bluuebunny/crossref_metadata_2025 huggingface dataset:
A non‐isentropic Euler–Poisson model for a collisionless plasma
Authors: Markowich Peter A. , Pietra Paola
Published: October 2005

We analyse transonic solutions of the one‐dimensional Euler–Poisson model for a collisionless gas of charged particles in the non‐isentropic steady‐state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self‐consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.

The analysis is based on representing solutions piecewise as orbits in the particle‐density‐electric‐field phase plane and connecting the orbit segments by the jump and entropy conditions.

We characterize the set of all solutions of the Euler–Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one‐shock and (in certain cases) two‐shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
Study of global solutions of parabolic equations via a priori estimates. Part I: Equations with principal elliptic part equal to the laplacian
Authors: Lieberman Gary M.
Published: October 2005

We study global solutions of ut=Δu + f(u, Du) with zero boundary data. Under suitable hypotheses on f, we show that an energy, which is roughly the H1 norm of u, cannot change too rapidly. When f depends only on u, this estimate implies that all global solutions are bounded.
The existence and regularity of solutions to the non‐linear equation of flotating water
Authors: Sidz Leszek
Published: October 2005

The existence of solutions to the nonlinear equations including the equation of flotating water is proved using the subellipticity of an operator in the equation and the contraction argument. Moreover a regularity result is given.
Global existence of classical solutions to the dynamical von Kármán equations
Authors: Koch Herbert , Stahel Andreas
Published: October 2005

This paper derives an improved energy inequality for the non‐linear dynamical von Kármán equations. The existence of global classical solutions is a consequence of this a priori inequality.
Exact and approximate boundary conditions at artificial boundaries
Authors: Lill Georg
Published: October 2005

The use of transformation methods for the derivation of boundary conditions at artificial boundaries had been initiated by Engquist and Majda [4. 5]. They considered the scalar wave equation and strictly hyperbolic systems. This has been extended by Gustafsson [11] to inhomogeneous conditions, by Hagstrom [15] to parabolic and Halpern et al. [17, 20] to incompletely parabolic systems. Here a systematic method is developed which unifies these approaches. Additionally, inhomogeneities with non‐compact support are taken into account. Exact and first‐order approximate boundary conditions for the compressible Navier–Stokes equations are presented.
Boundary conditions in acoustic scattering with respect to the reciprocity relation
Authors: Reissinger Jörg
Published: October 2005

A new concept associated with the reciprocity relation in acoustic scattering is introduced. Motivated by this well‐known relation, which holds in all the classical cases, more general boundary value problems for the scalar Helmholtz equation are studied. These generalized boundary conditions are characterized by the validity of the reciprocity relation and seem to be an appropriate unification of a large class of boundary value problems in acoustic scattering. The well‐known results for the classical problems can be extended to this general case and also new connections with the question about existence and uniqueness of solutions to the boundary value problems can be derived. A constructive procedure shows that this approach is applicable for a large class of boundary conditions.
Schauder estimates for boundary layer potentials
Authors: Wiegner Michael
Published: October 2005

Boundary layer potentials with Hölder‐continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type
equation image
with |ρ| odd and a density λ of class Ck+α. This paper presents a self‐contained exposition of the fact that the potential v may be continued as Ck+α‐functions onto G and ℝn\G respectively (together with estimates for the Hölder‐norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
General interface problems—II
Authors: Nicaise Serge , Sändig Anna‐Margerete
Published: October 2005

We continue the study of general interface problems. We prove regularity and asymptotics of solutions in usual Sobolev spaces for non‐constant coefficients operators. We also give the stabilization procedure when unstable decompositions appear near a critical angle.
Weak solutions of the initial‐boundary value problem for the Vlasov–Poisson system
Authors: Abdallah Naoufel Ben
Published: October 2005

In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov–Poisson system. First, we regularize the system in order to apply a fixed‐point theorem. Then we pass to the limit using an energy estimate.
Local existence of solutions to the Landau–Maxwell system
Authors: Zhan Mei‐Qin
Published: October 2005

We study here the Landau–Maxwell system in its classical form. We prove the local existence of weak solution with initial data of unrestricted size. The main tools consist of an approximation method and a regularity result for velocity averages of solutions of some general linear transport equations.
A finite element method and stabilization method for a non‐linear tricomi problem
Authors: Lar'kin N. A. , Schneider M.
Published: October 2005

We prove using the Faedo‐Galerkin method the existence of a generalized solution of an initial‐boundary value problem for the non‐linear evolution equationmagnified image0 ⩽ Q ⩽ 2, in a cylinder QT = Ω × (0, T), where 𝒯 u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
Approximation of solutions to evolution equations
Authors: Miletta Peter D.
Published: October 2005

The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form u′(t)= − Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self‐adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non‐linear map defined on D(A½) which satisfies a Lipschitz condition on balls in D(A½).
On a semi‐coercive problem in a porous journal bearing with cavitation problem as boundary condition and subject to an integral condition
Authors: Boukrouche Mahdi
Published: October 2005

We study a non‐linear problem in pressure saturation modelling of a free boundary problem, arising in self‐lubricating bearings, with Neumann boundary conditions for the pressure and a non‐local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo‐characteristics discretization method and semi‐coercive variational inequalities.
Unique solvability of the periodic Cauchy problem for wave‐hierarchy problems with dissipation
Authors: Göz Manfred F.
Published: October 2005

Wave‐hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier‐Stokes equations with specific non‐linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.
Two canonical wedge problems for the Helmholtz equation
Authors: Meister E. , Penzel F. , Speck F.‐O. , Teixeira F. S.
Published: October 2005

Boundary‐transmission problems for two‐dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one‐medium case, but the two‐media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this reasoning.
On identification of memory kernels in linear theory of heat conduction
Authors: von Wolfersdorf L.
Published: October 2005

A linear integrodifferential equation describing the heat flow in a material with memory is considered. This equation contains a pair of time‐dependent convolution kernels that are unknown. Such kernels are determined as solutions of an optimal control problem by using additional data obtained from measurements of average temperature around some fixed points of the domain over some finite time interval. We show the existence of an optimal solution of this problem and derive optimality conditions for it.
Quantitative error estimates for coefficient idealization in linear elliptic problems
Authors: Han Weimin
Published: October 2005

We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
On the boundary transmission problem of thermoelastostatics in a plane domain with interface corners
Authors: Jentsch Lothar
Published: October 2005

This paper deals with bimetal problems of thermoelastostatics. By means of an explicit particular solution a reduction to problems of elastostatics is given. An indirect boundary integral method is applied for solving the traction boundary value problem. The solution is represented by a potential of single layer type having Green's contact tensor as the kernel. Thus, from the first the transmission conditions are satisfied. The Fredholm property of the boundary integral operator as well as the asymptotics of the potential density at an interface corner depend on the symbol of a Mellin convolution operator. The singular functions at corners can be obtained by calculating the potential for terms in the asymptotic expansion of the density.
Stokes flow of a micropolar fluid exterior to several non‐intersecting closed surfaces, but contained by an exterior contour
Authors: Power Henry , Ramkissoon Harold
Published: October 2005

The problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double‐layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double‐layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.
Reciprocity relations and completeness of far‐field pattern vectors for obstacle scattering of acoustic wave in a stratified medium
Authors: Xu Yongzhi
Published: October 2005

Under a generalized Sommerfeld radiation condition, we proved the uniqueness and existence of the direct obstacle scattering problem of time‐harmonic acoustic waves in a stratified medium [8]. In this paper, we study the asymptotic behaviour of the scattered waves and prove three reciprocity relations among the free‐wave far‐field patterns and the guided‐wave far‐field pattern vectors corresponding to incident distorted plane waves and normal mode waves. Then we prove conditions under which a set of far‐field patterns is complete in a Hilbert space based on the reciprocity relation. These properties are important in investigating the inverse obstacle scattering problems.
Non‐orthogonal expansions on the sphere
Authors: Freeden Willi , Schreiner Michael
Published: October 2005

Discrete families of functions with the property that every function in a certain space can be represented by its formal Fourier series expansion are developed on the sphere. A Fourier‐series‐type expansion is obviously true if the family is an orthonormal basis of a Hilbert space, but it also can hold in situations where the family is not orthogonal and is ‘overcomplete’. Furthermore, all functions in our approach are axisymmetric (depending only on the spherical distance) so that they can be used adequately in (rotation) invariant pseudo‐differential equations on the sphere. The three classes of examples particularly studied here are (i) Abel‐Poisson frames (ii) Gauss‐Weierstrass frames and (iii) frames consisting of locally supported kernel functions. Abel‐Poisson frames form families of harmonic functions and provide us with powerful approximation tools in potential theory. Gauss‐Weierstrass frames are intimately related to the diffusion equation on the sphere and play an important role in multiscale descriptions of image processing on the sphere. The third class enables us to discuss spherical ‘Fourier expansions’ by means of ‘axisymmetric finite elements’.
On the sharp singular limit for slightly compressible fluids
Authors: Beirão da Veiga H.
Published: October 2005

We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well‐specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.
The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge
Authors: Mirschinka Dirk
Published: October 2005

This paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half‐spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half‐plane. This leads to invertibility criteria for the boundary integral operators.
Optimal preconditioner for boundary element formulation of the Dirichlet problem in elasticity
Authors: Rjasanow S.
Published: October 2005

An optimal preconditioning procedure for the numerical solution of two‐dimensional Dirichlet problem for Lamé equations by boundary element method is constructed. An efficient algorithm for the above problem is also developed.
Calculation of microstrains and microstresses in a thick non‐symmetric heterogeneous plate by homogenization
Authors: Tapiéro Roland
Published: October 2005

We consider the thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use the Reissner‐Mindlin thermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non‐uniformly and rapidly oscillating functions of the space variable. Two‐scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution of microstrains and microstresses inside the plate when a macroscopic behaviour is given.
Global in time existence of small solutions of non‐linear thermoviscoelastic equations
Authors: Shibata Yoshihiro
Published: October 2005

We prove a global in time existence theorem of classical solutions of the initial boundary value problem for a non‐linear thermoviscoelastic equation in a bounded domain for very smooth initial data, external forces and heat supply which are very close to a specific constant equilibrium state. Our proof is a combination of a local in time existence theorem and some a priori estimates of local in time solutions. Such a priori estimates are proved basically for suitable linear problems by using some multiplicative techniques. An exponential stability of the constant equilibrium state also follows from our proof of the existence and regularity theorems.
A discrete velocity coagulation‐fragmentation model
Authors: Slemrod M. , Qi A. , Grinfeld M. , Stewart I.
Published: October 2005

A discrete velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in a volume V with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker‐Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. Results of numerical experiments are presented.
Weak solutions to a non‐linear hyperbolic system arising in the theory of dielectric liquids
Authors: Feireisl Eduard
Published: October 2005

We consider a model of the motion of a viscous dielectric liquid subjected to a DC electric field in the case when the bulk conduction results from the presence of a dissociation‐recombination process. The effects of both magnetic field and ionic diffusion are neglected. The existence of at least one weak solution is proved via the method of renormalized solutions.
On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems
Authors: Dan Wakako
Published: October 2005

We prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non‐linear thermoelastic equation as an important physical example.
Skin biopsy and quantitative sensory testing do not predict response to lidocaine patch in painful neuropathies
Authors: Herrmann David N. , Pannoni Valerie , Barbano Richard L. , Pennella‐Vaughan Janet , Dworkin Robert H.
Published: October 2005

Predictors of response to neuropathic pain treatment in patients with painful distal sensory neuropathies are lacking. The 5% lidocaine patch is believed to exert its effects on neuropathic pain via a local stabilizing effect on cutaneous sensory afferents. As such, it provides a model to assess whether the status of epidermal innervation as determined by skin biopsy or quantitative sensory testing (QST) of small‐ and large‐diameter sensory afferents might serve as predictors of response to topical, locally active treatment. In this study we assessed associations between epidermal nerve fiber (ENF) densities, sensory nerve conduction studies (NCS), QST, and response to a 5% lidocaine patch in patients with painful distal sensory neuropathies. We observed no association between distal leg epidermal and subepidermal innervation and response to the lidocaine patch. Several patients with complete loss of distal leg ENF showed a response to the lidocaine patch. Similarly we observed no consistent association between treatment response and QST for vibration, cooling, warm, heat‐pain, and cold‐pain thresholds, or distal sensory NCS. Thus, distal‐leg skin biopsy, QST, and sensory NCS cannot be used to identify patients with painful polyneuropathy likely to respond to a lidocaine patch in clinical practice. Further studies are required to clarify precisely the mechanism and site of action of the lidocaine patch in patients with peripheral neuropathic pain. Muscle Nerve, 2005
Gene‐based treatment of motor neuron diseases
Authors: Federici Thais , Boulis Nicholas M.
Published: October 2005

Motor neuron diseases (MND), such as amyotrophic lateral sclerosis (ALS) and spinal muscular atrophy (SMA), are progressive neurodegenerative diseases that share the common characteristic of upper and/or lower motor neuron degeneration. Therapeutic strategies for MND are designed to confer neuroprotection, using trophic factors, anti‐apoptotic proteins, as well as antioxidants and anti‐excitotoxicity agents. Although a large number of therapeutic clinical trials have been attempted, none has been shown satisfactory for MND at this time. A variety of strategies have emerged for motor neuron gene transfer. Application of these approaches has yielded therapeutic results in cell culture and animal models, including the SOD1 models of ALS. In this study we describe the gene‐based treatment of MND in general, examining the potential viral vector candidates, gene delivery strategies, and main therapeutic approaches currently attempted. Finally, we discuss future directions and potential strategies for more effective motor neuron gene delivery and clinical translation. Muscle Nerve, 2005
Intracellular signaling during skeletal muscle atrophy
Authors: Kandarian Susan C. , Jackman Robert W.
Published: October 2005

A variety of conditions lead to skeletal muscle atrophy including muscle inactivity or disuse, multiple disease states (i.e., cachexia), fasting, and age‐associated atrophy (sarcopenia). Given the impact on mobility in the latter conditions, inactivity could contribute in a secondary manner to muscle atrophy. Because different events initiate atrophy in these different conditions, it seems that the regulation of protein loss may be unique in each case. In fact differences exist between the regulation of the various atrophy conditions, especially sarcopenia, as evidenced in part by comparisons of transcriptional profiles as well as by the unique triggering molecules found in each case. By contrast, recent studies have shown that many of the intracellular signaling molecules and target genes are similar, particularly among the atrophies related to inactivity and cachexia. This review focuses on the most recent findings related to intracellular signaling during muscle atrophy. Key findings are discussed that relate to signaling involving muscle ubiquitin ligases, the IGF/PI3K/Akt pathway, FOXO activity, caspase‐3 activity, and NF‐kappaB signaling, and an attempt is made to construct a unifying picture of how these data can be connected to better understand atrophy. Once more detailed cellular mechanisms of the atrophy process are understood, more specific interventions can be designed for the attenuation of protein loss. Muscle Nerve, 2006
Selective activation of the sacral anterior roots for induction of bladder voiding
Authors: Bhadra Narendra , Grünewald Volker , Creasey Graham H. , Mortimer J. Thomas
Published: October 2005

Aim

We investigated the efficacy of selective activation of the smaller diameter axons in the sacral anterior roots for electrically induced bladder voiding.

Materials and Methods

Acute experiments were conducted in five adult dogs. The anterior sacral roots S2 and S3 were implanted bilaterally with tripolar electrodes. Pressures were recorded from the bladder and from the proximal urethra and the external urethral sphincter. A detector and flow meter monitored fluid flow. A complete sacral dorsal rhizotomy was carried out. The effects of two types of pulse trains at 20 Hz were compared; quasitrapezoidal pulses (500 µsec with 500 µsec exponential decay) and interrupted rectangular (100 µsec, 2 sec on/2 sec off). Before rhizotomy, rectangular pulse trains (100 µsec) to activate all fibers were also applied. The experimental design was block randomized before and after rhizotomy.

Results

Quasitrapezoidal pulses showed block of sphincter activation with average minimum current for maximum suppression of 1.37 mA. All pulse types evoked average bladder pressures above the basal sphincter closure pressure. The pressure patterns in the proximal urethra closely followed the bladder pressures. Before dorsal rhizotomy, stimulation evoked a superadded increase in sphincter pressures with slow rise time. After rhizotomy, the sphincter pressure patterns followed the bladder pressures during selective activation and voiding occurred during stimulation with quasitrapezoidal trains and in between bursts with interrupted rectangular stimulation.

Conclusions

Selective activation of sacral ventral roots combined with dorsal rhizotomy may provide a viable means of low‐pressure continuous voiding in neurological impairment. Neurourol. Urdynam. © 2005 Wiley‐Liss, Inc.
A row relaxation method for large ℓp least norm problems
Authors: Dax Achiya
Published: October 2005

This paper presents a row relaxation method for solving the regularized ℓp least norm problem

where e and p are positive constants, 1<p<∞ The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem

It is shown that the dual of the regularized problem has the form

where q = p /(p ‐ 1). Moreover, if y solves the dual problem then X = ATy/ϵ solves the primal problem and P(ATy/ϵ) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.
Local refinement techniques for elliptic problems on cell‐centered grids; II. Optimal order two‐grid iterative methods
Authors: Ewing R. E. , Lazarov R. D. , Vassilevski P. S.
Published: October 2005

Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell‐centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher‐order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG‐LS in the nonsymmetric case) are presented.
GMRESR: a family of nested GMRES methods
Authors: Van der Vorst H. A. , Vuik C.
Published: October 2005

Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU‐time and memory requirements in typical CFD applications.
Backward error, sensitivity, and refinement of computed solutions of algebraic Riccati equations
Authors: Ghavimi Ali R. , Laub Alan J.
Published: October 2005

In this paper, a new backward error criterion, together with a sensitivity measure, is presented for assessing solution accuracy of nonsymmetric and symmetric algebraic Riccati equations (AREs). The usual approach to assessing reliability of computed solutions is to employ standard perturbation and sensitivity results for linear systems and to extend them further to AREs. However, such methods are not altogether appropriate since they do not take account of the underlying structure of these matrix equations. The approach considered here is to first compute the backward error of a computed solution X̂ that measures the amount by which data must be perturbed so that X̂ is the exact solution of the perturbed original system. Conventional perturbation theory is used to define structured condition numbers that fully respect the special structure of these matrix equations. The new condition number, together with the backward error of computed solutions, provides accurate estimates for the sensitivity of solutions. Optimal perturbations are then used in an iterative refinement procedure to give further more accurate approximations of actual solutions. The results are derived in their most general setting for nonsymmetric and symmetric AREs. This in turn offers a unifying framework through which it is possible to establish similar results for Sylvester equations, Lyapunov equations, linear systems, and matrix inversions.
Eigenvalue translation based preconditioners for the GMRES(k) method
Authors: Kharchenko S. A. , Yu. Yeremin A.
Published: October 2005

The paper considers a possible approach to the construction of high‐quality preconditionings for solving large sparse unsymmetric offdiagonally dominant, possibly indefinite linear systems. We are interested in the construction of an efficient iterative method which does not require from the user a prescription of several problem‐dependent parameters to ensure the convergence, which can be used in the case when only a procedure for multiplying the coefficient matrix by a vector is available and which allows for an efficient parallel/vector implementation with only one additional assumption that the most of eigenvalues of the coefficient matrix are condensed in a vicinity of the point 1 of the complex plane. The suggested preconditioning strategy is based on consecutive translations of groups of spread eigenvalues into a vicinity of the point 1. Approximations to eigenvalues to be translated are computed by the Arnoldi procedure at several GMRES(k) iterations. We formulate the optimization problem to find optimal translations, present its suboptimal solution and prove the numerical stability of consecutive translations. The results of numerical experiments with the model CFD problem show the efficiency of the suggested preconditioning strategy.
Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion
Authors: Elsner Ludwig , He Chunyang , Mehrmann Volker
Published: October 2005

We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
Some inverse eigenproblems for Jacobi and arrow matrices
Authors: Borges Carlos F. , Frezza Ruggero , Gragg William B.
Published: October 2005

We consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.
Regions of convergence of the Rayleigh quotient iteration method
Authors: Pantazis Ricardo D. , Szyld Daniel B.
Published: October 2005

The Rayleigh quotient iteration method finds an eigenvector and the corresponding eigenvalue of a symmetric matrix. This is a fundamental problem in science and engineering. Parlett and Kahan have shown, in 1968, that for almost any initial vector in the unit sphere, the Rayleigh quotient iteration method converges to some eigenvector. In this paper, the regions of the unit sphere which include all possible initial vectors converging to a specific eigenvector are studied. The generalized eigenvalue problem Ax = λBx is considered. It is shown that the regions do not change when the matrix is shifted or multiplied by a scalar. These regions are completely characterized in the three‐dimensional case. It is shown that, in this case, the area of the region of convergence corresponding to the interior eigenvalue is larger than the area of those corresponding to any extreme one. This can be interpreted, with the appropriate choice of probability distribution, as: the probability of converging to an eigenvector corresponding to the interior eigenvalue is larger than the probability of converging to an eigenvector corresponding to any extreme eigenvalue. It is conjectured that the same is true for matrices of any order. Experiments in higher dimensions are presented which conform with the conjecture.
Completely parallelizable preconditioning methods
Authors: Gustafsson Ivar , Lindskog Gunhild
Published: October 2005

A class of parallelizable preconditioned iterative methods for the solution of certain finite difference or finite element linear systems of equations is presented. The methods are based on calculation of approximate inverses of the SSOR factorization. The speed of the methods may be increased by making the approximation of the inverse more accurate. The construction of the preconditioning as well as the solution of the preconditioning systems (realized by matrix–vector multiplication) can be made in parallel over the total amount of meshpoints. The methods are suitable for implementation on massively parallel computers such as connection machines. Problems with constant as well as strongly varying orthotropy are examined and the methods are compared to other parallel techniques with respect to rate of convergence, computational complexity and consumed CM200 computing time. We report a small but significant decrease in computing time compared to the (until now) most frequently used completely parallel preconditioning, the Jacobi method.
A saxpy formulation for plane rotations
Authors: Ypma Tjalling J.
Published: October 2005

An algorithm for pre‐ or post‐multiplication of a matrix by a plane rotation, using only three vector saxpy operations instead of the four vector operations usually considered necessary, is described. No auxiliary storage for overwriting is required. The method is shown to be numerically stable.
Note on a modified Conjugate Gradient Method
Authors: Wood Winifred L.
Published: October 2005

Mr. Bruce Irons recently1 proposed a modification of the Conjugate Gradient Method. This note shows that if the matrix of the original set of equations is symmetric this method will have the same terminal property as the usual Conjugate Gradient Method except for a particular case when it will not converge at all. If the matrix is not symmetric we cannot deduce the usual terminal property.
Exact Mises limit loads for cylindrical shells
Authors: Haydl H. M. , Sherbourne A. N.
Published: October 2005

Numerical solutions for limit loads of pressurized cylindrical cantilever shells are given for the exact Il'yushin yield surface.

It is suggested that the numerical approach can be used for more complex problems for which the exact solution based on equation (2) has not been obtained to date.
Multiple constraints in structural optimization
Authors: Gellatly R. A. , Helenbrook R. G. , Kocher L. H.
Published: October 2005

This paper considers the problem of solving the optimality criteria equations for a truss structure. A unique Newton‐Raphson method for optimizing redundant structures subject to multiple constrainsts on displacement and member sizes is presented. Both equality and inequality constraints are considered. The characteristics of this approach along with least squares and recursive techniques for the solution of the non‐linear optimality criteria equations are examined numerically for several sample problems. This new formulation offers the advantages of a reduction in the number of dependent variables, ease of incorporation of various types of constraints, and very rapid convergence.
Optimal design of bending elements
Authors: Armand Jean‐Louis , Lodier Bernard
Published: October 2005

Derivation of an optimality criterion for finite element structural representations using constant‐moment plate‐bending triangular elements ispresented. Numerical examples of minimum‐mass design of both simply‐supported and clamped elastic plates for concentrated and distributed loading conditions under a single displacement constraint serve to illustrate the suggested procedure. Interpretation of the solution obtained and difficulties involved are discussed in the light of recent application of optimal control theory to structural optimization.
A comparison of stability and accuracy of some numerical models of two‐dimensional circulation
Authors: Sasaki Y. K. , Reddy J. N.
Published: October 2005

The purpose of the paper is two‐fold: Firstly, we develop stream function‐‐vorticity and primitive variable finite element models of two‐dimensional barotropic equations that satisfy the conservation of mean vorticity, mean squared vorticity (or enstrophy) and mean kinetic energy, and scondly, we present a comparative study of a number of numerical schemes for their accuracy in phase speed as well as in amplitude calculations for a two‐dimensional, time‐dependent, stream function‐‐vorticity equation for periodic fluid motion in a channel. A circular vortex is placed in a uniform channel flow of a constant velocity (U) as an initial condition. An analytic solution exists for the problem such that the vortex moves with a constant speed U conserving the shape of the vortex:

where U, ψ0 a are constants. This example makes it easier to identify the cause of phase speed error, either due to linear or non‐linear processes, and furthermore, to find a satisfactory scheme for time integration. The numerical schemes compared include: Arakawa Jacobian,1 Arakawa–Matsuno scheme, Galerkin finite element, Lax–Wendroff, leap‐frog, and Crank–Nicholson. The effect of a variational adjustment (see Sasaki16) is also studied. Computational time, RMS errors in stream function and vorticity, and the conservation of the mean kinetic energy and enstrophy are compared at the end of 120 (one period) and 240 (two periods) time steps. The study indicates that the numerical scheme that employs finite elements in space (same as Arakawa Jacobian) and Crank–Nicholson in time is the most accurate among the schemes studied.
A conforming solution to curved plate bending problems
Authors: Caramanlian C.
Published: October 2005

A curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary.

To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight‐sided triangle and a ‘curved segment’. The straight‐sided triangle is extensively documented in the literature2‐5 and is referred to in the paper as the Cowper triangle. The curved segment is a two‐noded element with 12 degrees‐of‐freedom. It has one straight side and one curved side.

Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries.

The method is easily extended to elements of higher order.
Elastoplastic BIE analysis of cracked plates and related problems. Part 1: Formulation
Authors: Cruse T. A. , Polch E. Z.
Published: October 2005

The boundary‐integral equation formulation for two‐dimensional, planar fracture mechanics based on the use of a special Green's function forms the basis of this analytical paper. The Green's function method is extended to problems of anelastic strain distributions (e.g. elastoplasticity, thermal gradients, residual strains) through a volume (area) integral. The role of the elastic Green's function for the crack problem on the distribution of elastoplastic strains is reviewed. Further, new analytical results for elastic stress intensity factor models for the residual strain and thermal gradient problems are presented. Part 2 of this paper outlines the numerical solution strategy and results for several test problems.
A new triangular discrete Kirchhoff plate/shell element
Authors: Dhatt G. , Marcotte L. , Matte Y.
Published: October 2005

We present a new 6‐node triangular bending element (called DKTP) based on a discrete Kirchhoff model. A corresponding new flat‐shell element, DLTP, having quadratic variation of in‐plane displacement is also presented. This element has 6 degrees‐of‐freedom (u, v, w, θx, θy, θz) at each corner node and 3 degrees‐of‐freedom (u, v, w) at each mid‐side node. Detailed numerical experimentation is presented to demonstrate the efficiency and reliability of these elements.
Computation of hybrid element matrices by elimination techniques
Authors: Chieslar J. D. , Ghali A.
Published: October 2005

Three functionals, the modified forms of the Hu–Washizu, Hellinger‐Reissner, and complementary energy principles, as developed by Pian, Chen, and Kang1.2 are stated. Finite element discretization of each is presented and the ensuing computations developed, resulting in the element stiffness matrix, with displacement degrees‐of‐freedom only, and the stress recovery matrices. Subroutines are presented for this purpose where the close relationship of the three principles is exploited to result in a compact hybrid element technique. The techniques herein reviewed are assumed applicable at the individual element level. The usual summation over all elements in the model is implied.
Three‐dimensional elastic finite element study of the skid resistance of grooved pavement
Authors: Moore I. D. , Purushothaman N. , Heaton B. S.
Published: October 2005

A three‐dimensional finite element model has been developed to simulate the sliding of a rubber block over a grooved road surface. The model makes use of the symmetries of the problem to simplify the analysis, so that two‐dimensional isoparametric elements of both rectangular and triangular configuration have been extended into the third dimension. A procedure for analysing the behaviour of any one groove to groove unit of the pavement is also developed, and this is extended so that the contact between the sliding rubber block and the leading edge of each raised pavement section is analysed. Preliminary comparisons between theoretical calculations and experimental measurements indicate that the finite element procedure provides an accurate and economical estimate of the behaviour of the rubber slider as it is pressed into a grooved pavement. Elastic predictions of sliding resistance seem reasonable at low sliding speeds, but viscoelastic rubber analysis appears necessary if higher speed skid resistance is to be predicted.
Accuracies of numerical solution methods for the pressure‐modified von Mises model
Authors: Lee J. H.
Published: October 2005

The accuracy of three numerical algorithms—the tangent‐stiffness radial‐return, secant‐stiffness radial‐return and simple radial‐return methods—is analysed against exact solutions for the pressure‐modified von Mises yield criterion with the associated flow rule. The governing equations of the exact solutions are derived using a simple and innovative geometrical approach, in terms of a pair of non‐linear, first order differential equations, in rate change of the deviatoric radius and in rate change of angular locations on the deviatoric plane. For both accuracy and efficiency, and for small and large time steps, the secant‐stiffness radial‐return method is the best of all.
Finite element analysis of plane couple‐stress problems using first order stress functions
Authors: Wood R. D.
Published: October 2005

A complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple‐stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting C0 finite element ‘equilibrium stress model’ is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.
A mixed explicit‐implicit (EI) algorithm for creep stress analysis
Authors: Chen G. G. , Hsu T. R.
Published: October 2005

A mixed explicit‐implicit numerical integration algorithm for creep stress analysis is presented in this paper. This method allows simultaneously use of, and thus benefit from, both these integration schemes. The continuum damage constitutive model is also implemented in this algorithm. The present method is suitable for the prediction of creep crack growth in solids using the continuum damage approach.

Numerical examples using different constitutive equations have been included to demonstrate the high efficiency of the proposed algorithm.
Assumed strain stabilization procedure for the 9‐node Lagrange shell element
Authors: Belytschko Ted , Wong Bak Leong , Stolarski Henryk
Published: October 2005

An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9‐node shell element. The stabilization procedure can be justified based on the Hellinger–Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co‐ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9‐node element. Example problems show good accuracy and an almost optimal rate of convergence.
Eigenvalue analysis of compatible and incompatible rectangular four‐node quadrilateral elements
Authors: Hacker W. L. , Schreyer H. L.
Published: October 2005

Exact analytical expressions for the eigenvalues of the elastic stiffness matrix are obtained for the four‐node, rectangular, quadrilateral element. A procedure is given for identifying alternative hourglass modes and eigenvalues which render the element incompatible but with non‐monotonic convergence assured. A convergence study confirms that for the special case of when the hourglass modes coincide with beam bending the element can serve as a beam element. Analytical expressions are given for the resulting element stiffness matrix.