Showing papers in "Archives of Computational Methods in Engineering in 2007"
TL;DR: (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations are considered.
Abstract: In this paper we consider (hierarchical, La-grange)reduced basis approximation anda posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equa-tions. The essential ingredients are (primal-dual)Galer-kin projection onto a low-dimensional space associated with a smooth “parametric manifold” - dimension re-duction; efficient and effective greedy sampling meth-ods for identification of optimal and numerically stable approximations - rapid convergence;a posteriori er-ror estimation procedures - rigorous and sharp bounds for the linear-functional outputs of interest; and Offine-Online computational decomposition strategies - min-imummarginal cost for high performance in the real-time/embedded (e.g., parameter-estimation, control)and many-query (e.g., design optimization, multi-model/ scale)contexts. We present illustrative results for heat conduction and convection-diffusion,inviscid flow, and linear elasticity; outputs include transport rates, added mass,and stress intensity factors.
1,090 citations
TL;DR: This paper reviews the CAE modelling techniques which can be used for the analysis of time-harmonic acoustic problems and focusses on techniques which have the Trefftz approach as baseline methodology.
Abstract: Over the last decade, Computer Aided Engineering (CAE) tools have become essential in the assessment and optimization of the acoustic characteristics of products and processes. The possibility of evaluating these characteristics on virtual prototypes at almost any stage of the design process reduces the need for very expensive and time consuming physical prototype testing. However, despite their steady improvements and extensions, CAE techniques are still primarily used by analysis specialists. In order to turn them into easy-to-use, versatile tools that are also easily accessible for designers, several bottlenecks have to be resolved. The latter include, amongst others, the lack of efficient numerical techniques for solving system-level functional performance models in a wide frequency range. This paper reviews the CAE modelling techniques which can be used for the analysis of time-harmonic acoustic problems and focusses on techniques which have the Trefftz approach as baseline methodology. The basic properties of the different methods are highlighted and their strengths and limitations are discussed. Furthermore, an overview is given of the state-of-the-art of the extensions and the enhancements which have been recently investigated to enlarge the application range of the different techniques. Specific attention is paid to one very promising Trefftz-based technique, which is the so-called wave based method. This method has all the necessary attributes for putting a next step in the evolution towards truly virtual product design.
138 citations
TL;DR: In this paper, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed, as well as some interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex sideconstraints, strongly nonlinear terms.
Abstract: The Landau-Lifshitz (LL) equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex side-constraints, strongly nonlinear terms. These effects influence also numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed.
128 citations
TL;DR: It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.
Abstract: The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh).
123 citations
TL;DR: Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures as mentioned in this paper, where the most important and widely used depth averaged turbulence models are reviewed and discussed.
Abstract: Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures This paper deals with depth averaged turbulence modelling The most important and widely used depth averaged turbulence models are reviewed and discussed, and a depth averaged algebraic stress model is presented A finite volume model for solving the depth averaged shallow water equations coupled with several turbulence models is described with special attention to the modelling of wet-dry fronts In order to asses the performance of the model, several flows are modelled and the numerical results are compared with experimental data
115 citations
TL;DR: In this paper, the authors present a review of the numerical strategies used for metal cutting and a short discussion of their relative merits and drawbacks, and illustrate what numerical techniques, models and pertinent parameters are needed for successful simulations.
Abstract: The modelling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. The present work outlines the wide range of complex physical phenomena involved in the chip formation in a descriptive manner. In order to improve and understand the process different numerical strategies have been used for simulation. Several of these numerical strategies are reviewed and a short discussion of their relative merits and drawbacks is presented. By means of several examples, where a combined experimental/numerical effort was undertaken, we try to illustrate what numerical techniques, models and pertinent parameters are needed for successful simulations.
97 citations
TL;DR: In this paper, a hierarchical model for the analysis of multifield problems related to multilayered plates subjected to mechanical, electric and thermal loads is presented, and results in form of tables and graphs are given in order to validate the proposed elements.
Abstract: The paper presents a hierarchic model for the analysis of multifield problems related to multilayered plates subjected to mechanical, electric and thermal loads. In the framework of a unified formulation (UF), the finite element method has been used to derive a complete family of plate elements distinguished from one another by the variational statement and the laminate kinematic assumptions upon which each of them is based. Depending on the accuracy required by the analysis, the most appropriate element can be easily derived choosing the primary unknowns of the model by selecting between displacement or partially mixed formulations (Principle of Virtual Displacement, Reissner’s mixed variational theorem). The complete derivation of fully coupled variational statements (classical and partially mixed) is also given for thermopiezoelastic analysis. The description of the unknowns can then be chosen between global (ESL) and layerwise (LW). Finally the order of the expansion can be set in the range from 1 to 4 thus selecting first order or higher order plate models. Then, results in form of tables and graphs are given in order to validate the proposed elements.
95 citations
TL;DR: A critical review of past and current techniques for the computational modelling of diarthrodial joints is provided in this paper, with emphasis on the relationship of tissue microstructure with its continuum mechanical behavior.
Abstract: This paper provides a critical review of past and current techniques for the computational modelling of diarthrodial joints. The objective of the paper is to describe strategies for addressing the computational modelling of joint mechanics using the finite element (FE) method, differentiating between geometry, constitutive modelling of the components, computational aspects and applications. The structure and function of the main components of the joints are reviewed, with emphasis on the relationship of tissue microstructure with its continuum mechanical behavior. Applications to two diarthrodial joints (human knee and temporomandibular joint) in physiological, pathological andpos-surgery situations are presented and discussed. The paper concludes with a discussion of future research directions.
55 citations
TL;DR: In this article, the authors present a fully implicit iterative solution strategy which resolves the strong coupling and allows for an optimal rate of convergence of the residuals, which is a viable competitor for the solution of the highly nonlinear interaction of fluid flow with solid structures that experience large displacements and deformations.
Abstract: This article summarises the authors’ research work in the area of computational modelling of interaction of fluid flow with solid structures. Our approach relies on a fully implicit iterative solution strategy which resolves the strong coupling and allows for optimal rate of convergence of the residuals. Therefore, the methodology is a viable competitor for the solution of the highly nonlinear interaction of fluid flow with solid structures that experience large displacements and deformations.
The key ingredients of our strategy include the following: Stabilised low order velocity–pressure finite elements are used for the modelling of the fluid flow combined with an arbitrary Lagrangian–Eulerian (ALE) strategy. For the temporal discretisation of both fluid and solid bodies, the discrete implicit generalised-α method is employed. An important aspect of the present work is the introduction of the independent interface discretisation, which allows an efficient, modular and expandable implementation of the solution strategy. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of nonlinear equations is solved by means of a partitioned solution procedure, which is based on the Newton–Raphson methodology and incorporates the full linearisation of the overall incremental problem. Thus, asymptotically quadratic convergence of the residuals is achieved.
Numerical examples are presented to demonstrate the robustness and efficiency of the methodology. Finally, we present the results obtained by combining the presented methodology with a remeshing procedure.
51 citations
TL;DR: In this article, the authors show that cracks that take place in reinforced concrete elements due to tangential internal forces, such as shear and torsion, produce a nonisotropic response on the structure in the post-cracked regime and up to failure, also known as crack-induced-anisotropy.
Abstract: Inclined cracks that take place in reinforced concrete elements due to tangential internal forces, such as shear and torsion, produce a non-isotropic response on the structure in the post-cracked regime and up to failure, also known as crack-induced-anisotropy. The result is that all six internal forces acting in a cross-section are generally coupled.
43 citations
TL;DR: This work is an overview of algebraic pressure segregation methods for the incompressible Navier-Stokes equations, and has introduced predictor-corrector methods, one-loop algorithms where nonlinearity and iterations towards the monolithic system are coupled.
Abstract: This work is an overview of algebraic pressure segregation methods for the incompressible Navier-Stokes equations. These methods can be understood as an inexact LU block factorization of the original system matrix. We have considered a wide set of methods: algebraic pressure correction methods, algebraic velocity correction methods and the Yosida method. Higher order schemes, based on improved factorizations, are also introduced. We have also explained the relationship between these pressure segregation methods and some widely used preconditioners, and we have introduced predictor-corrector methods, one-loop algorithms where nonlinearity and iterations towards the monolithic system are coupled.
TL;DR: A mathematical model for fluid-dynamic flows on networks which is based on conservation laws based on Riemann problems is considered, and its application to some simple test cases and to portions of urban network is presented.
Abstract: We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.
TL;DR: The methodology of embedded mesh, immersed body or ficticious domain techniques, used for many years as a way to discretize geometrically complex domains with structured grids, is reviewed from an implementational perspective.
Abstract: Embedded mesh, immersed body or ficticious domain techniques have been used for many years as a way to discretize geometrically complex domains with structured grids. The use of such techniques within adaptive, unstructured grid solvers is relatively recent. The combination of body-fitted functionality for some portion of the domain, together with embedded mesh or immersed body functionality for another portion of the domain offers great advantages, which are increasingly being exploited. The present paper reviews the methodology from an implementational perspective.
TL;DR: In this article, the main direct, indirect and mixed integral numerical methods for a model of scattering of thermal waves by many obstacles are reviewed and discussed, and some transient problems are solved with boundary element methods using the Laplace transform and with coupled finite and boundary element schemes for non-homogeneous obstacles.
Abstract: In this paper we survey computational techniques based on boundary integral formulations for the simulation of thermal waves. Time-harmonic solutions to diffusion problems appear in many physical situations of interest and give rise to many interesting problems related to material characterization, parameter assessment or detection of defects. We review the main direct, indirect and mixed integral numerical methods for a model of scattering of thermal waves by many obstacles and discuss how multiple scattering techniques and other physical tools can be understood as iterative methods or used as preconditioners. We also deal with some transient problems that can be solved with boundary element methods using the Laplace transform and with coupled finite and boundary element schemes for non-homogeneous obstacles