Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used

Fast neutron spectrum unfolding for nuclear nonproliferation and safeguards applications

We present new neutron spectrum unfolding results obtained from measurements with Cf-252 and plutonium-oxide sources. The precise knowledge of the neutron energy spectrum provides information about the presence or absence of fissile material and about the characteristics of the material. We used a neutron spectrum unfolding technique based on a modification of the least-squares method. The main innovation is the use of a Krylov subspace iteration which performs better on ill-conditioned systems of linear equations than standard direct-solution methods. The proposed technique performed well in the unfolding of measured neutron pulseheight distributions from a Cf-252 neutron source and from plutonium-oxide samples and could be easily implemented in a portable neutron spectroscopy system for nuclear nonproliferation and safeguard applications

An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained nonlinear systems

AbstractIn this paper, we propose a new affine scaling trust-region algorithm in association with nonmonotonic interior backtracking line search technique for solving nonlinear equality systems subject to bounds on variables. The trust-region subproblem is defined by minimizing a squared Euclidean norm of linear model adding the augmented quadratic affine scaling term subject only to an ellipsoidal constraint. By using both trust-region strategy and interior backtracking line search technique, each iterate switches to backtracking step generated by the general trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm

Robust Convergence of Power Flow using Tx Stepping Method with Equivalent Circuit Formulation

Robust solving of critical large power flow cases (with 50k or greater buses) forms the backbone of planning and operation of any large connected power grid. At present, reliable convergence with applications of existing power flow tools to large power systems is contingent upon a good initial guess for the system state. To enable robust convergence for large scale systems starting with an arbitrary initial guess, we extend our equivalent circuit formulation for power flow analysis to include a novel continuation method based on transmission line (Tx) stepping. While various continuation methods have been proposed for use with the traditional PQV power flow formulation, these methods have either failed to completely solve the problem or have resulted in convergence to a low voltage solution. The proposed Tx Stepping method in this paper demonstrates robust convergence to the high voltage solution from an arbitrary initial guess. Example systems, including 75k+ bus test cases representing different loading and operating conditions for Eastern Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.Interconnection of the U.S. power grid, are solved from arbitrary initial guesses

Design of ternary signals for MIMO identification in the presence of noise and nonlinear distortion

A new approach to designing sets of ternary periodic signals with different periods for multi-input multi-output system identification is described. The signals are pseudo-random signals with uniform nonzero harmonics, generated from Galois field GF(q), where q is a prime or a power of a prime. The signals are designed to be uncorrelated, so that effects of different inputs can be easily decoupled. However, correlated harmonics can be included if necessary, for applications in the identification of ill-conditioned processes. A design table is given for q les 31. An example is presented for the design of five uncorrelated signals with a common period N = 168 . Three of these signals are applied to identify the transfer function matrix as well as the singular values of a simulated distillation column. Results obtained are compared with those achieved using two alternative methods