Numerical Experience with a Superfast Real Toeplitz Solver

1989 ◽  
Author(s):  
William Gragg ◽  
Gregory S. Ammar
Keyword(s):  
Numerical Experience

Mechanism Design with MP-Neural Networks

1998 ◽  
Vol 120 (4) ◽  
pp. 527-532 ◽  
Author(s):  
J. Li ◽  
K. C. Gupta
Keyword(s):  
Error Function ◽  
Least Square ◽  
Numerical Experience ◽  
Variable Approach ◽  
Structural Error ◽  
Augmented Lagrange Multiplier ◽  
Equation Error ◽  
Complex Structural ◽  
Alm Method ◽  
New Algorithms

The prevalent Mathematical Programming Neural Network (MPNN) models are surveyed, and MPNN models have been developed and applied to the unconstrained optimization of mechanisms. Algorithms which require Hessian inversion and those which build up a variable approach matrix, are investigated. Based upon a comprehensive investigation of the Augmented Lagrange Multiplier (ALM) method, new algorithms have been developed from the combination of ideas from MPNN and ALM methods and applied to the constrained optimization of mechanisms. A relationship between the weighted least square minimization of design equation error residuals and the mini-max norm of the structure error for function generating mechanisms is developed and employed in the optimization process; as a result, the computational difficulties arising from the direct usage of the complex structural error function have been avoided. The paper presents relevant theory as well as some numerical experience for four MPNN algorithms.

scholarly journals Adaptive augmented Lagrangian methods: algorithms and practical numerical experience

2015 ◽  
Vol 31 (1) ◽  
pp. 157-186 ◽  
Author(s):  
Frank E. Curtis ◽  
Nicholas I.M. Gould ◽  
Hao Jiang ◽  
Daniel P. Robinson
Keyword(s):  
Augmented Lagrangian ◽  
Augmented Lagrangian Methods ◽  
Numerical Experience ◽  
Lagrangian Methods

Two Efficient Algorithms of Plastic Integration for Sheet Forming Modeling

2007 ◽  
Vol 129 (4) ◽  
pp. 698-704 ◽  
Author(s):  
Y. M. Li ◽  
B. Abbès ◽  
Y. Q. Guo
Keyword(s):  
Equivalent Stress ◽  
Sheet Forming ◽  
Efficient Algorithms ◽  
Integration Scheme ◽  
Fast Method ◽  
Numerical Experience ◽  
Mapping Algorithm ◽  
Inverse Approach ◽  
Return Mapping ◽  
Return Mapping Algorithm

A fast method called the “inverse approach” for sheet forming modeling is based on the assumptions of the proportional loading and simplified tool actions. To improve the stress estimation, the pseudo-inverse approach was recently developed: some realistic intermediate configurations are geometrically determined to consider the deformation paths; two new efficient algorithms of plastic integration are proposed to consider the loading history. In the direct scalar algorithm (DSA), an elastic unloading-reloading factor γ is introduced to deal with the bending-unbending effects; the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress, thus the plastic multiplier Δλ can be directly obtained without iterative resolution scheme. In the γ-return mapping algorithm, the equivalent plastic strain increment estimated by DSA is taken as the initial solution in Simo’s return mapping algorithm, leading to a stable, efficient, and accurate plastic integration scheme. The numerical experience has shown that these two algorithms give a considerable reduction of CPU time in the plastic integration.

scholarly journals Numerical Investigation of Corium Coolability in Core Catcher: Sensitivity to Modeling Parameters

2018 ◽  
Author(s):  
Liancheng Guo ◽  
Andrei Rineiski
Keyword(s):  
Fast Reactor ◽  
Large Scale ◽  
Mass Transfer Process ◽  
Severe Accident ◽  
Liquid Sodium ◽  
Numerical Experience ◽  
The Core ◽  
Sodium Fast Reactor ◽  
Core Catcher ◽  
Fuel Pin

To avoid settling of molten materials directly on the vessel wall in severe accident sequences, the implementation of a ‘core catcher’ device in the lower plenum of sodium fast reactor designs is considered. The device is to collect, retain and cool the debris, created when the corium falls down and accumulates in the core catcher, while interacting with surrounding coolant. This Fuel-Coolant Interaction (FCI) leads to a potentially energetic heat and mass transfer process which may threaten the vessel integrity. For simulations of severe accidents, including FCI, the SIMMER code family is employed at KIT. SIMMER-III and SIMMER-IV are advanced tools for the core disruptive accidents (CDA) analysis of liquid-metal fast reactors (LMFRs) and other GEN-IV systems. They are 2D/3D multi-velocity-field, multiphase, multicomponent, Eulerian, fluid dynamics codes coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model. However, the experience of SIMMER application to simulation of corium relocation and related FCI is limited. It should be mentioned that the SIMMER code was not firstly developed for the FCI simulation. However, the related models show its basic capability in such complicate multiphase phenomena. The objective of the study was to preliminarily apply this code in a large-scale simulation. An in-vessel model based on European Sodium Fast Reactor (ESFR) was established and calculated by the SIMMER code. In addition, a sensitivity analysis on some modeling parameters is also conducted to examine their impacts. The characteristics of the debris in the core catcher region, such as debris mass and composition are compared. Besides that, the pressure history in this region, the mass of generated sodium vapor and average temperature of liquid sodium, which can be considered as FCI quantitative parameters, are also discussed. It is expected that the present study can provide some numerical experience of the SIMMER code in plant-scale corium relocation and related FCI simulation.

Mathematical Programming Neural Networks (MPNN) for Mechanism Design

1997 ◽  
Author(s):  
Jianmin Li ◽  
Krishna C. Gupta
Keyword(s):  
Mathematical Programming ◽  
Error Function ◽  
Least Square ◽  
Numerical Experience ◽  
Variable Approach ◽  
Structural Error ◽  
Augmented Lagrange Multiplier ◽  
Complex Structural ◽  
Alm Method ◽  
New Algorithms

Abstract The prevalent Mathematical Programming Neural Network (MPNN) models are surveyed, and MPNN models have been developed and applied to the unconstrained optimization of mechanisms. Algorithms which require Hessian inversion and those which build up a variable approach matrix, are investigated. Based upon a comprehensive investigation of the Augmented Lagrange Multiplier (ALM) method, new algorithms have been developed from the combination of ideas from MPNN and ALM methods and applied to the constrained optimization of mechanisms. A relationship between the weighted least square minimization of design equation error residuals and the mini-max norm of the structure error for function generating mechanisms is developed and employed in the optimization process; as a result, the computational difficulties arising from the direct usage of the complex structural error function have been avoided. The paper presents relevant theory as well as some numerical experience for four MPNN algorithms.

scholarly journals Comparative cognition of number and space: the case of geometry and of the mental number line

2018 ◽  
Vol 373 (1740) ◽  
pp. 20170120 ◽  
Author(s):  
Giorgio Vallortigara
Keyword(s):  
Hippocampal Formation ◽  
Comparative Cognition ◽  
Number Line ◽  
Mental Number Line ◽  
Geometric Information ◽  
Human Infants ◽  
Numerical Experience ◽  
Surface Layout ◽  
Spatial Reorientation ◽  
Underlying Mechanisms

Evidence is discussed about the use of geometric information for spatial orientation and the association between space and numbers in non-human animals. A variety of vertebrate species can reorient using simple Euclidian geometry of the environmental surface layout, i.e. in accord with metric and sense (right/left) relationships among extended surfaces. There seems to be a primacy of geometric over non-geometric information in spatial reorientation and, possibly, innate encoding of the sense of direction. The hippocampal formation plays a key role in geometry-based reorientation in mammals, birds, amphibians and fish. Although some invertebrate species show similar behaviours, it is unclear whether the underlying mechanisms are the same as in vertebrates. As to the links between space and number representations, a disposition to associate numerical magnitudes onto a left-to-right-oriented mental number line appears to exist independently of socio-cultural factors, and can be observed in animals with very little numerical experience, such as newborn chicks and human infants. Such evidence supports a nativistic foundation of number–space association. Some speculation about the possible underlying mechanisms is provided together with consideration on the difficulties inherent to any comparison among species of different taxonomic groups. This article is part of a discussion meeting issue ‘The origins of numerical abilities'.

Numerical experience with diagonalization algorithms for asymmetric demand traffic assignment

1983 ◽  
Vol 1 (2) ◽  
pp. 63-68 ◽  
Author(s):  
Terry L. Friesz ◽  
Jack Weiss ◽  
Joel Gottfried
Keyword(s):  
Traffic Assignment ◽  
Numerical Experience

scholarly journals MURAME parameter setting for creditworthiness evaluation: data-driven optimization

2021 ◽  
Author(s):  
Marco Corazza ◽  
Giovanni Fasano ◽  
Stefania Funari ◽  
Riccardo Gusso
Keyword(s):  
Optimization Problem ◽  
Balance Sheet ◽  
Data Driven ◽  
Mathematical Programming Problem ◽  
Parameter Setting ◽  
Constrained Optimization Problem ◽  
Numerical Experience ◽  
Evolutionary Metaheuristic ◽  
Preference Disaggregation

AbstractIn this paper, we amend a multi-criteria methodology known as MURAME, to evaluate the creditworthiness of a large sample of Italian Small and Medium-sized Enterprises, using as input their balance sheet data. This methodology produces results in terms of scoring and of classification into homogeneous rating classes. A distinctive goal of this paper is to consider a preference disaggregation method to endogenously determine some parameters of MURAME, by solving a nonsmooth constrained optimization problem. Because of the complexity of the involved mathematical programming problem, for its solution we use an evolutionary metaheuristic, coupled with a specific efficient initialization. This is combined with an unconstrained reformulation of the problem, which provides a reasonable compromise between the quality of the solution and the computational burden. An extensive numerical experience is reported, comparing an exogenous choice of MURAME parameters with our approach.

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