Abstract: This paper presents a complete formulation of a model of coupled associative thermoplasticity at finite strains, addresses in detail the numerical analysis aspects involved in its finite element implementation, and assesses the performance of the proposed mechanical and finite element models in a comprehensive set of numerical simulations. On the thermomechanical side, novel aspects of the proposed model of thermoplasticity are (1) the explicit characterization of the plastic (configurational) entropy as an independent internal variable, (2) a thermomechanical extension of the principle of maximum dissipation consistent with the multiplicative decomposition of the deformation gradient, and (3) the exploitation of this extended principle in the formulation of an associative flow which characterizes the evolution of the plastic entropy in terms of the change of the flow criterion with respect to temperature. On the numerical analysis side, salient features of the proposed approach are (4) a new global product formula algorithm constructed via an operator split of the nonlinear initial value problem, which leads to a two-step solution procedure, (5) a unified class of local return mapping algorithms which preserves exactly the incompressibility constraint on the plastic flow and reduces to the classical radial return method for isothermal J 2 - flow theory, and (6) the formulation of a mixed finite element method in terms of the elastic entropy and the temperature field which circumvents well-known difficulties associated with the incompressibility constraint on the plastic flow. The exact linearization of both the product formula algorithm and an alternative simulataneous solution scheme for the coupled thermomechanical problem is given in two appendices.

Abstract: A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Abstract: The author surveys several numerical tools that can be used for the analysis and solution of systems of linear algebraic equations derived from Fredholm integral equations of the first kind. These tools are based on the singular value decomposition (SVD) and the generalized SVD, and they allow the user to study many details of the integral equation. The tools also aid the user in choosing a good regularization parameter that balances the influence of regularization and perturbation errors.

Abstract: Basic Field Theory. Images. The Solution of Laplace's Equation by Separation of the Variables. Fields with Distributed Currents: Poisson and Diffusion Equations. Conformal Transformation: Basic Ideas. Polygonal Boundaries. General Considerations. Computational Modeling--Basic Methods. Two-Dimensional Static Linear Problems. Non-Linear Effects in Two-Dimensional Fields. Two-Dimensional Time-Dependent Fields. Three-Dimensional Problems. Electromagnetic Software Environment. Appendices. Bibliography. Index.

Abstract: The book (paperback edition) is the second edition of the work published under the title ``Numerical methods for computer science, engineering, and mathematics'' (1987). The intention of the author is to give an introduction to numerical methods for undergraduate students in computer science, engineering, and mathematics. On more than 600 pages, the book provides an ample material in different fields of numerical analysis such as the solution of nonlinear equations and linear systems of equations, interpolation and polynomial approximation, curve fitting, numerical differentiation, numerical integration, numerical optimization, solution of ordinary and partial differential equations, and calculation of eigenvalues as well as eigenvectors.\par It is assumed that the reader is familiar with calculus and basic aspects of structured programming languages. The book contains a well-balanced minimum of the theory of numerical analysis and takes care to provide a good understanding of the essential ideas of numerical methods. Otherwise, special emphasis is placed on the presentation of algorithms for various numerical processes. Some algorithms are described by pseudo-code and are easy to translate into BASIC, C, FORTRAN, or Pascal. Computer calculations given in the form of tables and graphs, and many examples as well as figures improve the readability of the text. Numerous exercises and the computer-oriented presentation of numerical methods are special features of this book.

Abstract: We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv?0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.

Abstract: Eleven numerical methods for estimation of AUC(including 4 new methods) and 22 methods for AUMC(including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral, and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC.Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.

Abstract: A fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analysed. Existence and uniqueness of the numerical solution and its convergence to the solution of the continuous problem are proved. Two iterative schemes to solve the resulting algebraic problem are proposed and some numerical results in one space dimension are presented.

Abstract: A numerical scheme for the approximation of a parameter-dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value. A robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter. Precise mathematical definitions for these terms are developed, their quantitative characterization is given, and some general theorems involving locking and robustness are proven. A model problem involving heat transfer is analyzed in detail using this mathematical framework, and various related computational results are described. Applications to some different problems involving locking are presented.

Abstract: We address the problem of estimating parameters in systems of ordinary differential equations which give rise to chaotic time series. We claim that the problem is naturally tackled by boundary value problem methods. The power of this approach is demonstrated by various examples with ideal as well as noisy data. In particular, Lyapunov exponents can be computed accurately from time series much shorter than those required by previous methods.

Abstract: The authors propose a technique, which they call superabsorption, for improving absorbing boundary conditions in finite-difference time-domain methods. This method can be applied to every known absorbing boundary condition and greatly reduces the numerical error caused by the boundary reflection. The principle and analysis of the superabsorption method are presented. Numerical tests indicating the improvements obtained on many absorbing boundary conditions are reported. >

Abstract: Computer arthimetic and errors iterative solution of nonlinear equations approximate evaluation of elementary functions polynomial interpolation other interpolation functions systems of linear equations approximation of functions optimization numerical calculus ordinary differential equations the eigenvalue problem boundary value problems the impact of parallel computers.

Abstract: An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically. >

Abstract: An exact Riemann solver for the shallow water equations along with several approximate Riemann solvers are presented. These solutions are then used locally to help compute numerically the global solution of the general initial boundary value problem for the shallow water equations. The numerical method used is the weighted average flux method (WAF) proposed by the author. This is a conservative, shock capturing high resolution TVD method. For shallow water flows where nonlinear effects are important or where abrupt changes (hydraulic jumps) are to be expected the present algorithms can be useful in practice. One and two-dimensional solutions are presented to assess both the Riemann solvers and the WAF method.

Abstract: The addition of a dissipation step to the widely used McCormack numerical scheme is proposed for solving one-dimensional open-channel flow equations. The extra step is devised according to the theory of total variation diminishing (TVD) schemes that are capable of capturing sharp discontinuities without generating the spurious oscillations that more classical methods do. At the same time, the extra step does not introduce any additional difficulty for the treatment of the source terms of the equations. Results from several computations are presented and comparison with the analytical solution for some test problems is shown. The overall performance of the method can be considered very good, and it allows for accurate open-channel flow computations involving hydraulic jumps and bores.

Abstract: This paper describes thee different numerical methods for the computation of flows with moving immersed elastic boundaries. A two-dimensional incompressible fluid and a boundary in the form of a simple closed curve are considered. The inertia is assumed to be negligible and the Stokes equations are solved. The three methods are explicit, approximate-implicit, and implicit. The first two have been used before, but the implicit method is new in the context of flows with moving immersed boundaries. They differ only with respect to the computation of the boundary force. The results of the above methods at various values of the time-step size are compared in order to explore the numerical stability of the computation.

Abstract: The scattering of an incident plane wave from an array of parallel circular dielectric and/or conducting cylinders is derived rigorously using a boundary value approach. Both transverse electric (TE) and transverse magnetic (TM) polarized incident plane waves are considered. The validity and accuracy of the method are verified by comparing the numerical results with those based on other available methods. The advantage of the proposed analysis is the simplicity and efficiency in computation. The modeling of two-dimensional objects of arbitrary cross section and composite material is outlined and sample numerical results are presented to illustrate the versatility of the method. >

Abstract: We analyse the problem of membrane locking in (h, p) finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution. We show that in the standard finite element method, locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder. A general strategy of avoiding locking by using modified bilinear forms is introduced, and a special implementation of this strategy on aligned rectangular grids is considered.

Abstract: The MAC (Marker and Cell) discretization of fluid flow is analysed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard ${\bf H}^1 $ and $L^2 $ norms are given for the velocity and pressure, respectively.

Abstract: This report is a description of the two-dimensional version of CAVEAT, a computer code which solves numerically the equations of transient, multimaterial, compressible fluid dynamics CAVEAT is written to treat a wide variety of problems It has the ability, for example, to describe material interfaces and the large slip along interfaces, to describe complex geometries without sacrificing vector processing, and to apply tabular equations of state Its numerical methods were chosen to minimize numerical diffusion, achieve a high degree of vectorization, and facilitate extension to three dimensions CAVEAT uses an explicit time-marching, conservative finite-volume numerical technique in which all state variables, including velocity, are cell centered; values at vertices and cell faces are derived The technique is a variation of the Godunov method that uses an approximate Riemann solver and accommodates arbitrary equations of state Spatial differencing may either be first order or second order with a choice of limiters of the gradient in an attempt to preserve monotonicity The formulation is spatially two-dimensional with options for Cartesian and curvilinear geometries Discretization is achieved with a mesh of arbitrary quadrilateral cells whose vertices can move with time Arbitrary mesh motion is supported by allowing transport of material between cells accordingmore » to the Arbitrary Lagrangian-Eulerian technique This report is a second edition of an earlier report on CAVEAT Because of the maturity and expanded use of CAVEAT, this report includes new sections directed toward first-time users We have chosen to document in this report only the hydrodynamics part of the much larger version of CAVEAT« less