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Performance of the BEM solution in 3D acoustic wave scattering

Tadeu, A. J. B.; Godinho, L.; Santos, P.
Fonte: Universidade de Coimbra Publicador: Universidade de Coimbra
Tipo: Artigo de Revista Científica Formato: aplication/PDF
Português
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A fixed cylindrical circular cavity and a cylindrical circular column of fluid of infinite length submerged in a homogeneous fluid medium, and subjected to a pressure point source, for which closed form solutions are known, are used to assess the performance of constant, linear and quadratic boundary elements in the analysis of acoustic scattering.; http://www.sciencedirect.com/science/article/B6V1P-43CB9CN-3/1/002dea35b84a8e01ba5193ee8925f4e6

3D scattering by multiple cylindrical cavities buried in an elastic formation

António, Julieta; Tadeu, António
Fonte: Universidade de Coimbra Publicador: Universidade de Coimbra
Tipo: Artigo de Revista Científica Formato: aplication/PDF
Português
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This paper presents the three-dimensional scattering field obtained when multiple cylindrical circular cavities of infinite length buried in a homogeneous elastic medium, are subjected to dilatational point loads placed at some point in the medium. The solution is formulated using boundary elements for a wide range of frequencies and spatially harmonic line loads, which are then used to obtain time series by means of (fast) inverse Fourier transforms into space-time. The method and the expressions presented are implemented and validated by applying them to a cylindrical circular cavity buried in an infinite homogeneous elastic medium subjected to a dilatational point load, for which the solution is calculated in closed form. The boundary elements method is then used to evaluate the wave-field elicited by a dilatational point load source in the presence of a different number of cylindrical oval cavities. Simulation analyses using this idealized model are then applied to the study of wave propagation patterns in the vicinity of these inclusions. The amplitude of the wavefield in the frequency vs axial-wavenumber domain is presented, allowing the recognition, identification, and physical interpretation of the variation of the wavefield.; http://www.sciencedirect.com/science/article/B6VKW-430NR63-2/1/4f284136d4939dc660fa33a3cf4fa92c

Use of constant, linear and quadratic boundary elements in 3D wave diffraction analysis

Tadeu, A.; António, J.
Fonte: Universidade de Coimbra Publicador: Universidade de Coimbra
Tipo: Artigo de Revista Científica Formato: aplication/PDF
Português
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The performance of the Boundary Element Method (BEM) depends on the size of the elements and the interpolation function used. However, improvements in accuracy and efficiency obtained with both expansion and grid refinement increases demand on the computational effort. This paper evaluates the performance of constant, linear and quadratic elements in the analysis of the three-dimensional scattering caused by a cylindrical cavity buried in an infinite homogeneous elastic medium subjected to a point load. A circular cylindrical cavity for which analytical solutions are known is used in the simulation analysis. First, the dominant BEM errors are identified in the frequency domain and related to the natural vibration modes of the inclusion. Comparisons of BEM errors are then made for different types of boundary elements, maintaining similar computational costs. Finally, the accuracy of the BEM solution is evaluated when the nodal points are moved inside linear and quadratic discontinuous elements.; http://www.sciencedirect.com/science/article/B6V2N-3YN93TX-1/1/28e4a46d3da333118f419ca7b5266239

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

RIBEIRO, Dimas Betioli; PAIVA, Joao Batista de
Fonte: ELSEVIER SCI LTD Publicador: ELSEVIER SCI LTD
Tipo: Artigo de Revista Científica
Português
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A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

Aplicação do acoplamento entre o MEC e o MEF para o estudo da interação dinâmica elastoplástica entre o solo e estruturas ; BEM/FEM coupling application to the study of the elastoplastic dynamic interaction between soil and structures

Almeida, Francisco Patrick Araujo
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 24/10/2003 Português
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O objetivo do presente trabalho é o desenvolvimento de um código computacional que possibilite a análise dinâmica de estruturas tridimensionais em regime elástico-linear acopladas ao solo, tratado como meio infinito elastoplástico. As superestruturas são tratadas por elementos finitos simples de casca e de barra geral, as estruturas de fundações são tratadas por elementos de casca que simulam o contato com o solo, modelando radiers, túneis e reservatórios enterrados. Blocos são modelados por elementos de contorno tridimensionais. O solo é modelado de duas maneiras distintas: na região plastificada emprega-se a solução fundamental de Kelvin (estática) e na região não plastificada (elástica) adota-se a solução fundamental do problema de Stokes. O acoplamento entre os meios é feito aplicando-se a técnica de subregiões. Deve ficar claro que todo procedimento estático equivalente foi implementado. Vários exemplos numéricos são apresentados, onde se percebe a eficiência do código computacional desenvolvido; The objective of the present work is the development of a computational code that makes possible dynamic analyses of three-dimensional structures in elastic-linear behavior coupled to the soil, modeled as elastoplastic infinite medium. Simple finite elements...

Desenvolvimento de um novo algoritmo para análise viscoplástica com o método dos elementos de contorno.; Development of a new boundary elements algorithm for viscoplastic analysis.

Carbone, Nicholas
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 30/07/2007 Português
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A busca por novos modelos matemáticos e técnicas inovadoras para análises numéricas tem sido tema de muitas pesquisas. Em análises de modelos que possuem domínios infinitos e semi-infinitos, o Método dos Elementos de Contorno (MEC) sobressai-se como uma das mais eficientes ferramentas numéricas. Por outro lado, em análises não-lineares o MEC requer a avaliação de integrais de domínio, diminuindo as vantagens de uma discretização apenas do contorno do modelo analisado. Neste trabalho apresenta-se uma técnica inovadora que trata as integrais de domínio, não adequadas para uma representação pura do contorno, em análises de modelos com materiais viscoplásticos. Na abordagem proposta, utiliza-se um novo algoritmo de visualização proposto por Noronha & Pereira para detectar as regiões de plastificação automaticamente. Este procedimento de detecção é realizado de forma incremental por meio de predições (gradiente como direção de busca) e iterações (Newton-Raphson). Uma vez que as regiões sejam obtidas, torna-se possível transformar as integrais de domínio em integrais de contorno de forma direta. Obtém-se assim uma abordagem baseada apenas na discretização do contorno dos modelos, mantendo uma das principais vantagens da utilização do MEC. Foram realizados neste trabalho alguns exemplos numéricos que apresentaram excelentes resultados em comparação com o Método dos Elementos Finitos (MEF) e com resultados encontrados na literatura.; The search for new mathematical models and innovative techniques for numerical analyses has been subject of many research studies. In analysis of models with infinite and semi-infinite domains...

Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF; Study and application of an infinite boundary element for soil-structure interaction analysis via FEM/BEM coupling

Ribeiro, Dimas Betioli
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 26/03/2009 Português
Relevância na Pesquisa
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Neste trabalho, é desenvolvido um programa de computador para a análise estática e tridimensional de problemas de interação solo-estrutura. O programa permite considerar várias camadas de solo, cada qual com características físicas diferentes. Sobre este solo, o qual pode conter estacas, podem ser apoiados diversos tipos de estruturas, tais como placas e até um edifício. Todos os materiais considerados são homogêneos, isotrópicos, elásticos e lineares. O solo tridimensional é modelado com o método dos elementos de contorno (MEC), empregando as soluções fundamentais de Kelvin e uma técnica alternativa na consideração do maciço não-homogêneo. Esta técnica, que é uma contribuição original deste trabalho, é baseada no relacionamento das soluções fundamentais de deslocamento dos diferentes domínios, permitindo que sejam analisados como um único sólido sem a necessidade de equações de equilíbrio e compatibilidade. Isso reduz o sistema de equações final e melhora a precisão dos resultados, conforme comprovado nos exemplos apresentados. Para reduzir o custo computacional sem prejudicar a precisão dos resultados, é utilizada uma malha de elementos de contorno infinitos (ECI) nas bordas da malha de ECs para modelar o comportamento das variáveis de campo em longas distâncias. A formulação do ECI mapeado utilizado é outra contribuição original deste trabalho...

Método dos elementos de contorno aplicado na análise do escorregamento de estacas.; Boundary element method applied in pile slip analysis.

Vick, Guilherme Basílio
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 04/04/2014 Português
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Neste trabalho apresenta-se um modelo numérico para a análise de problemas tridimensionais envolvendo a interação mecânica estaca-solo, acoplando-se o Método dos Elementos de Contorno (MEC) ao Método dos Elementos Finitos (MEF). O solo é modelado com o MEC utilizando-se as soluções fundamentais de Mindlin, assumindo um meio semi-infinito, homogêneo, isotrópico e elástico-linear. As estacas, modeladas com o MEF, consistem em um elemento único, com quatro nós e 14 parâmetros nodais (três deslocamentos em cada nó e mais duas rotações no topo da estaca). Cada uma das estacas é levada em consideração no MEC como uma linha de carga. Considera-se o escorregamento das estacas em relação ao maciço, empregando modelos de aderência para a definição da evolução das tensões tangenciais ao longo do comprimento das estacas. São empregados, como funções de forma, polinômios do quarto grau para os deslocamentos horizontais, cúbicos para os deslocamentos verticais e tensões horizontais ao longo do fuste e quadráticos para as tensões verticais do fuste e escorregamento. A reação da ponta da estaca é calculada assumindo tensão constante na base.; This work presents a method for tri-dimensional pile-soil interaction problems...

Numerical methods for the dynamics of unbounded domains

Mesquita,Euclides; Pavanello,Renato
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2005 Português
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The present article discusses the relation between boundary conditions and the Sommerfeld radiation condition underlying the dynamics of unbounded domains. It is shown that the classical Dirichlet, Neumann and mixed boundary conditions do not fulfill the radiation condition. In the sequence, three strategies to incorporate the radiation condition in numerical methods are outlined. The inclusion of Infinite Elements in the realm of the Finite Element Method (FEM), the Dirichlet-to-Neumann (DtN) mapping and the Boundary Element Method (BEM) are described. Examples of solved dynamic problems in unbounded domains are given for the Helmholtz and the Navier operators. The advantages and limitations of the methodologies are discussed and pertinent literature is provided.

Three-Dimensional Dynamic Analyses of Track-Embankment-Ground System Subjected to High Speed Train Loads

Fu, Qiang; Zheng, Changjie
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
Publicado em 26/02/2014 Português
Relevância na Pesquisa
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A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

Day, Brad Allen
Fonte: Universidade Rice Publicador: Universidade Rice
Português
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A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. (Abstract shortened by UMI.)

A practical scheme for 3D geoelectrical forward modeling with finite-infinite element coupling method

Tang, J.T.; Gong, J.
Fonte: Electromagnetics Academy; United States Publicador: Electromagnetics Academy; United States
Tipo: Conference paper
Publicado em //2010 Português
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In this study, fast and visualized pre and post processing for infinite element method was achieved by customized development based on the universal 3D modeling software named GiD, while infinite elements were introduced to form the finite-infinite element coupling method, which could substitute the conventional mixed boundary conditions and solve the problems cased by artificial boundary conditions. For the customized development on GiD, we only need to program the so-called problem types with simple script language, then models could be build in the graphic interface and output in the format fitting our calculation program. As to our finite-infinite element method, Astley mapped wave envelope infinite elements were employed to continue the electrical potential to infinity. Then, a new type of shape functions was created and it was proved to be the optimal one in both accuracy and time consumption by comparing with several other shape functions. Finally, the availability and superiority of this coupling algorithm were confirmed by several numerical tests with various electrode arrays.; Jing-Tian Tang and Jin-Zhe Gong

Infinite reduced words and the Tits boundary of a Coxeter group

Lam, Thomas; Thomas, Anne
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish that when W is word hyperbolic, the limit weak order is the disjoint union of weak orders of finite Coxeter groups. We also establish, for each boundary point \xi, a natural order-preserving correspondence between infinite reduced words which "point towards" \xi, and elements of the reflection subgroup of W which fixes \xi.; Comment: 28 pages, 2 figures. Version 2: additional references in introduction. Version 3: results are unchanged but exposition has been substantially revised following referee's suggestions. To appear in Int. Math. Res. Not

High order Curl-conforming Hardy space infinite elements for exterior Maxwell problems

Nannen, Lothar; Hohage, Thorsten; Schädle, Achim; Schöberl, Joachim
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/03/2011 Português
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A construction of prismatic Hardy space infinite elements to discretize wave equations on unbounded domains $\Omega$ in $H^1_{loc}(\Omega)$, $H_{loc}(curl;\Omega)$ and $H_{loc}(div;\Omega)$ is presented. As our motivation is to solve Maxwell's equations we take care that these infinite elements fit into the discrete de Rham diagram, i.e. they span discrete spaces, which together with the exterior derivative form an exact sequence. Resonance as well as scattering problems are considered in the examples. Numerical tests indicate super-algebraic convergence in the number of additional unknowns per degree of freedom on the coupling boundary that are required to realize the Dirichlet to Neumann map.; Comment: 27 pages

Distance to boundary and minimum-error discrimination

Haapasalo, Erkka; Sedlak, Michal; Ziman, Mario
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any explicit topology) how far the given element is from the boundary. It is shown that one of the elements from the boundary can be always chosen to be an extremal element. We focus on evaluation of this quantity for quantum sets of states, channels and observables. We show that boundariness is intimately related to (semi)norms that provide an operational interpretation of this quantity. In particular, the minimum error probability for discrimination of a pair of quantum devices is lower bounded by the boundariness of each of them. We proved that for states and observables this bound is saturated and conjectured this feature for channels. The boundariness is zero for infinite-dimensional quantum objects as in this case all the elements are boundary elements.; Comment: 14 pages, 6 figures (final version)

Effect of PCC Joint Skew on Reflective Cracking in HMA Overlays

Ghauch, Ziad G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Reflective cracking is a relatively premature distress that occurs in HMA materials overlaying cracked and jointed underlying pavements. The high concentration of stresses and strains in the vicinity of the discontinuity of the old pavement causes the cracks to reflect into the newly placed HMA overlay. While it is a common practice to use skewed transverse joints in rigid pavements to improve the latter's performance, the impact of such a practice on the cracking of a potential HMA overlay has not been examined so far. In this context, this study investigates the effect of using skewed transverse joints in rigid pavements on reflective cracking development in the HMA overlay. Advanced three-dimensional Finite Element models including viscoelastic material properties for the HMA overlay, 3D beam modeling of dowel bars, non-uniform tire-pavement contact stresses, friction interfaces, and infinite boundary elements were constructed for both normal and skewed transverse joints using ABAQUS v-6.11. The potential for reflective cracking was monitored through the fracture mechanics J-integral parameter. Results obtained show, among other things, that the practice of skewing transverse joints increases the potential for reflective cracking development in the asphalt concrete overlay.; Comment: This paper has been withdrawn by the author

On Robin boundary conditions and the Morse potential in quantum mechanics

Belchev, B.; Walton, M. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/02/2010 Português
Relevância na Pesquisa
27.890125%
The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example of a contact interaction. A non-relativistic particle moving freely on the half-line is treated as moving on the full line in the presence of an infinite potential wall, realized as a limit of a Morse potential. We show that the wave functions for the Morse states can become those for a free particle on the half-line with Robin boundary conditions. However, Dirichlet boundary conditions (standard walls) are obtained unless a mass-dependent fine tuning (to a reflection resonance) is imposed. This phenomenon was already observed for piece-wise flat potentials, so it is not removed by smoothing. We argue that it explains why standard quantum walls are standard. Next we consider the Wigner functions (the symbols of both diagonal and off-diagonal density operator elements) of phase-space quantum mechanics. Taking the (fine-tuned) limit, we show that our Wigner functions do reduce to the expected ones on the half-line. This confirms that the Wigner transform should indeed be unmodified for this contact interaction.; Comment: 19 pages

The half-infinite XXZ chain in Onsager's approach

Baseilhac, P.; Belliard, S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed `Onsager's approach'. Inspired by the finite size case, for any type of integrable boundary conditions it is shown that the transfer matrix is simply expressed in terms of the elements of a new type of current algebra recently introduced. In the massive regime $-1

Domains in Infinite Jets: C-Spectral Sequence

Vinogradov, A. M.; Moreno, G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/09/2006 Português
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Domains in infinite jets present the simplest class of diffieties with boundary. In this note some basic elements of geometry of these domains are introduced and an analogue of the C-spectral sequence in this context is studied. This, in particular, allows cohomological interpretation and analysis of initial data, boundary conditions, etc, for general partial differential equations and of transversality conditions in calculus of variations. This kind applications and extensions to arbitrary diffieties will be considered in subsequent publications.; Comment: 7 pages; no proofs given

Modeling Specular and Diffuse Reflection Sound Fields in Enclosures with an Energy-Intensity Boundary Element Method

Michalis, Krista
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2011 Português
Relevância na Pesquisa
47.59698%

Steady-state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics that are orthogonal on the half-space. The amplitudes of these harmonics are determined by a Lagrange multiplier method to satisfy the energy conservation integral constraint. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Monotonic convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. The method is very computationally efficient. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and a broadband image method, demonstrating high accuracy. The method of absorption scaling is verified for complicated 3-D cases...