Multipoint Approximation Research Articles

Semiempirical Formula for Removing the Higher Mode Components of Detector Responses in Subcriticality Measurements

There are two main reasons generally suggested for the measurement of the subcriticalities of nuclear fuel systems, power reactors (during initial loading and refueling), fuel storage, and processing facilities: Knowledge of the subcriticality first provides a method to analyze and predict nuclear performance and second is helpful in obtaining the operational and safety aspects of the system. Here, a semiempirical formula for neutron detector responses, to be used to infer reactivities in subcriticality measurements, is presented. A formal theory for the multipoint approximation of the Boltzmann operators makes possible the description of a large variety of nuclear fuel systems by means of an equivalent two-point model that regards a whole system as the coupled system made up of an arbitrary number of nuclear fuels. Because the analytical formula includes the fitting parameter associated with the detector configuration and because the removal of spatial effects or higher mode contaminations in the detector responses is accomplished by devising the detector configurations, the conventional point approximation can be used to infer the reactivity of a far-subcritical system. For an example of an application to existing experiments, the current method is used to analyze subcriticality measurements by using the [sup 252]Cf source-driven neutron noisemore » analysis method.« less

Multiparameter structural optimization using FEM and multipoint explicit approximations

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (multipoint approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the method is compared with other optimization techniques.

Extension of matrix method for complete multipoint Padé approximation

A recent multipoint Pade approximation technique for linear system reduction is extended to include expansion points infinity. The method is then seen to be completely general, covering the cases of real, complex, multiple and infinite points. An example is given to illustrate its application.

Improving the solution of the symmetric eigenvalue problem and an extension

Based on a multipoint approximation of polynomial values, we accelerate the bisection and divide-and-conquer algorithms for the symmetric eigenvalue problem. We also propose a new extension of the bisection algorithm to the unsymmetric eigenvalue problem.

New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction

Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.

Low cycle fatigue crack propagation and fractography of a SUS 304 stainless steel at elevated temperature: Koterazwa, R. and Nosho, T. J. Soc. Mater. Sci. Jpn. Sept. 1988 37, (420), 1090–1096 (in Japanese)

The present paper proposes a novel approach to the identification of the mechanical properties of individual component layers of a bimetallic sheet. In this approach, a set of material parameters in a constitutive model of cyclic elasto-plasticity are identified for the two layers of the sheet simultaneously by minimizing the difference between the experimental results and the corresponding results of numerical simulation. This method has an advantage of using the experimental data (tensile load vs strain curve in the uniaxial tension test and the bending moment vs curvature diagram in the cyclic bending test) for a whole bimetallic sheet but not for individual component layers. An optimization technique based on the iterative multipoint approximation concept is used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification, and the verification of this approach using two types of constitutive models (the Chaboche-Rousselier and the Prager models) for an aluminum clad stainless steel sheet.

A multipoint finite-difference scheme for the problem of bending of rectangular orthotropic plates with freely supported edges: Construction and convergence estimate

The boundary-value problem $$\begin{gathered} D_1 \frac{{\partial ^4 w}}{{\partial x^4 }} + 2D_2 \frac{{\partial ^4 w}}{{\partial x^2 \partial y^2 }} + D_3 \frac{{\partial ^4 w}}{{\partial y^4 }} = f\left( {x,y} \right) \hfill \\ w\left| {_{y = 0;b} } \right. = 0, \frac{{\partial ^2 w}}{{\partial y^2 }}\left| {_{y = 0;b} } \right. = 0; w\left| {_{x = - a;a} } \right. = 0,\frac{{\partial ^2 w}}{{\partial y^2 }}\left| {_{x = - a;a} } \right. = 0 \hfill \\ \end{gathered} $$ of static deflection of a rectangular orthotropic plate is replaced with a finite-difference problem. The rectangle [−a⩽x⩽a, O⩽y⩽b] is partitioned into a mesh with step h in the direction y and h1, in the direction x; second derivatives with respect to y and x are replaced with multipoint approximations using the templates 2p+1, 2p1+1 (where p and p1 · are arbitrary natural numbers) with errors O(h2p), O(h2p1); the fourth-order derivatives are replaced with approximations using the templates 4p+1 and 4p1+1 with the same errors. The finite-difference system of linear algebraic equations is transformed into a decomposable system. The convergence of the proposed method is estimated.

Linear self-adjoint multipoint boundary value problems and related approximation schemes

Linear self-adjoint multipoint boundary value problems are investigated. The case of the homogeneous equation is shown to lead to spline solutions, which are then utilized to construct a Green's function for the case of homogeneous boundary conditions. An approximation scheme is described in terms of the eigen-functions of the inverse of the Green's operator and is shown to be optimal in the sense of then-widths of Kolmogorov. Convergence rates are given and generalizations to more general boundary value problems are discussed.