Search

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear θ method which consists, basically, of computing the response at the time tn+1 from the response previously computed at the time tn+θ, θ⩾ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time tn+1. Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

PISO (pressure-implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier-Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non-symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non-linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power-law method for modelling advection-diffusion transport. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction–diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for analysis of periodic oscillations of forced elastic systems with geometric nonlinearity is presented in this paper. Modal decomposition of the solution, computation of periodic oscillations for every eigenmode and estimation of geometric nonlinearities using the method of initial deformations enable to construct a computational technique that can be very effective in computation of steady-state periodic motions of slightly damped structures under periodic forcing. It is shown that the developed algorithm can be successfully exploited for the calculation of structural response of a micromechanical cantilever. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation of a transformation defined between the loops of boundary nodes of the cap surfaces in the parametric spaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped to the target surface according to its parameterization. Therefore, in contrast with the usual techniques, the developed algorithm does not require solving any root finding problem to ensure that the projected nodes are on the target surface. Finally, this projection algorithm is extended to three-dimensional cases and included in a sweep meshing tool in order to generate the inner layers of elements in the physical space. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a finite element solution algorithm for the numerical solution of large size three-dimensional flow problems on a personal computer. To demonstrate the algorithm, the Stokes equations in velocity–vorticity form are solved for a lid-driven cubical cavity problem. The Galerkin's weighted residual form of the governing equations is evaluated for all the elements of the computational domain and kept as element-matrices and element-vectors. This results in a set of simultaneous equations corresponding to the global nodes of each element. Those elements that contain the boundary nodes are modified to incorporate the Dirichlet boundary conditions. A conjugate gradient iterative scheme is employed to solve the simultaneous equations in element form to get the solution at the global nodes. The matrix–vector products used in the conjugate gradient iterative solver are performed in element level, assembling only the element-level vectors to form the global vectors. Since the element-level computation has eluded the formation of global matrices, the numerical solution of three-dimensional Stokes equations using a mesh of size as high as 513 could be achieved on a personal computer. The algorithm is validated by comparing the results for a three-dimensional transient diffusion problem and Stokes flow in a lid-driven cubical cavity. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton–Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non-linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible—a condition met in a vast number of practical engineering applications. The one-equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents an implementation of the Newton–Krylov–Schwarz methodology for stabilized, adaptive finite element approximations of compressible Navier–Stokes equations. Special emphasis is laid on preconditioning of the GMRES method within Newton iterations. Several Schwarz preconditioners are compared on a benchmark problem, including a new implementation of multiplicative preconditioner for matrix-free GMRES, that can be interpreted as accelerated block Gauss–Seidel iterations. Numerical examples show a good performance of the new algorithm, for single step problems and overall simulations. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to give analysis of the covolume method for solving general self-adjoint elliptic problems. We first present some useful superconvergence results for the deviation between the solution of the covolume method and the solution of the induced finite element method, in the energy norm and maximum norm, respectively. With these results, we then reproduce the maximum norm estimates obtained by Chou and Li for the covolume method easily. Furthermore, based on the covolume method, we propose a high-accuracy algorithm for solving general self-adjoint elliptic problems. Compared with the original covolume method, the computation work of the new algorithm is increased slightly, but the approximate error is improved remarkably. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for the generation of general shape functions is presented here. The algorithm is coded using the Macsyma program which has symbolic/algebraic manipulation capabilities. The current technique is based on the direct approach of calculating shape functions which is seldom used due to manual algebraic tediousness. Listing of the code is included in this paper as well as examples showing how it correctly generates some of the common shape functions with ease. Two examples of new shape functions were created for C2 elements. Hence, the more useful purpose of this algorithm is that it can be used to investigate the existence of new types of shape functions by making use of the power of symbolic computational software. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The efficiency of the frontal method for the solution of finite-element problems depends on the order in which the elements are assembled. This paper looks at using variants of Sloan's algorithm to reorder the elements. Both direct and indirect reordering algorithms are considered and are used in combination with spectral orderings. Numerical experiments are performed on a range of practical problems and, on the basis of the results, a hybrid Sloan element resequencing algorithm is proposed for use with a frontal algorithm. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes an analytical model for a beam system, based on a modified Timoshenko theory, where the beam is pinned to a hub driven by an actuator at one end and is subject to a heavy load at the other end. A new efficient computational algorithm is then proposed for solving the higher-order non-canonical partial differential equation model, which is developed based on the generalized difference method. This allows a suitable selection of different trial and test spaces, so as to improve the computational efficiency while preserving the high convergence rate of the standard finite element method. With the trial space of cubic Hermite finite elements and the test space of piecewise linear functions, the computational scheme reduces to a semi-discretized or even fully discretized computational algorithm. A numerical simulation result is included to visualize the theoretical modelling and computational results. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviors with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability. [ABSTRACT FROM AUTHOR]

The paper presents a distributed computing approach for concurrent finite element analysis of truss structures. The client-server model of distributed computation is applied to the plane frame finite element algorithm and implemented on SUN workstations. The remote procedure call combined with the ability to create threads of computation allows one to efficiently implement distributed and concurrent programs. The present approach is demonstrated through a typical truss structure to illustrate the details of the implementation. This approach can be used for very large finite element systems. [ABSTRACT FROM AUTHOR]

The investigation of the non-linear response of shell-like structures requires insight into stability behavior. In the paper we compare two strategies to compute singular points based on different eigenvalue problems. We show a simple algorithm to calculate critical load factors A used in engineering buckling analysis from the eigenvalues of the standard eigenvalue problem (KT - ωl)φ = 0. Some numerical examples illustrate the derived results and algorithms. [ABSTRACT FROM AUTHOR]

Explicit finite-element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite-element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non-iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors. [ABSTRACT FROM AUTHOR]