bluuebunny/crossref_metadata_2025_split huggingface dataset:
CLP(ℛ) as a general finite element model definition language
Authors: Strooper P. A. , Stylianou M. , Tabarrok B. 
Published: August 2005

AbstractThere are today as many finite element input languages as there are finite element programs. These input languages were developed to serve one purpose: to provide the analyst with the means to convey the necessary analysis and design criteria to specific finite element programs. They were not developed as general finite element model‐definition languages, and as a result their syntax and semantics are often unnatural and contrived. In this work we do not invent a new input language. Instead, we propose and evaluate the Contraint Logic Programming language CLP(ℛ) as a general finite element model‐definition and input language.
Merits and limitations of optimality criteria method for structural optimization
Authors: Patnaik Surya N. , Guptill James D. , Berke Laszlo 
Published: August 2005

AbstractThe merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.
A new approach to free‐form surface mesh control in a CAD environment
Authors: Noel F. , Leon J. C. , Trompette P. 
Published: August 2005

AbstractAn adaptive process controlling the position of nodes on a surface mesh is presented. The control can depend on one (or more) criterion(ria) about element quality. The mesh is attached, through the concept of classification, to a geometric model issued by a computer aided design software. Thus, the surface domain is described by entities currently available in such systems, i.e. any free‐form patches like Non‐Uniform Rational B‐Spline or Bézier patches can be used, even if they are restricted. Multi‐connected surface domains can be treated using the same geometrical definition. The method described allows nodes to slide on a patch or jump from a patch onto another one. Such movements greatly improve the mesh quality with regard to a chosen criterion. Problems occurring with patch‐by‐patch meshing techniques when surfaces patches exhibit significant size differences are then overcome. The adaptation technique can be made independent of CAD data structures and meshing techniques, hence it constitutes the basis of a mesh management module.
Conformal grid generation for high aspect ratio simply and doubly connected regions
Authors: Baty Roy S. , Morris Philip J. 
Published: August 2005

AbstractConformal co‐ordinate transformations are used to map rectangular computational domains onto arbitrary simply and doubly connected regions with smooth boundaries. The efficient numerical schemes of Wegmann involving the solution of the inverse boundary correspondence function problems associated with the mapping of the unit disc or circular annulus onto simply or doubly connected domains, respectively, are employed. The numerical implementation of these schemes is emphasized. Examples are generated for regions with elliptic inner and outer boundaries. Additional examples are used to demonstrate the accuracy and convergence of the schemes and their practical limitations. The techniques are found to converge well if holomorphic functions are used to describe the boundaries. The use of preconditioning maps is also discussed.
A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems
Authors: Farhat Charbel , Chen Po‐Shu , Mandel Jan 
Published: August 2005

AbstractWe present a new efficient and scalable domain decomposition method for solving implicitly linear and non‐linear time‐dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time‐independent problems. Computational results confirm that the optimal convergence properties of the time‐independent FETI method are preserved in the time‐dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large‐scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time‐dependent problems, including the fictitious domain decomposition method.
Adaptive two‐step methods for semidiscretized wave equations
Authors: Franco J. M. , Petriz F. 
Published: August 2005

AbstractAdaptive two‐step direct integration methods are constructed for the integration of second‐order semidiscrete evolution equations possessing oscillatory solutions. The methods are based on a class of adaptive multistep methods for a semilinear test model whose frequency is known. They are constructed following the notion of diagonally implicit RK‐methods by using efficient rational approximations to cos v, v ≥ 0. Our interest is centered on the dispersion (or phase errors) of the dominant components in the numerical oscillations when these methods are applied to a linear homogeneous test model. Two‐step methods which have high order of dispersion (up to 12), whereas the algebraic order is relatively low (2 or 4), are derived. Applications of these methods to linear as well as non‐linear test models and to semidiscretized hyperbolic equations reveal a good behaviour with regard to error propagation when they are compared with other conventional methods.
Elimination of spurious pressure and kinematic modes in biquadratic nine‐node plane element
Authors: Sze K. Y. , Fan H. , Chow C. L. 
Published: August 2005

AbstractIn two‐dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9‐node quadrilateral with three assumed quasi‐pressure modes, is the most popular element not bothered by spurious pressure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3×18 matrix and a 3×3 symmetric matrix. The inverse of the symmetric matrix is then post‐ and pre‐multiplied by the 3×18 matrix and its transpose, respectively. By employing a rank subtraction technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff. On the other hand, there are two spurious kinematic modes should the element be sub‐integrated. In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher‐order assumed stress modes in conjunction with a modified Hellinger‐Reissner functional. It will be demonstrated that the element is of good accuracy and high efficiency.
Analysis of time varying errors in quadratic finite element approximation of hyperbolic problems
Authors: Khelifa Ali , Ouellet Yvon 
Published: August 2005

AbstractA methodology for analysing the numerical errors generated by schemes using high‐order approximation is presented. Based on Fourier analysis, this methodology is illustrated through the study of the θ‐weighting Taylor–Galerkin finite element model applied to an unsteady one‐dimension advection problem with quadratic elements. Results show that the dissipation and dispersion errors may be computed by considering simultaneously the so‐called physical and computational modes and then, contrarily to what is shown when linear approximation is considered, these errors present a transient behaviour. Moreover, it appears that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another. Numerical tests are presented to support the validity of the proposed strategy. We recommend strongly the use of this method for studying the behaviour of numerical schemes based on high‐order approximations.
A finite element model for liquid phase electroepitaxy
Authors: Qin Z. , Dost S. , Djilali N. , Tabarrok B. 
Published: August 2005

AbstractA finite element numerical simulation model for the liquid phase electroepitaxial growth process of gallium arsenide is presented. The basic equations obtained from the fundamental principles of electrodynamics of continua, the constitutive equations for the liquid and solid phases derived from a rational thermodynamic theory, and the associated interface and boundary conditions are presented for a two‐dimensional axisymmetric growth cell configuration.The field equations are solved numerically by an adaptive finite element procedure. The effect of moving interfaces is taken into account. Numerical simulations are carried out for different convection levels by changing the value of the gravitational constant. Results show that convection has significant effect on the growth process under normal gravity conditions and results in thickness non‐uniformity of the grown layers. The thickness non‐uniformity leads to curved interfaces of growth and dissolution, which enhance convection.
A spectral multipole method for efficient solution of large‐scale boundary element models in elastostatics
Authors: Peirce A. P. , Napier J. A. L. 
Published: August 2005

AbstractIn this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models from O(N3)operations to O(N2logN) operations (where N is the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method is O(N) whereas the memory required for the traditional Boundary Element method is O(N2). We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break‐even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large‐scale problems, but that it also provides a useful bridge between the small‐scale and large‐scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large‐scale granular assembly models. The large‐scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture.
Tracing postbuckling paths of structures containing multi‐loops
Authors: Kuo Shyh‐Rong , Yang Yeong‐Bin 
Published: August 2005

AbstractMost incremental‐iterative methods for tracing the postbuckling paths of structures have failed to achieve convergent solutions when the paths make sharp turns in regions where nearby equilibrium paths exist. This is largely due to the fact that iterations are not performed along a correct direction in these regions. To overcome this issue, two parameters for detecting the change in direction of loading and for guiding the direction of iteration are proposed. Also, a unit conversion factor is introduced into the constraint (arc length) equation to make it physically consistent. With these modifications, the present method is capable of tracing the postbuckling paths of structures with multi‐loops. A two‐member truss well known for its looping characteristics in the post‐buckling response has been solved as an illustration.
A numerical study of chaos in a reaction‐diffusion equation
Authors: Mitchell A. R. , Bruch J. C. 
Published: August 2005

AbstractA study is made using numerical experiments to see the effect of the parameters in the explicit Euler‐discretized form of a one‐dimensional, nonlinear, reaction‐diffusion equation. Based on a series of these experiments, one of the main results obtained is that diffusion, which is usually perceived as having a stabilizing effect, is able to produce chaotic as well as divergent numerical solutions. Furthermore, the discretization parameters are also able to produce chaotic results. From the results presented herein, it is shown that varying the parameters can produce solutions that are single numbers, periodic, aperiodic (chaos), or divergent.
Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields
Authors: Herrera Ismael 
Published: August 2005

AbstractApplying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions, a direct method of analysis is developed. The scheme includes finite differences, finite elements, and boundary methods. This is the first of a sequence of articles in which the methodology is presented. A fundamental ingredient of the procedure are general Green's formulas for operators defined in discontinuous fields. They are developed in this first article.
Mixed finite element methods for the approximation of time‐dependent problems
Authors: Suri Manil 
Published: August 2005

AbstractA given elliptic boundary problem can, in general, be approximated by several different mixed finite element methods, depending on what physical unknowns are most desired. The use of certain mixed methods for time‐dependent problems has been proposed by Johnson and Thomee [5]. We analyze here some additional mixed methods for the time‐dependent case which can be used to obtain direct approximations to alternate physical quantities of interest.
Finite element treatment of boundary singularities by augmentation with non‐exact singular functions
Authors: Beagles A. E. , Whiteman J. R. 
Published: August 2005

AbstractA two‐dimensional Poisson problem which contains both an interface and a reentrant corner is considered. For this problem the singular form of the solution at the reentrant corner is not known explicitly, with the result that a (nonexact) approximation to the singular form has to be calculated. The finite element method is applied to the Poisson problem, with the test and trial function spaces augmented with the nonexact singular functions. An error analysis for the nonexact augmentation is presented.
Finite difference solution of viscoelastic flows by preconditioned conjugate gradients
Authors: Manero O. 
Published: August 2005

AbstractAttention is given to preconditioned conjugate gradients in the solution of systems of partial differential equations which arise in flows of viscoelastic liquids simulated by rheological implicit models. Finite differences discretization is used together with a generalization of the incomplete Cholesky conjugate‐gradient method to include asymmetric nonsingular matrices, resulted from the discretization of the kinemetic fields and the pressure recovery problem in also considered in a two‐dimensional planar flow.
On a moving boundary problem of transitional ballistics
Authors: Cooke Charlie H. , Hwang Jen‐Ing G. 
Published: August 2005

AbstractA hybrid algorithm for calculating the flow around a flat‐nosed projectile moving through a fluid is established. At cells of fixed volume away from the projectile, Harten's total variation diminishing (TVD), second‐order accurate, shock capturing scheme is utilized. Due to projectile motion, cells adjacent to the projectile can be treated as compressing or expanding in volume. For such cells, a local finite volume approach has been employed to derive a cell update algorithm.Proof of concept for the expanding cell scheme is established through calculating the one‐dimensional flow behind a moving piston, whose theoretical solution is well‐known. The resulting hybrid scheme is applied to the problem of blast wave simulation in axisymmetric geometries. Flow around a vertical muzzle brake is calculated for the case of an embedded moving projectile.
A Tensor product generalized ADI method for the method of planes
Authors: Dyksen Wayne R. 
Published: August 2005

AbstractWe consider solving separable, second order, linear elliptic prtial differential equations in three independent variables. If the partial differential opertor separates into two terms, one depending on x and y, and one depending on z, then we use the method of planes to obtain a discrete problem, which we write in tensor product from as

We apply a new interative method, the tensor product generalized alternating direction implicit method, to solve the discrete problem. We study a specific implementation that uses Hermite bicubic collocation in the xy direction and symmetric finite differences in the z direction. We demostrate that this method is a fast and accurate way to solve the large linear systems arising from three‐dimensional elliptic problems.
The performance of numerical methods for elliptic problems with mixed boundary conditions
Authors: Dyksen Wayne R. , Ribbens Calvin J. , Rice John R. 
Published: August 2005

AbstractWe consider solving linear, second order, elliptic partial differential equations with boundary conditions of types Dirichlet (DIR), mixed (MIX), and nearly Neumann (Neu) by using software modules that implement five numerical methods (one finite element and four finite differences). They represent both the new generation of improved methods and the traditional ones; they are: Hermite collocation plus band Gauss elimination (HC), ordinary finite differences plus band Gauss elimination (5P), ordinary finite differences with Dyaknov iteration (DY), DY with Richardson extrapolation to achieve fourth order convergence (D4), and ordinary finite differences with multigrid iteration (MG). We carry out a performance evaluation in which we measure the grid size and the computer time needed to achieve three significant digits of accuracy in the solution. We compute the changes in these two measures as we change boundary condition types from DIR to MIX and MIX to NEU and then test the following hypotheses: (i) the performance of all the modules is degraded by introducing the derivative terms into the boundary conditions; (ii) finite element collocation (HC) is least affected; (iii) the fourth order modules (HC and D4) are less affected than the other second order modules; and (iv) the traditional 5‐point finite differences (5P) are most affected. We establish these hypotheses with high levels of confidence by using several sample problems. The most significant conclusion is that a high order collocation method is preferred for problems with general operators and derivatives in the boundary conditions. We also establish with considerable confidence that these modules have the following rankings in absolute comparative time performance: MG (best), HC and D4, DY, and 5P (worst).
A fourth‐order difference method for elliptic equations with nonlinear first derivative terms
Authors: Jain M. K. , Jain R. K. , Mohanty R. K. 
Published: August 2005

AbstractWe present a nine‐point fourth‐order finite difference method for the nonlinear second‐order elliptic differential equation Auxx + Buyy = f(x, y, u, ux, uy) on a rectangular region R subject to Dirichlet boundary conditions u(x, y) = g(x, y) on ∂R. We establish, under appropriate conditions O(h4)‐convergence of the finite difference scheme. Numerical examples are given to illustrate the method and its fourth‐order convergence.
Some numerical experiments on the splitting of Burgers' equation
Authors: Iskandar Labib , Mohsen Adel 
Published: August 2005

AbstractThe combined approach of linearization and splitting up is used for devising new algorithms to solve a one‐dimensional Burgers' equation. Two schemes are discussed and the computed solutions are compared with the exact solution. For this problem it is found that the schemes proposed yield excellent numerical results for Reynolds number R ranges from 50 up to 1500. The schemes were also tested for another problem whose R = 10000. In this case a filtering technique is used to overcome the nonlinear instability.
Semidiscrete least squares methods for linear hyperbolic systems
Authors: Chen Tsu‐Fen 
Published: August 2005

AbstractSome approximate methods for solving linear hyperbolic systems are presented and analyzed. The methods consist of discretizing with respect to time and solving the resulting hyperbolic system for fixed time by least squares finite element methods. An analysis of least squares approximations is given, including optimal order estimates for piecewise polynomial approximation spaces. Numerical results for the inviscid Burgers' equation are also presented. © 1992 John Wiley & Sons, Inc.
Multigrid solvers and preconditioners for first kind integral equations
Authors: Von Petersdorff T. , Stephan E. P. 
Published: August 2005

AbstractWe discuss multigrid methods and multilevel preconditioners for first kind boundary integral equations with weakly and hypersingular kernels. We find that the number of iterations needed is bounded or grows no worse than logarithmically in the numbers of unknowns. We also discuss the complexity for parallel implementations.
Modeling of multimaterial interfaces in the finite difference method
Authors: Dow J. O. , Hardaway J. L. 
Published: August 2005

AbstractThis work develops a procedure for representing multimaterial interfaces in finite difference models. The boundary separating the two materials can be on or between a row of nodes. The development is validated by embedding the boundary between two regions in a single, larger region and comparing the results. The development is facilitated by the use of a physically based notation that represents the displacement approximations in terms of rigid‐body rotations and strain gradient quantities that produce the displacements. Four example problems are presented.
Fast numerical method for the solution of the quasigeostrophic vorticity equation
Authors: Dahleh Marie Dillon 
Published: August 2005

AbstractParticle methods are typically O(N2), where N is the number of computational elements. We present an O(N) particle method for the equations for the conservation of potential vorticity. This method is based on the idea of grouping the particles. The necessary expansions and truncation errors are given. The accuracy and speed of the method are presented for both scalar and vector machines. © 1993 John Wiley & Sons, Inc.