bluuebunny/crossref_metadata_2025_split huggingface dataset:
Single heartbeat cardiac tagging for the evaluation of transient phenomena
Authors: Herzka Daniel A. , Derbyshire J. Andrew , Kellman Peter , McVeigh Elliot R. 
Published: November 2005

AbstractMany cardiac abnormalities are of a transient nature, creating a beat‐to‐beat variation in myocardial function. This work presents the cardiac imaging technique for the measurement of regional function during transient cardiac phenomena. All information necessary for the reconstruction of a cine loop is acquired within a single heartbeat, avoiding the temporal blurring introduced by segmented imaging due to the assumption of cardiac cycle periodicity. This method incorporates a gradient‐optimized, high‐efficiency EPI‐SSFP sequence and TSENSE parallel imaging. For acquisitions with readout resolutions of 128,160, 192, and 256 points, the technique produced images with average temporal resolution of 35, 39, 43, and 52 ms and average spatial resolutions of 2.65, 2.12, 1.77, and 1.32 mm in the readout direction, respectively, and 2.88 and 2.08 mm in the phase encode direction for acceleration rates of 3 and 4, respectively. Local apparent strains in the single slice and measurements of ventricular end‐systolic and end‐diastolic areas were used as quantitative measures to validate the single heartbeat technique. To demonstrate the utility of the sequence, movie loops were acquired for multiple heartbeats in non‐breath‐held acquisitions as well as during a Valsalva maneuver. A heartbeat‐interleaved acquisition allowed for the reconstruction of nonaccelerated images from R contiguous heartbeats. Images reconstructed from such data displayed tag blurring and reduced tag persistence due to motion and interheartbeat variability. Images acquired during the Valsalva maneuver demonstrated apparent beat‐to‐beat variability, visible both in the images and as changing strain patterns and ventricular volumes. Magn Reson Med, 2005. Published 2005 Wiley‐Liss, Inc.
Quantitative assessment of coronary artery plaque vulnerability by high‐resolution magnetic resonance imaging and computational biomechanics: A pilot study ex vivo
Authors: Zheng Jie , El Naqa Issam , Rowold Faith E. , Pilgram Thomas K. , Woodard Pamela K. , Saffitz Jeffrey E. , Tang Dalin 
Published: November 2005

AbstractThe risk of atherosclerotic plaque disruption is thought to be closely related to plaque composition and rupture triggers such as external mechanical forces. The purpose of this study was to integrate MR imaging and computational techniques for the quantification of plaque vulnerability with morphologic data and biomechanical stress/strain distributions that were all based on high‐resolution MR images of coronary artery plaque specimens ex vivo. Twenty‐two coronary artery plaque specimens were selectively collected from 10 cadavers. Multislice T2‐weighted spin echo images were acquired with a resolution of 100 × 100 μm2. Histopathological images were used as the gold standard for the identification of plaque components and vulnerability. Plaque components were classified on MR images, and the stress/strain components were calculated with a two‐dimensional computational model with fluid–structure interactions. As expected, vulnerable plaques appeared to result from a large lipid pool, a thin fibrous cap, and some critical stress/strain conditions. An empiric vulnerability marker was derived and was closely related to the vulnerability score that was determined through pathologic examination. Noninvasive quantification of the MR contrast and mechanical properties of plaque may provide a comprehensive biomarker for the assessment of vulnerability of atherosclerotic plaques. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
The concept of special inner products for deriving new conjugate gradient‐like solvers for non‐symmetric sparse linear systems
Authors: Meyer Arnd 
Published: November 2005

AbstractYserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE‐systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG‐like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N‐vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.
Diagonally compensated reduction and related preconditioning methods
Authors: Axelsson O. , Kolotilina L. 
Published: November 2005

AbstractWhen solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M‐matrices (H‐matrices). In some application areas, however, the arising coefficient matrices are not H‐matrices. This is the case, for instance, when higher‐order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M‐matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
Algebraic multilevel iteration method for Stieltjes matrices
Authors: Axelsson O. , Neytcheva M. 
Published: November 2005

AbstractThe numerical solution of elliptic selfadjoint second‐order boundary value problems leads to a class of linear systems of equations with symmetric, positive definite, large and sparse matrices which can be solved iteratively using a preconditioned version of some algorithm. Such differential equations originate from various applications such as heat conducting and electromagnetics. Systems of equations of similar type can also arise in the finite element analysis of structures.We discuss a recursive method constructing preconditioners to a symmetric, positive definite matrix. An algebraic multilevel technique based on partitioning of the matrix in two by two matrix block form, approximating some of these by other matrices with more simple sparsity structure and using the corresponding Schur complement as a matrix on the lower level, is considered.The quality of the preconditioners is improved by special matrix polynomials which recursively connect the preconditioners on every two adjoining levels. Upper and lower bounds for the degree of the polynomials are derived as conditions for a computational complexity of optimal order for each level and for an optimal rate of convergence, respectively.The method is an extended and more accurate algebraic formulation of a method for nine‐point and mixed five‐ and nine‐point difference matrices, presented in some previous papers.
On the convergence of difference schemes for a heat conduction equation
Authors: Andreev Andrey , Juboury Hussain 
Published: November 2005

AbstractSufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
Authors: Freund Roland W. , Hochbruck Marlis 
Published: November 2005

AbstractRecently, Freund and Nachtigal proposed the quasi‐minimal residual algorithm (QMR) for solving general nonsingular non‐Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose‐free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov‐subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.
A fast minimal residual algorithm for shifted unitary matrices
Authors: Jagels Carl F. , Reichel Lothar 
Published: November 2005

AbstractA new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non‐Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
Efficient reduction algorithms for bordered band matrices
Authors: van Huffel Sabine , Park Haesun 
Published: November 2005

AbstractVarious plane rotation patterns are presented, which provide stable algorithms for reducing a b‐band matrix bordered by p rows and/or columns to (b + p)‐band form. These schemes generalize previously presented O(N2) reduction algorithms for matrices of order N, b = 1, and p = 1 to the reduction of more general b‐band, p‐bordered matrices where b ≥ 1 and p ≥ 1. Moreover, by splitting the matrix into two similarly structured submatrices and chasing nonzeros to the corners in two directions, the newly proposed patterns reduce the number of required rotations and hence the computational cost by one half compared to the other existing one‐way chasing algorithms. Symmetric, as well as more general matrices, are considered. An example of the first type is the symmetric arrowhead matrix that arises in solving inverse eigenvalue problems. Examples of the second type are found in updating the singular value decomposition (SVD) and the partial SVD.
Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
Authors: Druskin Vladimir , Knizhnerman Leonid 
Published: November 2005

AbstractMany researchers are now working on computing the product of a matrix function and a vector, using approximations in a Krylov subspace. We review our results on the analysis of one implementation of that approach for symmetric matrices, which we call the spectral lanczos decomposition method (SLDM).We have proved a general convergence estimate, relating SLDM error bounds to those obtained through approximation of the matrix function by a part of its Chebyshev series. Thus, we arrived at effective estimates for matrix functions arising when solving parabolic, hyperbolic and elliptic partial differential equations. We concentrate on the parabolic case, where we obtain estimates that indicate superconvergence of SLDM. For this case a combination of SLDM and splitting methods is also considered and some numerical results are presented.We implement our general estimates to obtain convergence bounds of Lanczos approximations to eigenvalues in the internal part of the spectrum. Unlike Kaniel‐Saad estimates, our estimates are independent of the set of eigenvalues between the required one and the nearest spectrum bound.We consider an extension of our general estimate to the case of the simple Lanczos method (without reorthogonalization) in finite computer arithmetic which shows that for a moderate dimension of the Krylov subspace the results, proved for the exact arithmetic, are stable up to roundoff.
Progress in the numerical solution of the nonsymmetric eigenvalue problem
Authors: Bai Zhaojun 
Published: November 2005

AbstractWith the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.
On Parlett's matrix norm inequality for the Cholesky decomposition
Authors: Edelman Alan , Mascarenhas Walter F. 
Published: November 2005

AbstractWe show that a certain matrix norm ratio studied by Parlett has a supermum that is O(\documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[\sqrt n \] $\end{document}) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2‐norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.
Optimal backward perturbation bounds for the linear least squares problem
Authors: Waldén Bertil , Karlson Rune , Sun Ji‐Guang 
Published: November 2005

AbstractLet A be an m × n matrix, b be an m‐vector, and x̃ be a purported solution to the problem of minimizing ‖b — Ax‖2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes ‖b — (A+E)x‖2. This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.
On the solution of block Hessenberg systems
Authors: Stewart G. W. 
Published: November 2005

AbstractThis paper describes a divide‐and‐conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.
Optimal algebraic multilevel preconditioning for local refinement along a line
Authors: Margenov S. , Maubach J. 
Published: November 2005

AbstractThe application of some recently proposed algebraic multilevel methods for the solution of two‐dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.
Peaceman—Rachford procedure and domain decomposition for finite element problems
Authors: Layton William J. , Rabier Patrick J. 
Published: November 2005

AbstractThis paper presents a general method to associate the operator splitting for the Peaceman—Rachford procedure with a decomposition of the domain in problems arising from finite element discretization of partial differential equations. The algorithm is provably convergent without any symmetry requirement. Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman—Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher‐dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial machine.
Multilevel preconditioners for discretizations of the biharmonic equation by rectangular finite elements
Authors: Oswald Peter 
Published: November 2005

AbstractRecently, some new multilevel preconditioners for solving elliptic finite element discretizations by iterative methods have been proposed. They are based on appropriate splittings of the finite element spaces under consideration, and may be analyzed within the framework of additive Schwarz schemes. In this paper we discuss some multilevel methods for discretizations of the fourth‐order biharmonic problem by rectangular elements and derive optimal estimates for the condition numbers of the preconditioned linear systems. For the Bogner–Fox–Schmit rectangle, the generalization of the Bramble–Pasciak–Xu method is discussed. As a byproduct, an optimal multilevel preconditioner for nonconforming discretizations by Adini elements is also derived.
Finite element procedures for strain estimations of sheet metal forming parts
Authors: Guo Y. Q. , Batoz J. L. , Detraux J. M. , Duroux P. 
Published: November 2005

AbstractA finite element algorithm is developed to predict the strain distribution of sheet forming parts and to evaluate their formability at the design stage. The algorithm is simply called the inverse approach since we know the positions of the material points on the final product and we determine the positions of the corresponding material points in the initial blank. This is also a direct algorithm which avoids the path dependent incremental procedure of plasticity and contact. This paper presents some theoretical aspects related to the large logarithmic strains with membrane triangular elements, the deformation theory of plasticity, the isotropic and anisotropic material properties of metal sheets and the non‐linear solution techniques. Some particular problems are also studied, such as the influence of friction forces under the punch and blankholders, the ‘optimization’ of the initial blank's contour and the deep drawing in several steps. The results are compared with those obtained by experiments and by the more classical incremental approach.
Application of the finite element method to the simulation of sheet forming processes: Comparison of calculations and experiments
Authors: Keck P. , Wilhelm M. , Lange K. 
Published: November 2005

AbstractElastic‐plastic finite element calculations have been carried out to analyse sheet forming processes such as hydrostatic bulging of circular and rectangular blanks and the axisymmetric stretching of sheets (with different punch radii). The results, partly obtained by different finite element models, are compared with experimental data. It could be shown that, regarding the examples considered, experiments and calculations fit well and that a more sophisticated modelling of the contact boundary conditions improves the accuracy of the results. As a first attempt to handle more complex sheet forming operations, the deep drawing of a rectangular cup has been analysed. A summary of the theoretical background as well as some comments on the solution method and the implementation are given.
Finite element simulation of three‐dimensional deformation in shape rolling
Authors: Mori K. , Osakada K. 
Published: November 2005

AbstractA method for simulating three‐dimensional steady‐state deformation in shape rolling with grooved rolls by the rigid‐plastic finite element method is proposed. For the three‐dimensional element mesh, contact of the nodal points with the roll surface and detachment from the surface are judged in each step of calculation. The boundary conditions of metal flow along the curved roll surface and of friction between the roll and the workpiece are dealt with at each node over the interface. Complex steady‐state deformation in shape rolling is simulated by using the non‐steady‐state scheme and the remeshing technique. As examples of simulation, rolling processes of bars and beams with grooved rolls are chosen. The deforming shape, the rolling torque, the roll separating force and the distributions of stress and strain in the workpiece are computed.
Optimal placement of actuators and sensors in control‐augmented structural optimization
Authors: Sepulveda Abdon E. , Schmit Lucien A. 
Published: November 2005

AbstractA control‐augmented structural synthesis methodology is presented in which actuator and sensor placement is treated in terms of (0, 1) variables. Structural member sizes and control variables are treated simultaneously as design variables. A multiobjective utopian approach is used to obtain a compromise solution for inherently conflicting objective functions such as structural mass, control effort and number of actuators. Constraints are imposed on natural frequencies, peak transient displacements and accelerations, peak actuator forces and dynamic stability as well as controllability and observability of the system. The combinatorial aspects of the mixed (0, 1)‐continuous variable design optimization problem are made tractable by combining approximation concepts with branch and bound techniques. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.
Incompressibility without tears—HOW to avoid restrictions of mixed formulation
Authors: Zienkiewicz O. C. , Wu J. 
Published: November 2005

AbstractThe severe restrictions of the Babuška‐Brezzi stability criteria permit only a limited number of interpolations for velocities (displacements) and pressure to be used for incompressible behaviour. These restrictions preclude the use of many useful elements. We show in this paper how such difficulties can be side‐stepped by seeking the steady state solution through the use of various time marching schemes. This permits a simple iterative approach to incompressible (or nearly incompressible) problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow, etc.
Fourth order Runge‐Kutta method in 2d for linear boundary value problems
Authors: Demendy Zoltan 
Published: November 2005

AbstractThe standard formulae of the fourth order Runge‐Kutta method are transformed into a finite difference equation which allow us to solve linear boundary value problems. This equation is manipulated further and extended into 2D for solving second order linear partial differential equations. The various transformations result in four equations for the two first derivatives, mixed second derivative and the function value in the depicted point of the mesh. Each of these quantities is expressed by the linear combination of values of the function given in the eight nearest nodes around the depicted node. Explicit formulation of the equations for corner, boundary, symmetry and internal nodes is given. The results of the new computer code are compared with an analytical result and precise measurements, as well as a FEM calculation. It is concluded, for the specific example investigated, that the new method is about ten or more times precise than the FEM with the same number of elements. The major merit of the method lies in the fact that it can be implemented on personal computers.