-dependent problems.
(2004) Araújo, Francisco Célio de; Mansur, Webe João; Dors, Cleberson; Martins, Cláudio José
In this paper, new developments concerning the use of BE/BE coupling algorithms for solving 3D time-harmonic problems are reported. The algorithms are derived by considering different iterative solvers. Their chief idea is to work with the global sparse matrix of the coupled system, however without considering the many zero blocks associated with the non-coupled nodes of different subregions. The use of iterative solvers makes it possible to store and manipulate only the block matrices with non-zero coefficients. Preconditioned iterative solvers based on the Lanczos, bi-conjugate gradient, and GMRES (generalized minimal residual) methods are used to derive the BE/BE coupling algorithms. A description of the formulation of these solvers, which are completely general and can be applied to any non-singular, non-hermitian systems of equations, is provided. The performance of the algorithms is verified by solving some foundation-soil interaction problems. Important parameters for estimating the efficiency of the algorithms as required CPU times, matrix sparsity, and accuracy of the obtained responses are presented in the results of the paper.
On the use of pseudo-forces to consider initial conditions in 3D time- and frequency-domain acoustic analysis.
(2006) Martins, Cláudio José; Carrer, José Antonio Marques; Mansur, Webe João; Araújo, Francisco Célio de
This work is mainly concerned with a general strategy, based on well known concepts of classical mechanics, for taking into account initial conditions in frequency-domain (FD) and time-domain (TD) analyses. A general approach, extended here to three-dimensional applications, is presented. Special problems associated with analyses through Discrete-Fourier-Transform (DFT) algorithms, as those occurring in consequence of a non-correct choice of extended period or those connected with aliasing phenomenon, are also discussed. Furthermore, an alternative starting procedure for time-marching schemes (in TD analyses) is proposed. At the end of the paper, to validate the proposed techniques and to demonstrate their generality, two- and three-dimensional problems with non-homogeneous initial conditions are solved through frequency- and time-domain approaches by employing the Finite Element Method (FEM). Numerical results are compared with existing analytical solutions.

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