A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models

2021 ◽  
Vol 290 (3) ◽  
pp. 982-999
Author(s):  
Muqing Du ◽  
Heqing Tan ◽  
Anthony Chen
Keyword(s):  
Traffic Equilibrium ◽  
Equilibrium Models ◽  
Step Size

On Traffic Equilibrium Models with a Nonlinear Time/Money Relation

2006 ◽  
pp. 19-31 ◽  
Author(s):  
Torbjörn Larsson ◽  
Per Olov Lindberg ◽  
Michael Patriksson ◽  
Clas Rydergren
Keyword(s):  
Traffic Equilibrium ◽  
Equilibrium Models

The Added Value of Graphical Input and Display for Electron Lens Design

1990 ◽  
Vol 48 (1) ◽  
pp. 190-191
Author(s):  
B. Lencova ◽  
G. Wisselink
Keyword(s):  
Flux Density ◽  
Numerical Data ◽  
Added Value ◽  
Lens Design ◽  
Step Size ◽  
Magnetic Lens ◽  
Flux Lines ◽  
Fine Mesh ◽  
Electron Lens ◽  
User Friendly

Recent progress in computer technology enables the calculation of lens fields and focal properties on commonly available computers such as IBM ATs. If we add to this the use of graphics, we greatly increase the applicability of design programs for electron lenses. Most programs for field computation are based on the finite element method (FEM). They are written in Fortran 77, so that they are easily transferred from PCs to larger machines.The design process has recently been made significantly more user friendly by adding input programs written in Turbo Pascal, which allows a flexible implementation of computer graphics. The input programs have not only menu driven input and modification of numerical data, but also graphics editing of the data. The input programs create files which are subsequently read by the Fortran programs. From the main menu of our magnetic lens design program, further options are chosen by using function keys or numbers. Some options (lens initialization and setting, fine mesh, current densities, etc.) open other menus where computation parameters can be set or numerical data can be entered with the help of a simple line editor. The "draw lens" option enables graphical editing of the mesh - see fig. I. The geometry of the electron lens is specified in terms of coordinates and indices of a coarse quadrilateral mesh. In this mesh, the fine mesh with smoothly changing step size is calculated by an automeshing procedure. The options shown in fig. 1 allow modification of the number of coarse mesh lines, change of coordinates of mesh points or lines, and specification of lens parts. Interactive and graphical modification of the fine mesh can be called from the fine mesh menu. Finally, the lens computation can be called. Our FEM program allows up to 8000 mesh points on an AT computer. Another menu allows the display of computed results stored in output files and graphical display of axial flux density, flux density in magnetic parts, and the flux lines in magnetic lenses - see fig. 2. A series of several lens excitations with user specified or default magnetization curves can be calculated and displayed in one session.

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