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International Journal for Numerical Methods in Engineering July 2 - September 24,2006: Volume 67-68 , Issue INDEX/CONTENTS. Digitized from IA1643936-05 . Previous issue: sim_international-journal-numerical-methods-engineering_2006-06-25_66_13 . Next issue: sim_international-journal-numerical-methods-engineering_2006-07-02_67_1 .

International Journal for Numerical Methods in Engineering July 2 - September 24,2006: Volume 67-68 , Issue INDEX/CONTENTS. Digitized from IA1643936-05 . Previous issue: sim_international-journal-numerical-methods-engineering_2006-06-25_66_13 . Next issue: sim_international-journal-numerical-methods-engineering_2006-07-02_67_1 .

International Journal for Numerical Methods in Engineering July 2 - September 24,2006: Volume 67-68 , Issue INDEX/CONTENTS. Digitized from IA1643936-05 . Previous issue: sim_international-journal-numerical-methods-engineering_2006-06-25_66_13 . Next issue: sim_international-journal-numerical-methods-engineering_2006-07-02_67_1 .

International Journal for Numerical Methods in Engineering July 2 - September 24,2006: Volume 67-68 , Issue INDEX/CONTENTS. Digitized from IA1643936-05 . Previous issue: sim_international-journal-numerical-methods-engineering_2006-06-25_66_13 . Next issue: sim_international-journal-numerical-methods-engineering_2006-07-02_67_1 .

International Journal for Numerical Methods in Fluids 1994: Volume 18 , Issue Contents. Digitized from IA1643919-02 . Previous issue: sim_international-journal-for-numerical-methods-in-fluids_1993-12-30_17_12 . Next issue: sim_international-journal-for-numerical-methods-in-fluids_1994-01-15_18_1 .

International Journal for Numerical Methods in Engineering 2000: Volume 47 , Issue Contents. Digitized from IA1643935-04 . Previous issue: sim_international-journal-numerical-methods-engineering_1999-12-30_46_12 . Next issue: sim_international-journal-numerical-methods-engineering_january-10-30-2000_47_1-3 .

International Journal for Numerical Methods in Engineering 2003: Volume 57 , Issue CONTENTS. Digitized from IA1643935-03 . Previous issue: sim_international-journal-numerical-methods-engineering_2003-04-21_56_15 . Next issue: sim_international-journal-numerical-methods-engineering_2003-05-07_57_1 .

International Journal for Numerical Methods in Engineering 2006: Volume 68 , Issue INDEX/CONTENTS. Digitized from IA1643936-05 . Previous issue: sim_international-journal-numerical-methods-engineering_2006-09-24_67_13 . Next issue: sim_international-journal-numerical-methods-engineering_2006-10-01_68_1 .

International Journal for Numerical Methods in Engineering 2002: Volume 53 , Issue CONTENTS. Digitized from IA1643935-03 . Previous issue: sim_international-journal-numerical-methods-engineering_2001-12-30_52_12 . Next issue: sim_international-journal-numerical-methods-engineering_2002-01-10_53_1 .

International Journal for Numerical and Analytical Methods in Geomechanics 2002: Volume 26 , Issue CONTENTS. Digitized from IA1643932-02 . Previous issue: sim_intl-journal-numerical-methods-in-geomechanics_2001-12-25_25_15 . Next issue: sim_intl-journal-numerical-methods-in-geomechanics_2002-01_26_1 .

International Journal for Numerical and Analytical Methods in Geomechanics 1994: Volume 18 , Issue CONTENTS. Digitized from IA1643932-02 . Previous issue: sim_intl-journal-numerical-methods-in-geomechanics_1993-12_17_12 . Next issue: sim_intl-journal-numerical-methods-in-geomechanics_1994-01_18_1 .

International Journal for Numerical and Analytical Methods in Geomechanics 1994: Volume 18 , Issue CONTENTS. Digitized from IA1643932-02 . Previous issue: sim_intl-journal-numerical-methods-in-geomechanics_1993-12_17_12 . Next issue: sim_intl-journal-numerical-methods-in-geomechanics_1994-01_18_1 .

Thesis advisor, Ashok Gopinath

Thesis advisor, Ashok Gopinath

Includes bibliographical references and indexes

International Journal for Numerical Methods in Fluids 1996: Volume 22 , Issue Contents. Digitized from IA1643919-02 . Previous issue: sim_international-journal-for-numerical-methods-in-fluids_1995-12-30_21_12 . Next issue: sim_international-journal-for-numerical-methods-in-fluids_1996-01-15_22_1 .

International Journal for Numerical Methods in Engineering 1973: Volume 7 , Issue INDEX/CONTENTS. Digitized from IA1643935-02 . Previous issue: sim_international-journal-numerical-methods-engineering_1973_6_4 . Next issue: sim_international-journal-numerical-methods-engineering_1973_7_1 . Note: This issue has no cover

International Journal for Numerical Methods in Engineering 1973: Volume 7 , Issue INDEX/CONTENTS. Digitized from IA1643935-02 . Previous issue: sim_international-journal-numerical-methods-engineering_1973_6_4 . Next issue: sim_international-journal-numerical-methods-engineering_1973_7_1 . Note: This issue has no cover

International Journal for Numerical and Analytical Methods in Geomechanics 1995: Volume 19 , Issue CONTENTS. Digitized from IA1643932-02 . Previous issue: sim_intl-journal-numerical-methods-in-geomechanics_1994-12_18_12 . Next issue: sim_intl-journal-numerical-methods-in-geomechanics_1995-01_19_1 .

We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in three-dimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.

Future extreme-scale computer systems may expose silent data corruption (SDC) to applications, in order to save energy or increase performance. However, resilience research struggles to come up with useful abstract programming models for reasoning about SDC. Existing work randomly flips bits in running applications, but this only shows average-case behavior for a low-level, artificial hardware model. Algorithm developers need to understand worst-case behavior with the higher-level data types they actually use, in order to make their algorithms more resilient. Also, we know so little about how SDC may manifest in future hardware, that it seems premature to draw conclusions about the average case. We argue instead that numerical algorithms can benefit from a numerical unreliability fault model, where faults manifest as unbounded perturbations to floating-point data. Algorithms can use inexpensive "sanity" checks that bound or exclude error in the results of computations. Given a selective reliability programming model that requires reliability only when and where needed, such checks can make algorithms reliable despite unbounded faults. Sanity checks, and in general a healthy skepticism about the correctness of subroutines, are wise even if hardware is perfectly reliable.

We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the "quasi-degenerate density matrix" (QDDM) which is rooted in Anderson's observation that the degenerate symmetry-broken states valid in the thermodynamic limit, are manifested in finite systems as a set of low-energy "quasi-degenerate" states (in addition to the ground state). This method, its original form due to Furukawa et al.[Phys. Rev. Lett. 96, 047211 (2006)], is given a number of improvements here, above all the extension from two-fold symmetry breaking to arbitrary cases. This is applied to two test cases (1) interacting spinless hardcore bosons on the triangular lattice and (2) a spin-1/2 antiferromagnetic system at the percolation threshold. In addition, we survey a different method called the "correlation density matrix", which detects (possibly long-range) correlations only from the ground state, but using the reduced density matrix from a cluster consisting of two spatially separated regions.

The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. The methods that we investigate include Taylor and asymptotic series computations, Gauss-Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide 'roadmaps' with our recommendation for which methods should be used in each situation.

Hamiltonian Boundary Value Methods are a new class of energy preserving one step methods for the solution of polynomial Hamiltonian dynamical systems. They can be thought of as a generalization of collocation methods in that they may be defined by imposing a suitable set of extended collocation conditions. In particular, in the way they are described in this note, they are related to Gauss collocation methods with the difference that they are able to precisely conserve the Hamiltonian function in the case where this is a polynomial of any high degree in the momenta and in the generalized coordinates. A description of these new formulas is followed by a few test problems showing how, in many relevant situations, the precise conservation of the Hamiltonian is crucial to simulate on a computer the correct behavior of the theoretical solutions.

The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\'evy LIBOR model of Eberlein and \"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.

In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the entropy inequality and generalized Bose-Einstein distributions as steady states. These properties are essential in order to develop schemes that are able to capture the energy concentration behavior of bosons. In addition we develop fast algorithms for the numerical evaluation of the resulting quadrature formulas which allow the final schemes to be computed only in O(N^2 log N) operations instead of O(N^3).

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is developed for systems of partial differential equations with polynomial nonlinearities. The framework is rather general and allows for an arbitrary number of dependent and independent variables with derivatives of any order. It is proved formally that second order convergence is obtained. The procedure is applied to a test case and numerical experiments are provided.

We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long simulations on an energy and enstrophy preserving discretization. To this purpose, we compute the average fields and estimate statistical parameters. It is observed that the statistical parameters depend on the integrals of the discretization and that the computed parameters are affected by the error in those, even if the volume of the phase space is correctly preserved. We conclude that monitoring the error in the integrals by the explicit volume preserving method can be used as an indication of how good the estimated parameters are.

The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as $\alpha$-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth order accurate energy-momentum conserving time discretization, and with analytical explanation of the main numerical observations. Physically natural impulsive initial data associated with the energy released by ATP hydrolysis are used, and the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long wave approximation by the nonlinear Schr\"odinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schr\"odinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation, but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models.

The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as $\alpha$-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth order accurate energy-momentum conserving time discretization, and with analytical explanation of the main numerical observations. Physically natural impulsive initial data associated with the energy released by ATP hydrolysis are used, and the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long wave approximation by the nonlinear Schr\"odinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schr\"odinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation, but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models.

The Kineticist's Workbench is a computer program currently under development whose purpose is to help chemists understand, analyze, and simplify complex chemical reaction mechanisms. This paper discusses one module of the program that numerically simulates mechanisms and constructs qualitative descriptions of the simulation results. These descriptions are given in terms that are meaningful to the working chemist (e.g., steady states, stable oscillations, and so on); and the descriptions (as well as the data structures used to construct them) are accessible as input to other programs. Keywords: Symbolic computation; Chemical kinetics.

The Kineticist's Workbench is a computer program currently under development whose purpose is to help chemists understand, analyze, and simplify complex chemical reaction mechanisms. This paper discusses one module of the program that numerically simulates mechanisms and constructs qualitative descriptions of the simulation results. These descriptions are given in terms that are meaningful to the working chemist (e.g., steady states, stable oscillations, and so on); and the descriptions (as well as the data structures used to construct them) are accessible as input to other programs. Keywords: Symbolic computation; Chemical kinetics.

The long-germ goal of this research is to realize the potential for realistic-domain numerical models as tools for prediction and understanding of the dynamics and transport processes in the coastal ocean.

The computer program NERF (Numerical Evaluation of Reliability Functions) has been designed to evaluate the reliability functions that result from the application of reliability analysis to the fatigue of aircraft structures, in particular, those reliability functions derived by Payne and his co-workers at the Aeronautical Research Laboratories. The NERF program, although based on the Payne reliability models is capable of extension to more complex models as the need arises. This dcoument details the mathematical development of the reliability functions evaluated by NERF and describes the computer program in sufficient detail to allow desired modifications.

The completion and testing of a fast algorithm for the calculation of two-dimensional dopant redistribution during oxide growth is described. A numerical comparison with analytical, exact solutions for low-dose implants is made which shows negligible error.

The convergence estimates obtained for the Korteweg-de Virus equation have been generalized, under the assumption that the solution u is sufficiently regular. For p 4, it is not known whether a global smooth solution exists corresponding to smooth initial data. It is in fact conjectured that for these cases, the solution may develop a singularity in finite time. A code that uses a spatially and temporally adaptive strategy has been implemented. We are currently investigating the stability of solitary type solutions. As conjectured, these solutions are highly unstable for initial amplitudes larger than one.

Research was concerned with designing and analyzing efficient and novel iterative algorithms for solving large sparse linear systems, typically arising from the discretizations of partial differential equations, which are highly parallelizable and converge fast. These include domain decomposition algorithms and multilevel preconditioners. Some basic dense linear algebra problems, including rank-revealing QR factorizations and stable Toeplitz solvers, which have applications to signal processing were considered.

Finite element solution formulations have been carried out for a simple initial value problem based on two different variational statements; that of convolutional integral developed by Gurtin and that of large spring constants adapted by this writer for initial value problems. Numerical results indicate that both generate convergent solution to the given initial value problem of a spring-mass system subjected to a harmonic forcing function.

An indexed-based object recognition system using geometric invariance techniques has been designed, and used to recognize buildings in an image of a military site and for recognizing curved planar objects including gasless. New invariants and indexing techniques for polyhedral and curved objects with repetition or bilateral symmetry and objects with the imaged outline of a surface of revolution have been developed. A method to distinguish projectively equivalent but Euclidean distinct objects in an uncalibrated view has been investigated. A group-theoretic framework for relating quasi-invariants to invariants has been formulated. Computing invariants can be formulated as an algebraic manipulation problem involving variable elimination and solving nonlinear polynomial equations. Based on Dixon's formulation of resultants, new methods for eliminating variables have been developed and implemented. These methods are much faster and superior than other elimination techniques. A branch and prune approach for numerically solving polynomial equations has been developed. A simple algorithm for separating invariant relations among object and image features to compute invariants of object features has been designed. These algorithms can serve as a basis for building an invariant work-bench that would enable researchers to experiment with geometric configurations and investigate their geometric invariants.

In this project we have studied high order finite difference, finite element, and spectral methods for the numerical solution of discontinuous or high gradient solutions. Theoretical study of algorithm development, stability, accuracy and convergence analysis, as well as applications of the algorithms to computational fluid dynamics (both compressible and incompressible) and semiconductor device simulation are performed. Parallel implementation issues of these high order methods are also studied.

In this project we have studied high order finite difference, finite element, and spectral methods for the numerical solution of discontinuous or high gradient solutions. Theoretical study of algorithm development, stability, accuracy and convergence analysis, as well as applications of the algorithms to computational fluid dynamics (both compressible and incompressible) and semiconductor device simulation are performed. Parallel implementation issues of these high order methods are also studied.

The long-term goal of this research is to construct the Navy s next-generation global numerical weather prediction (NWP) model using new numerical methods specifically designed for distributed-memory computers. To take full advantage of the new computer architectures, the spherical global domain must be partitioned into local sub-domains, or elements, which can then be solved independently on the multiple processors of these computers. The numerical methods used on these sub-domains must be not only local in nature but also high-order in accuracy and highly efficient. Thus the final objective of this project is to construct a new global NWP model which is as accurate as the current spectral model Navy Operational Global Atmospheric Prediction Systems (NOGAPS) while much more efficient, thereby allowing for finer resolution forecasts.

An algorithm is discussed for computing the stationary probability vector of an infinite-state Markov chain whose transition probability matrix has a block-partitioned structure. Such matrices arise in a wide variety of queueing models as well as generalized random walk problems. Traditionally, the analytic approach to this type of problem has been through complex variable methods. An alternate and unified treatment of this problem is presented and an algorithm is obtained which utilizes only real arithmetic computations. In addition, most of the intermediate steps of the algorithm have useful probabilistic interpretations.

An algorithm is discussed for computing the stationary probability vector of an infinite-state Markov chain whose transition probability matrix has a block-partitioned structure. Such matrices arise in a wide variety of queueing models as well as generalized random walk problems. Traditionally, the analytic approach to this type of problem has been through complex variable methods. An alternate and unified treatment of this problem is presented and an algorithm is obtained which utilizes only real arithmetic computations. In addition, most of the intermediate steps of the algorithm have useful probabilistic interpretations.

An algorithm is discussed for computing the stationary probability vector of an infinite-state Markov chain whose transition probability matrix has a block-partitioned structure. Such matrices arise in a wide variety of queueing models as well as generalized random walk problems. Traditionally, the analytic approach to this type of problem has been through complex variable methods. An alternate and unified treatment of this problem is presented and an algorithm is obtained which utilizes only real arithmetic computations. In addition, most of the intermediate steps of the algorithm have useful probabilistic interpretations.

During the three-year period of this project, we conducted research on the development, analysis, and application of serial and parallel adaptive computational strategies for solving transient and steady partial differential systems. Concentrating on high-order methods and adaptive approaches that combine mesh refinement and coarsening (h-refinement, order variation (p- refinement), and occasionally, mesh motion (r-refinement), we addressed problems in combustion, materials science and compressible fluid mechanics. Special spatially-discrete finite element Galerkin methods were considered for the parallel and adaptive solution of hyperbolic conservation laws. Improved solution-limiting and error-estimation strategies increased the accuracy and efficiency of these methods which are being applied to two - and three- dimensional compressible flow problems. Adaptive techniques for dissipative systems are being applied to problems in the manufacture of ceramic composite media.

Exact numerical methods and stochastic simulation methods are developed to study the force stretching single RNA issue on the secondary structure level in equilibrium. By computing the force-extension curves on the constant force and the constant extension ensembles, we find the two independent methods agree with each other quite well. To show the precision of our methods in predicting unfolding experiments, the unfolding forces of different RNA molecules under different experimental conditions are calculated. We find that the ionic corrections on the RNA free energies alone might not account for the apparent differences between the theoretical calculations and the experimental data; an ionic correction to the persistent length of single-stranded RNA should be necessary.