MQSI is a Fortran 2003 subroutine for constructing monotone quintic spline interpolants to univariate monotone data. Using sharp theoretical monotonicity constraints, first and second derivative estimates at data provided by a quadratic facet model are refined to produce a univariate C 2 monotone interpolant. Algorithm and implementation details, complexity and sensitivity analyses, usage information, a brief performance study, and comparisons with other spline approaches are included.

VTMOP is a Fortran 2008 software package containing two Fortran modules for solving computationally expensive bound-constrained blackbox multiobjective optimization problems. VTMOP implements the algorithm of [ 32 ], which handles two or more objectives, does not require any derivatives, and produces well-distributed points over the Pareto front. The first module contains a general framework for solving multiobjective optimization problems by combining response surface methodology, trust region methodology, and an adaptive weighting scheme. The second module features a driver subroutine that implements this framework when the objective functions can be wrapped as a Fortran subroutine. Support is provided for both serial and parallel execution paradigms, and VTMOP is demonstrated on several test problems as well as one real-world problem in the area of particle accelerator optimization.

QNSTOP consists of serial and parallel (OpenMP) Fortran 2003 codes for the quasi-Newton stochastic optimization method of Castle and Trosset for stochastic search problems. A complete description of QNSTOP for both local search with stochastic objective and global search with “noisy” deterministic objective is given here, to the best of our knowledge, for the first time. For stochastic search problems, some convergence theory exists for particular algorithmic choices and parameter values. Both the parallel driver subroutine, which offers several parallel decomposition strategies, and the serial driver subroutine can be used for local stochastic search or global deterministic search, based on an input switch. Some performance data for computational systems biology problems is given.

A serial Fortran 95 implementation of the QNSTOP algorithm is presented. QNSTOP is a class of quasi-Newton methods for stochastic optimization with variations for deterministic global optimization. This discussion provides results from testing on various deterministic and stochastic optimization functions.

This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for solving nonconvex quadratic minimization problems with either box or±1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems (with zero duality gap). Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported.

Scattered data interpolation problems arise in many applications. Shepard's method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard's algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.

An isosceles triangular frame with rotationally resistive joints under a tip load is studied. The large in-plane deformation elastica equations are formulated. A stability analysis shows that the frame can buckle symmetrically or asymmetrically. The post-buckling behavior showing limit load and hysteresis are obtained by shooting and homotopy numerical algorithms. The behavior of a frame with rigid joints is studied in detail. The effects of joint spring constant and base length are found.

A rigid platform is supported by thin elastic legs. The legs are able to slide on the ground as they deform. The governing equations for large deformations are formulated and solved numerically by homotopy and quasi-Newton methods. Nonlinear phenomena such as nonuniqueness are found. A global critical load for nonlinear stability is presented.

The global critical load is an extremely useful index for flexible structures under large disturbances. The present technical note determines this index for a two-dimensional rigid solid supported by two flexible columns. The buckling and postbuckling problem is solved by a homotopy algorithm applied to a Galerkin formulation of the nonlinear elastica equations. The present results show the bifurcation curve is quite sensitive to an elevated mass center. The global buckling load is greatly reduced although the critical buckling load of linear stability analysis remains the same, showing that the linear stability index or bifurcation load is entirely erroneous in predicting the safe load under finite disturbances for flexible structures with elevated mass centers.

Recently we advocated a new stability index, the global critical load, for very elastic structures. This index is extremely useful for flexible structures under large disturbances such as earthquakes. The present note determines this index for a two-dimensional rigid solid supported by two flexible columns. Using the nonlinear elastica equations the buckling and postbuckling problem is solved by a homotopy nonlinear system solver. The present results show the bifurcation curve is quite sensitive to the elevated mass center. The global buckling load is drastically reduced although the critical buckling load of linear stability analysis is the same. An explanation is given through the study of a solid supported by one column.

A new stability index, the global critical load, is advocated. This index is useful for flexible structures prone to large disturbances such as earthquakes. A symmetric rigid body supported by flexible legs is studied in detail. The nonlinear equilibrium equations are solved and the results show that global stability depends heavily on the height of the mass center and the distance between the legs.

A heavy rigid platform is supported by thin elastic legs. The governing equations for large deformations are formulated and solved numerically by homotopy and quasi-Newton methods. Nonlinear phenomena such as non-uniqueness, catastrophe and hysteresis are found. A global critical load for nonlinear stability is introduced.

To compete successfully in a world that is becoming more international and more competitive, we must increasingly become more effective in using technology, especially in our educational institutions. It is clear that there is a strong parallel between the way current developments in information technology are significantly effecting our business organizations and the way machines helped to transform our society during the Industrial Revolution. Academic organizations must accelerate the integration of new information technology, such as parallel processing methodology into the classroom for our economic growth plans to be achieved. This paper discusses the Winthrop College Computer Science Department's methodology to increase the parallel processing content and experience in our educational offerings.

The nonaxisymmetric motion (produced by a buoyancy-induced cross flow) of afluid in contact with a rotating disk and in the presence of a magnetic field normal to the disk is studied. Using modern quasi-Newtonian techniques, B-splines, and a Galerkin approximation to the fluid motion equations, numerical solutions are obtained for a wide range of magnetic field strengths and Prandtl numbers (ratio of kinematic viscosity to thermal diffusivity). Results are presented in both tabular and graphical form in terms of two nondimensional parameters. There is excellent agreement with previous work.

In this paper we examine the flow of a conducting fluid between a solid rotating disk and a stationary porous disk with uniform injection of fluid through the porous disk in the presence of an axial magnetic field. The equations of motion are solved using least change secant update quasi-Newton and modern root finding techniques. The fluid motion depends on the crossflow Reynolds number, rotational Reynolds number and Hartmann number. The effects of the parameters on the flow field are presented graphically.

This paper examines the effects of a circular magnetic field on a rotating conducting fluid. The fluid is rotating with a uniform angular velocity ω at infinity and is in contact with a stationary infinite disk. The equations of motions are solved numerically using a least change secant update quasi-Newton technique. The effects of the parameters α (ratio of kinematic viscosity to magnetic diffusivity) and β (ratio of magnetic field strength to angular velocity of the fluid) on the flow are presented graphically.

This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magentic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three nondimensional parameters. There is excellent agreement with previous work and asymptotic formulas.

This paper studies the effects of an axial magnetic field on the flow and heat transfer about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths and injection and suction velocities. Results are presented graphically in terms of three nondimensional parameters. There is excellent agreement with previous work and asymptotic formulas.