Particle behavior analysis method, particle behavior analysis apparatus, and computer readable storage medium

Abstract

A particle behavior analysis method uses plural computers connected via a network to analyze particle behavior considering an interaction force with a different substance acting on a particle. The method includes analyzing the particle behavior by using a force decomposition paralleling algorithm using a force matrix considering at least two or more types of interaction forces.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments may be described in detail with reference to the accompanying drawings, in which:

FIGS. 1A and 1B are drawings showing one configuration example of a developing unit;

FIG. 2 is a block diagram to show a first exemplary embodiment of a particle behavior analysis system;

FIG. 3 is a block diagram to show a second exemplary embodiment of a particle behavior analysis system;

FIG. 4 is a block diagram to show one configuration example of a particle behavior analysis apparatus;

FIG. 5 is a diagram to show one hardware configuration example for implementing a particle behavior analysis apparatus using a computer;

FIG. 6 is a flowchart to show an example of a force decomposition parallel processing procedure;

FIG. 7 is a drawing to describe a technique of assigning particles to be analyzed to nodes;

FIG. 8 is a drawing to describe the interaction calculation targets in each node about the magnetic interaction;

FIG. 9 is a drawing to describe the interaction calculation targets in each node about the electrostatic interaction;

FIG. 10 is a drawing to describe the interaction calculation targets in each node about the mechanical interaction (contact force);

FIG. 11 is a drawing to describe addition processing of the interaction forces found in the nodes (particularly, in the row direction of the force matrix);

FIG. 12 is a drawing to describe other specific processors which need to communicate the interaction forces calculated in the row direction and the column direction;

FIGS. 13A and 13B are drawings showing the state of a developer at the initial and last stages of analysis processing;

FIG. 14 is a drawing to summarize processors to communicate when the force matrix in a force decomposition method is used with attention focused on node #6;

FIG. 15 is a drawing to describe the speed improvement ratio in spatial decomposition paralleling processing described in the related art;

FIG. 16 is a drawing to describe the nodes to communicate in a particle decomposition method, a replicated data method;

FIG. 17 is a drawing to describe the relationship between the computation time and the communication time and the number of nodes in particle decomposition paralleling processing, replicated data paralleling processing and that in force decomposition paralleling processing;

FIG. 18 is a comparison drawing to show the speed improvement ratio in force decomposition paralleling processing according to the relationship with spatial decomposition paralleling processing;

FIG. 19 is a flowchart to show a first example of force decomposition paralleling processing procedure;

FIG. 20 is a flowchart to show a second example of force decomposition paralleling processing procedure; and

FIG. 21 is a flowchart to show a third example of force decomposition paralleling processing procedure.

Claims

1. A particle behavior analysis method that uses a plurality of computers connected via a network to analyze particle behavior considering an interaction force with a different substance acting on a particle, comprising: analyzing behavior of the particle by using a force decomposition paralleling algorithm using a force matrix considering at least two or more types of interaction forces.

2. A particle behavior analysis apparatus for using a plurality of computers connected via a network to analyze particle behavior considering an interaction force with a different substance acting on a particle, the particle behavior analysis apparatus comprising: a data processing section that analyzes behavior of the particle using a force decomposition paralleling algorithm using a force matrix considering at least two or more types of interaction forces.

3. The particle behavior analysis apparatus as claimed in claim 2, wherein the data processing section analyzes the behavior of one particle and analyzes the behavior of another particle different from the one particle in at least one of physical properties and particle diameter based on the analyzed behavior of the one particle, the behavior of the another particle containing an interaction with the one particle.

4. The particle behavior analysis apparatus as claimed in claim 2, wherein the data processing section finds a sum total of interaction forces of one type acting on the particle using one force matrix, finds the sum total of interaction forces of another type acting on the particle using a different force matrix from the one force matrix, and calculates a sum of the sum total of interaction forces of the one type and the sum total of interaction forces of the another type, so as to analyze the behavior of the particle considering the plural types of interaction forces.

5. The particle behavior analysis apparatus as claimed in claim 4, wherein the data processing section sequentially finds the sum total of interaction forces of the one type and the sum total of interaction forces of the another type using one set of the plurality of computers.

6. The particle behavior analysis apparatus as claimed in claim 4, wherein the data processing section concurrently finds the sum total of interaction forces of the one type and the sum total of interaction forces of the another type using two or more sets of the plurality of computers.

7. The particle behavior analysis apparatus as claimed in claim 4, wherein the data processing section finds the sum total of the plural types of interaction forces acting on the one particle, finds the sum total of the plural types of interaction forces acting on the another particle, and calculates the sum of the sum total of the plural types of interaction forces acting on the one particle and the sum total of the plural types of interaction forces acting on the another particle, so as to analyze the behavior of the plural types of particles considering the plural types of interaction forces.

8. The particle behavior analysis apparatus as claimed in claim 7, wherein the data processing section concurrently finds the sum total of the plural types of interaction forces acting on the one particle and the sum total of the plural types of interaction forces acting on the another particle using two or more sets of the plurality of computers.

9. A computer readable medium storing a particle behavior analysis program that uses a plurality of computers connected via a network to analyze particle behavior considering an interaction force with a different substance acting on a particle using a force decomposition paralleling algorithm using a force matrix, the program causing the plurality of computers to execute: (a) finding a sum total of interaction forces of one type acting on the particle using one force matrix;(b) finding a sum total of interaction forces of another type acting on the particle using a force matrix different from the one force matrix;(c) finding a sum of the sum total of interaction forces of the one type according to the step (a) and the sum total of interaction forces of the another type according to the step (b); and(d) solving an equation of motion showing the behavior of the particle considering the plural types of interaction forces using the sum according to the step (c) to calculate the position of the particle.