bluuebunny/crossref_metadata_2025_split huggingface dataset:
Block diagonal scaling for iterative methods in thermal simulation
Authors: Díaz J. C. , Jines W. R. , McDonald A. E. , Steihaug T. 
Published: August 2005

AbstractLinear equations arising from reservoir simulation are closely coupled at the local‐cell level, and the variables and equations tend to be poorly equilibrated. Scaling by the inverse of the diagonal block has an equilibrating effect. It usually improves the condition of the matrix for solution by linear iteration. The effects of block diagonal scaling are illustrated for a thermal reservoir simulator, where the original matrix may be indefinite. These results illustrate that for difficult problems block diagonal scaling can significantly enhance the convergence rate of the iterative method. It is also illustrated that preconditioned generated by block incomplete LU decomposition (ILU) and block symmetric Gauss Seidel (BSGS) methods are effective preconditioned for use in thermal simulation.
Numerical solution of regular and singular biharmonic problems with the Tau lines method
Authors: El Misiery A. E. M. , Ortiz E. L. 
Published: August 2005

AbstractThe recursive formulation of the Tau method of Ortiz6 is a versatile tool for the numerical solution of linear and nonlinear systems of differential equations. In this paper it is combined with the method of lines to produce a hybrid Tau lines method which has been applied with success in the numerical treatment of partial differential equations. We report here results obtained in the numerical solution of the biharmonic equation and show that the Tau lines technique performs far better than a specially designed finite element method with which it is compared. We also report results obtained in the numerical solution of a singular boundary‐value problem, defined again by the biharmonic equation, which is relevant to fracture mechanics.
New symmetric finite difference methods for computing eigenvalues of a boundary‐value problem
Authors: Usmani Riaz A. , Agarwal Ravi P. 
Published: August 2005

AbstractWe develop a new finite difference method of order two and its refinement for computing the eigenvalues of a two‐point boundary‐value problem involving a fourth‐order linear ordinary differential equation. Our methods leads to generalized symmetric five‐ and seven‐band matrix eigenvalue problems. To demonstrate the effectiveness of the proposed methods, the numerical evidence is also included.
Analysis of tubular joint with weld toe crack by finite element methods
Authors: Bhuyan G. S. , Arockiasamy M. , Munaswamy K. 
Published: August 2005

AbstractFinite element methods are used to obtain the through‐thickness and surface stresses for the tubular T‐joint in the presence of a shallow weld toe crack. The crack tip stress intensity factors are obtained by comparing the stresses at the crack front with the theoretical solution. The embedded elliptical crack front is modelled as straight line segments. The region at the vicinity of the crack is discretized using special elements, which produce singular stress fields at the crack front. It is observed that in presence of a shallow weld toe crack, the stress along the chord surface near the weld toe is less than that of a joint without a crack; which is evident from the presence of the free surface of the crack face. But far from the crack, the stress is always greater than that of the uncracked joint.
Ill‐posed design methods for the computation of inviscid flows
Authors: Wirz H. J. 
Published: August 2005

AbstractIt is shown here that the solutions of the governing partial differential equations fail to behave well for three well‐known methods of analysis and design for the computation of inviscid flows in turbomachines and for time‐dependent transonic airflows. The first two examples are related to flows in turbomachines: the so‐called ‘streamline curvature methods’ and the proposition of C. H. Wu to reduce the solution of an essentially three‐dimensional internal flow problem to successive two‐dimensional ones. Finally, time‐dependent compressible and irrotational flows which employ the density and the velocity potential as dependent variables are considered.
The role of a mixed design and analysis method in a turbomachinery blade design system
Authors: Ceder R. D. , Stow P. 
Published: August 2005

AbstractIn this paper the requirements of a design method are considered, with particular emphasis given to the needs of designers of multi‐stage compressors. It is concluded that what is required is a quasi three‐dimensional compatible design and analysis method. The extension of the finite element blade‐to‐blade method FINSUP to include a design calculation compatible with the analysis calculation is presented. In this method, changes to the blade shape are modelled using a surface transpiration model. By displacing every point on the blade surface individually, the relationship between the blade shape and the surface velocity is determined. It is shown that with a Newton–Raphson procedure adopted in the method, a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. An example of the method is shown in which a transonic compressor blade with a suction surface shock is redesigned to give a blade with controlled suction surface diffusion.
On the Gaussian quadrature rule for finite‐part integrals with a first‐order singularity
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractThe Gaussian quadrature rule for finite‐part integrals of the form
equation image
, due to Kutt, is reconsidered. Several new results about this rule are proved. The main result is that the orthogonal polynomials associated with the above quadrature rule are of the form P (y) + an P (y), where P (y) are the shifted Legendre polynomials (orthogonal on [0,1]) and an well‐defined constants. The present results will permit the more systematic use of the above quadrature rule in engineering applications (e.g. in the boundary element method), where finite‐part integrals of the type
equation image
are quite frequently encountered (e.g. during the numerical computation of one‐ and two‐dimensional Cauchy type principal value integrals).
A generalized displacement method for finite element analysis of constrained problems
Authors: Xikui Li , Liu Guo Qiang 
Published: August 2005

AbstractA new approach to deal with the finite element analysis of structures with linear equality constraints is presented in this paper. By imposing the requirement that the displacement variables satisfy the linear constraint equations a priori, a procedure to form the so‐called generalized displacement subspace Ss is given. The constrained variational problem is then transformed into an unconsrained one defined on the subspace. This approach has been successfully used to analyse the incompressible problems1 and to overcome the shear locking phenomena in the thin plate–shell structure analysis2, 3.
Removal of singularities in tresca and mohr–coulomb yield functions
Authors: Sloan S. W. , Booker J. R. 
Published: August 2005

AbstractThe Tresca and Mohr–Coulomb yield functions are used widely in metal and soil plasticity computations. Both of these criteria, however, possess angular vertices at which the gradient with respect to the stresses, and hence the elastoplastic constitutive law, is undefined. This paper describes a modified yield function which may be used to ‘round‐off’ these vertices. When used in conjunction with the parent yield function, the modified yield function results in a yield surface which is continuous and differentiable for all values of the stresses. The modified yield function is used in the vicinity of the vertices and is given in a form suitable for finite element programming.
Communications oriented programming of parallel iterative solutions of sparse linear systems
Authors: Patrick Merrell L. , Pratt Terrence W. 
Published: August 2005

AbstractComputing systems of the future for large‐scale scientific and engineering computations will consist of many processors and memories working in parallel to solve a single problem. Efficient use and ease of use of these future systems are two basic problems facing potential users. The development of new parallel algorithms and parallel programming environments is essential for progress toward the solution of these problems. In this paper we develop parallel algorithms for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions are determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. We present three different parallel algorithms for solving the same class of problems and analyse their effectiveness from this point of view. The algorithms are programmed using a new programming environment. Run‐time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.
Calculation of confined swirling jets
Authors: Chen C. P. 
Published: August 2005

AbstractComputations of a confined coaxial swirling jet are carried out using a standard two‐equation (k‐ε) model and two modifications of this model based on Richardson number corrections of the length scale (ε) governing equation. To avoid any uncertainty involved in the setting up of inlet boundary conditions, actual measurements are used at the inlet plane of this calculation domain. The results of the numerical investigation indicate that the k‐ε model is inadequate for the predictions of confined swirling flows. Although marginal improvement of the flow predictions can be achieved by these two corrections, both cannot be judged satisfactory.
BEM—condition number of systems obtained when solving mixed boundary value potential problems
Authors: Migeot Jean‐Louis 
Published: August 2005

AbstractA study of the condition number of matrices appearing in the resolution of mixed boundary value potential problems through the boundary element method (BEM) is presented here. It is shown how this condition number varies with the size of the domain under consideration. An algorithm is provided giving the best scale factor, which is the one leading to the smallest possible condition number.
On the determination of the roots of some classes of transcendental equations
Authors: Mikhailov M. D. , Özişik M. N. 
Published: August 2005

AbstractA new approach is developed for fast, automatic and accurate computation of the roots of some classes of transcendental equations without the risk of missing any one of the roots. The method permits the calculation of as many eigenvalues as desired or any one of them directly, without the need for computing the previous ones. The computation procedure is based on the count of the number of roots of the transcendental equation lying between zero and some prescribed value in the eigenvalue spectrum. Basic rules in the application of this method are described, and its use for determining the roots of the transcendental equation is illustrated with examples.
Flow in a coiled tube: The effect of mesh pattern on the convergence rate of predicted critical points
Authors: Winters K. H. , Brown T. W. 
Published: August 2005

AbstractNon‐unique flows are possible in a coiled tube when the axial pressure gradient driving the flow exceeds a critical value. For a tube of square cross‐section, it is shown that the rate of convergence of the critical value with mesh size depends strongly on the mesh pattern. In the particular, the predictions obtained with mesh patterns which respect the symmetry of the problem converge more rapidly as the mesh size is reduced.
Some higher order methods for computing eigenvalues of two‐point boundary value problems
Authors: Usmani Riaz A. , Agarwal Ravi P. 
Published: August 2005

AbstractWe present new finite difference methods of order at most O(h6) for computing eigenvalues of two‐point boundary value problems. Our methods lead to generalized seven‐band matrix eigenvalue problems. Some typical boundary value problems are treated numerically and these numerical results are summarized in order to demonstrate the practical usefulness of our algorithms.
Evaluation of the leading band coefficients of the boundary integral system of equations
Authors: Sofianos A. I. 
Published: August 2005

AbstractNumerical integration of integrals that are either improper or have logarithmic integrands is required in order to evaluate some of the coefficients of the boundary integral system of equations in two‐dimensional elastostatics. This technique allows for the evaluation of these coefficients numerically with the use of the Gauss–Legendre quadrature formula.
An example of finite element analysis in a multiply connected region
Authors: Bolkowski Stanislaw , Sroka Jan 
Published: August 2005

AbstractThe temperature field of an underground cable line can be analysed in a simply connected region. Axial symmetry of the temperature distribution of the cable interiors enables them to be extracted from the region dealt with by the finite element method. This transforms the region into a multiply connected one. In this paper, the boundary procedure which replaced the cable interiors was derived. This procedure has the form of the boundary condition of the second kind. The only way to take into account the temperature dependence of the heat losses inside the cables in a simply connected region is to use an iterative process, which is time consuming. A multiply connected region is more effective in that respect, since only modification of the boundary procedure to the boundary condition of the third kind is needed for it. The temperature field of a cable line is an unbounded one. Therefore, the authors developed another boundary procedure in uniform earth which was based on the second Green formula. Numerical experiments confirmed that finite element analysis of the cable temperature field in a multiply connected region is more efficient than in a simply connected one.
Weighted Gaussian methods for three‐dimensional boundary element kernel integration
Authors: Aliabadi M. H. , Hall W. S. 
Published: August 2005

AbstractThe evalution of the inverse distance singular integrand which occurs in the three‐dimensional boundary element formulation of potential problems is treated using weighted Gaussian integration. Three methods are investigated. The first involves repeated use of a one‐dimensional Gaussian formula in which the weights are inverse powers. The second involves the inverse distance in the local parameter plane to which the surface elements are transformed. Comparisons with some exact integrals developed over plane parallelograms show that neither of these first two methods performs particularly well, with the second being appropriate only for integration over unit squares.A third method is developed using an approximation to the real space distance in the weighting. Such a method does take into account the local properties of the surface and gives integrals accurate to the precision of the computer being used for tests on a plane parallelogram. In a further test integrating over a curved element on a sphere, good accuracy is again achieved. Overall, however, in the type of integration test considered, none of these weighted Gaussian methods integrates as accurately as the expansion or transformation methods published elsewhere.
Analysis of the collocation time finite element method for the non‐linear heat transfer equation
Authors: Kujawski J. 
Published: August 2005

AbstractThe method of collocation time finite element is a modification of the well‐known generalized midpoint method. It has an additional free parameter. The method is applied to the one‐dimensional nonlinear heat transfer equation. Numerical results illustrate that the proposed algorithm is capable of improved performance over the standard generalized midpoint method.
An improved semi‐discrete approach for the solution of one‐dimensional linear boundary‐value problems
Authors: Bickford William B. , Rankin Robert L. 
Published: August 2005

AbstractA semi‐discrete method for solving inhomogeneous boundary‐value problems whose differential equations possess regular singular points is presented. The method is shown to exhibit substantially improved accuracy as compared with previous similar treatments of the same class of problems. Examples illustrating the improvements are presented.
On the computation of weakly separated laminar flows in a smoothly expanding channel
Authors: Szymczak W. G. , Myers G. 
Published: August 2005

AbstractIn Reference 1, a summary of results of numerical solutions to steady‐state laminar flows in an expanding planar channel from 15 research groups was presented. Both vorticity and pressure values computed along a wall of the channel were compared. This paper presents some possible explanations for the wide discrepancies in these computed results.
Geometrical properties in the B‐spline representation of arbitrary domains
Authors: Rozenthal Paulo , Gattass Marcelo 
Published: August 2005

AbstractThis paper presents a new method to compute areas and moments of arbitrary domains bounded by periodic cubic B‐splines. The proposed method gives exact answers, it is very efficient and relies only on the control points co‐ordinates of the B‐spline. One example is presented and compared with analytical results and with previous numerical work.
Multiderivative methods for nonlinear beam problems
Authors: Twizell E. H. , Tirmizi S. I. A. 
Published: August 2005

AbstractSecond, fourth and sixth order methods are developed and analysed for the numerical solution of nonlinear fourth order boundary value problems with boundary conditions given as two function values together with two second order derivatives or two first order derivatives. The methods arise from a five‐point recurrence relation involving exponential terms, these being replaced by Padé approximants. The methods are tested on two problems from the literature.
On the Bergan‐Wang approach for moderately thick plates
Authors: Abdalla Hamed , Hassan Kamal 
Published: August 2005

AbstractThe Bergan‐Wang approach for the transverse shear inclusion in thin and moderately thick plate deformation has led to an energy expression which is a function of the only lateral deflection. The corresponding Euler equation is an eighth‐order partial differential equation. A variety of examples has been analysed. Analytical solutions have been presented for different thickness to span ratios under different boundary conditions. Results show very close resemblance to solutions based on Reissner plate theory.
A study of the influence of the angle condition on plate bending of triangular finite elements
Authors: Hassan K. , Sarigul N. 
Published: August 2005

AbstractIn triangulating a domain to find a finite element approximation for the solution of a specific problem, the so‐called angle condition is essential. In this paper, a study of the effects of this condition on the spectral properties of the stiffness matrix has been performed for two plate bending elements: the constant moment triangle (CMT) and the discrete Kirchhoff triangle (DKT). This has been done on the element level and also for the global system. It is shown that as the smallest, rather than the largest, angle of the elements considered herein decreases, the condition number of the global stiffness matrix increases.
Extensional universal serendipity elements
Authors: Zhang Lin 
Published: August 2005

AbstractIn this paper, extensional universal serendipity elements (EUSE) are presented. The paper includes not only isoparametric elements with nodes from 2 to 32 having linear, quadratic and cubic node confiurations at their edges in an arbitrary manner, but also a series of transition isoparametric elements which can connect three‐dimensional solid elements, axisymmetric solid elements with shell elements with shell elements and axisymmetric shell elements, respectively. Shape functions and their derivatives for EUSE are expressed in terms of three one‐dimensional basic functions and their derivatives. EUSE is a more systematic, easy to program and ideal element family in the element libraries.
Performance of four numerical schemes for the unconfined flow (nonlinear Boussinesq) problem
Authors: Taigbenu Akpofure 
Published: August 2005

AbstractNumerical experiments are performed on four schemes of the boundary element method (BEM) for the unconfined flow (nonlinear Boussinesq) problem with a view to determining the scheme that gives the best performance. The performance measure of a scheme for a particular problem reflects the trade‐off between accuracy and the CPU simulation time—a surrogate for computational cost or efficiency. The four schemes are adaptations of the theory earlier proposed by Taigbenu and Liggett.1 Two of the schemes are predictor–corrector or iterative schemes, while the other two employ a linearization about the known initial data. The variety of schemes enhances the versatility of the boundary element theory in the sense that a program user has a greater flexibility in the choice of scheme which best serves his desired objectives.
On the development of an algorithm for solving stiff nonlinear dynamic equations based on the Broyden's updating method
Authors: Yuh J. , Holley W. E. 
Published: August 2005

AbstractThis paper describes a numerical procedure for the solution of stiff dynamic system equations which are written in implicit form f(x,ẋ,t)=0. This study, based on the Broyden's updating method, gives a more efficient way to solve the differential/algebraic equations simultaneously. Using a rank‐one inverse Jacobian updating formula, the inverse Jacobian matrix is corrected directly at each iteration. The algorithm is investigated for several dynamic systems.
New methods of determining the strange attractor by generalized cell mapping approach
Authors: Hua Zhu Wen , Tai Wu Qi 
Published: August 2005

AbstractThe generalized cell mapping method used in solving non‐linear dynamical systems is also a powerful means of determining the state volume in which strange attractors reside. Several methods of refining the size of cells are proposed in this paper. With the aid of these methods it is possible to describe the shape of a strange attractor in however much detail is required. Any part of the cell state space can be enlarged by the suggested zoom technique when the finte structure of this strange attractor is going to be studied. By using the limiting probability distribution calculated from the persistent group, the statistical meaning of the attractor is revealed. Results of examples which were computed on an IBM PC computer show the validity and efficiency of the methods.
Guyan reduction
Authors: Chen Su‐Huan , Pan H. H. 
Published: August 2005

AbstractBecause of the cost of generating computer solutions for a dynamic analysis, it is often desirable to reduce the size of the problem by performing a reduction on the mass and stiffness matrices of the governing set of equations of motion. The well‐known reduction proposed by Guyan is the technique used by most of the large structure codes. This paper is concerned with the accuracy in such reduction and the method to improve it. A formula for the estimate of the error induced by Guyan reduction is derived through from perturbation theory. Based on the same principle, an iterative pertubation scheme is developed to improve the solution accuracy by taking the Guyan solution as the starting value. To demonstrate the practical usefulness of the method, two numerical examples are included.
Boundary element study of an anisotropic plate
Authors: Heng Z. 
Published: August 2005

AbstractAn efficient boundary element technique is developed for use in the analysis of composite structures. The boundary element method is modified by an analytical scheme so as to evaluate the boundary integrals in those elements containing singularities. This technique, combined with a special integration quadrature formula for the remaining elements, significantly improves the computing accuracy of the boundary element method.