JP5874155B2 - Particle contact determination calculation method, particle contact determination calculation apparatus, and computer program - Google Patents

Description

  The present invention relates to a particle contact determination calculation method, a particle contact determination calculation apparatus, and a computer program, and in particular, a particle contact determination calculation method and a particle contact performed using a contact determination grid in a predetermined analysis target region. The present invention relates to a determination calculation device and a computer program.

  In particle analysis that considers contact by powder calculation or MPS (Moving Particle Semi-implicit) method, particle contact determination calculation is said to occupy much of the entire time, and speeding up is an essential process. Particularly in recent computers, CPUs capable of parallel execution of 8 threads or more are widely used in nodes. Therefore, speeding up by parallelization is an issue.

  Conventionally, in the particle contact determination calculation, a method of reducing the calculation amount of the contact determination calculation has been used. The contact determination calculation is not performed for all particles, but the physical quantity is calculated only for neighboring particles that may come into contact. In order to narrow down the particles in the vicinity, there is a method using a contact determination grid (for example, see Non-Patent Document 1). In addition, in order to increase the number effect at the time of parallelization by effectively using the cache, a method of rearranging the particles so that the computation at the time of contact determination is localized after numbering the particles is known ( For example, refer nonpatent literature 2).

Edited by Mikio Sakai: Numerical simulation of powder, Maruzen Publishing (2012) Taisuke Nishiura, Shu Sakaguchi: DEM acceleration algorithm using GPU, Transactions of JSCES, paper No.20100007 (2010)

  By the way, in the calculation of the addition of the contact force acting on each contacting particle, which is necessary in the discrete element method (DEM) used in powder calculation, conventionally, the amount of computation is calculated using the law of action-reaction. Reduction. When this conventional method is thread-parallelized, information on the contact partner is also updated at the same time, but this operation is nothing but rewriting of information updated by other threads. Therefore, data read / write conflicts among a plurality of threads, and exclusive control is required. In this exclusive control, when OpenMP is used, it is usual to insert a critical directive or an atomic directive (see, for example, Non-Patent Document 1).

  On the other hand, in parallel processing without inserting a critical directive or the like, exclusive control has been avoided by a method that does not update the partner's information at the time of contact. However, this method increases the amount of computation by about twice as much as the method of inserting a critical directive. In other words, the exclusive control method has an advantage that the amount of calculation is halved, but an overhead of thread parallelization by exclusive control occurs. On the other hand, in the method without exclusive control, the amount of computation increases, but the overhead at the time of thread parallelization is small. That is, both have drawbacks and advantages, and the optimum method differs depending on the situation.

  Therefore, the present invention has been made in view of such problems, and the object of the present invention is to provide a particle contact determination calculation method and a particle contact determination capable of further speeding up the contact determination calculation. A computer apparatus and a computer program are provided.

  In order to solve the above problems, according to the present invention, there are provided the following particle contact determination calculation method, particle contact determination calculation apparatus, and computer program.

Contact determination calculation method of the particles of the present invention is a contact determination calculation method of the particles contact determination computing device performs using a contact determination lattice in the three-dimensional analysis target area, the contact determination computing device, the contact of the particles A contact determination calculation unit that performs determination calculation, and the contact determination calculation unit performs in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i-1). And a step of performing the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i-1, 2i-1) in parallel, and the lattice number (2i-1, 2i, 2i-1) The step of performing the contact determination calculation of the particles in the contact determination lattice in parallel, the step of performing the contact determination calculation of the particles in the contact determination lattice of the number (2i, 2i, 2i-1) in parallel, and the lattice number of ( 2i-1, The step of performing the contact determination calculation of the particles in the contact determination grid of number i-1, 2i) in parallel and the contact determination calculation of the particles in the contact determination lattice of the number (2i, 2i-1, 2i) in parallel A step of performing in parallel a particle contact determination calculation in a contact determination grid having a grid number of (2i-1, 2i, 2i) and a contact determination grid having a grid number of (2i, 2i, 2i) The step of performing the particle contact determination calculation in parallel is repeatedly performed in a predetermined order (i is an integer of 1 or more).

  Another particle contact determination calculation method of the present invention is a particle contact determination calculation method performed using a contact determination grid in a one-dimensional analysis target region, and the particle contact in an odd-numbered contact determination grid The step of performing the determination calculation in parallel and the step of performing the contact determination calculation of the particles in the contact determination lattice having an even number of lattice numbers in parallel are alternately performed.

Another particle contact determination calculation method of the present invention is a particle contact determination calculation method performed using a contact determination grid in a two-dimensional analysis target region, and the grid number is (2i-1, 2i-1). The step of performing the contact determination calculation of the particles in the contact determination lattice of No.), the step of performing the contact determination calculation of the particles in the contact determination lattice of the number (2i, 2i-1) in parallel, and the lattice number of A step of performing in parallel the particle contact determination calculation in the (2i-1, 2i) contact determination lattice, and a step of performing in parallel the particle contact determination calculation in the contact determination lattice of the number (2i, 2i). Are repeatedly performed in a predetermined order (i is an integer of 1 or more).

Another particle contact determination calculation method of the present invention is a particle contact determination calculation method performed using a contact determination grid in an n-dimensional (n is an integer of 1 or more) analysis target region. The lattices are grouped into unit lattices composed of 2 ⁿ lattices, and in each unit lattice, the same value is given to lattices at the same positions in the unit lattices, so that 2 ⁿ pieces in the unit lattices are given. The step of assigning a value of 1 to 2 ^{n to} the lattice and performing the contact determination calculation of the particles in the lattice having the same value in parallel is repeatedly performed in a predetermined order.

  The particle contact determination calculation apparatus according to the present invention includes a contact determination calculation unit that performs particle contact determination calculation, and the contact determination calculation unit has the same technical characteristics as the particle contact determination calculation method described above. .

  Moreover, the computer program concerning this invention is a computer program for functioning a computer as said particle | grain contact determination calculation apparatus.

  According to the present invention, it is possible to perform parallel calculation after grouping contact determination grids so that particles do not contact. For this reason, it is possible to reduce the amount of calculation by using a so-called action-reaction law that simultaneously updates information on the contact partner. By performing such parallel calculation, the computation amount is halved as in the method using the critical directive, but exclusive control is not required. In this way, it is possible to further speed up the contact determination calculation.

  As described above, the basic technical feature of the present invention is to perform parallel calculation after grouping the contact determination grids so that the particles do not contact each other. This can be imagined as color-coding the contact determination grid into a plurality of colors. Therefore, in the present specification, the particle contact determination calculation method of the present invention is also referred to as “multi-color contact determination method”. The contact determination grid used in the multicolor contact determination method is also referred to as “multicolor contact determination grid”.

  According to the present invention, the amount of calculation is reduced using the action-reaction law, but exclusive control is not required. In this way, it is possible to further speed up the contact determination calculation. The other effects of the present invention will be described in the section for carrying out the invention below.

It is a figure which shows the image of a contact determination grid | lattice. It is a figure which shows notionally a one-dimensional multi-color contact determination grid. It is a figure which shows the program of the multi-color contact determination method. It is a figure which shows the flow of the one-dimensional multi-color contact determination method. It is a figure which shows notionally a two-dimensional multi-color contact determination grid. It is a figure which shows the flow of the two-dimensional multi-color contact determination method. It is a figure which shows notionally a three-dimensional multi-color contact determination grid. It is a figure which shows the flow of the three-dimensional multi-color contact determination method. It is a figure which shows the comparison of the effect of the method (Method3) of this embodiment, and the conventional method (Method1, Method2).

  Exemplary embodiments of the present invention will be described below in detail with reference to the accompanying drawings. Furthermore, the effectiveness of the multi-color contact determination method is verified by comparing the thread parallel execution performance of the conventional method and the multi-color contact determination method according to the present embodiment. In addition, in this specification and drawing, about the component which has the substantially same function structure, duplication description is abbreviate | omitted by attaching | subjecting the same code | symbol.

  First, the contact determination calculation which is a premise of the present embodiment will be described.

  First, register the particles. Here, as an example, particles are registered by generating pseudo-random numbers (hereinafter also simply referred to as random numbers). Next, the particle numbers are rearranged. In the present embodiment, an arbitrary number of particles are generated in a region to be analyzed (for example, a three-dimensional region). The position of the particle is determined by a random number. And contact determination calculation is performed about each particle | grain. In this contact determination calculation, a contact determination grid described below is used to determine particles that may come into contact.

  FIG. 1 is a diagram illustrating an image of a contact determination grid. As shown in FIG. 1, the analysis target area is divided into a grid. Thereafter, all particles 110 contained in the lattice 100 are registered on the corresponding determination lattice. By setting the lattice width to be equal to or larger than the particle diameter, it is possible to limit the particles that may come into contact to the particles existing in the same lattice and in the adjacent lattice, and thus the amount of calculation can be reduced. The lattice width is not necessarily the same as the particle diameter as long as it is equal to or larger than the particle diameter.

  When updating the contact force for the contacting particles, not only the information of itself but also the information of the other party is updated at the same time. At this time, contact determination is performed with particles on only the right adjacent (or upper adjacent) lattice. This is a process for reducing the amount of calculation to ½ using the action-reaction law.

  For this processing, consider OpenMP parallelization. At this time, for example, it is assumed that the particles of particle number 0 and particle number 1 are in the same lattice. Further, it is assumed that the particle number 0 is processed by the thread 0 and the particle number 1 is processed by the thread 1. At this time, there may be a situation where the update is performed in the thread 1 while the update is performed in the thread 0. That is, there may be a timing between the thread 0 and the thread 1 to update the value at the same time. In this state, only the result of thread 0 or thread 1 is reflected and does not match the sequential result. Therefore, this process requires exclusive control. Hereinafter, in the collision determination calculation, simultaneous writing of values between threads is referred to as “contention”.

  Conventionally, in order to avoid a conflict, the conflict problem has been controlled by performing exclusive control using a critical directive or an atomic statement that is a directive using a critical indicator provided by OpenMP (for example, non-patent literature). 1). In addition, as a method that does not use critical directives, conflicts have been avoided by not updating the other party's information at the time of contact. However, in this method, since the redundant calculation is performed with respect to the contact force calculation, the calculation amount is doubled. In the present specification, contact force calculation that does not use the action-reaction principle and does not update the partner's information at the time of contact is referred to as “redundant calculation”.

  As a method for solving the above problems, the multi-color contact determination method according to the present embodiment will be described in detail below.

  The multi-color contact determination method is a contact determination calculation method using a multi-color contact determination grid. The multi-color contact determination grid is a contact determination grid that uses a contact determination grid used in conventional contact determination calculation, but has a different access method for the contact determination calculation. Hereinafter, the algorithm of the multi-color contact determination method will be described first by showing an example in a one-dimensional case.

(1) One-dimensional analysis target region FIG. 2 is a diagram conceptually showing a one-dimensional multi-color contact determination grid. FIG. 2A shows the grid number of the contact determination grid, FIG. 2B shows the multi-color contact determination grid, and FIG. 2C shows the unit grid for attaching the multi-color. In addition, the premise of application of the multi-color contact determination method of this embodiment is to take the lattice width of the contact lattice to the particle diameter or more. Moreover, in the contact determination calculation using the contact determination grid, a method of calculating in parallel for each grid number (lattice parallel) and a method of calculating for each particle number (particle parallel) are known. Assuming grid parallel. That is, the contact determination calculation of particles existing in one contact lattice is performed by the same thread.

  Considering OpenMP parallelization, due to the nature of the contact determination grid, there are dependencies between the grid number (x−1) and the grid number (x + 1), which are both adjacent grids of the target grid number x. Has no dependencies. If this is generalized in the one-dimensional case, there is no dependency between the contact determination grids with odd-numbered grid numbers, and there is no dependency between the contact determination grids with even-numbered grid numbers. Here, when there is no dependency, it means that parallel execution is possible because there is no data contention, and when there is a dependency, it means that parallel execution is not possible because data contention can occur. .

Therefore, the multi-color contact determination grid shown in FIG. As shown in FIG. 2B, a value “1” is assigned to an odd-numbered lattice number x (x = 1, 3, 5, 7, 9,...) That can be executed in parallel. To do. A value “2” is assigned to even-numbered grid numbers x (x = 2, 4, 6, 8,...) That can be executed in parallel. The value "1" to the value "2" means that the color-coded collision detection grating color two-color (2 ^1-color). In this way, a multi-color contact determination grid can be defined. It should be noted that the value “1” and the value “2” merely distinguish the two, and the number itself has no special meaning. It goes without saying that the value “2” may be assigned to the odd-numbered lattice and the value “1” may be assigned to the even-numbered lattice.

As a method of assigning a value to the contact determination grid, it can be considered as follows. First, grouped in Figure 2 two contact determination lattice (a) (2 ¹ pieces) each unit cell of the (1-dimensional unit cell). FIG. 2C shows a one-dimensional unit cell (i is an integer of 1 or more). For each one-dimensional unit cell, the same value is assigned to the lattice at the same position in the unit cell. In the example of FIG. 2C, the value “1” is assigned to the lattice at the left position (lattice number 2i−1) of the one-dimensional unit lattice. The value “2” is assigned to the lattice at the right position (lattice number 2i). This is performed for all one-dimensional unit cells. In this way, the multi-color contact determination grid shown in FIG. 2B can be defined.

A particle contact determination calculation method using the multi-color contact determination grids numbered as described above will be described with reference to FIGS. FIG. 3 is a diagram showing a program for the multi-color contact determination method. Here, since it is one-dimensional, n = 1 and MAX_COLOR = 2 ¹ = 2. As shown in FIG. 4, first, the contact determination calculation of the lattice to which the value “1” is assigned is performed in parallel (step S102). Thereafter, the contact determination of the grid with the value “2” is performed (step S104). This contact determination is repeated as necessary. For example, in the case of powder analysis in which the position and speed of individual particles are updated little by little with a small time interval (ΔT), particle contact determination is performed at each time step to make contact. The contact force may be obtained for the particles.

  As described above, the premise of the application of the multi-color contact determination method of the present embodiment is that the lattice width of the contact lattice is set to the particle diameter or more. By doing so, particles in the same value (color) lattice do not contact each other. Further, in this embodiment, on the premise of lattice parallel, contact determination calculation of particles existing in one contact lattice is performed by the same thread. Therefore, in the multi-color contact determination method, there is no competition in principle when updating the contact force between the user and the opponent. As a result, even if parallelization is performed, there is no data contention among multiple threads. In the multi-color contact determination method, the order of addition / subtraction is different from the sequential contact determination calculation. However, the coincidence of calculation results in mathematics is guaranteed. As described above, in the multi-color contact determination method, parallel execution (calculation) is possible.

  The above is the description of the multi-color contact determination method for the one-dimensional analysis target. Even when the analysis target is expanded to two dimensions or three dimensions, the multi-color contact determination method can be expanded by extending the multi-color contact determination grid to two dimensions or three dimensions. Hereinafter, it demonstrates in order.

(2) Two-dimensional analysis target region First, a two-dimensional analysis target region will be described with reference to FIGS. 5 and 6. FIG. 5 is a diagram conceptually showing a two-dimensional multi-color contact determination grid. FIG. 5A shows a two-dimensional multi-color contact determination grid, and FIG. 5B shows a unit grid for applying multi-color. FIG. 6 is a diagram illustrating a flow of a two-dimensional multi-color contact determination method.

In order to extend the multi-color contact determination method in two dimensions, as shown in FIG. As shown in FIG. 5 (a), in order to avoid data dependency on contact determination grid, color coded to four colors (2 ³ colors). Thus, a multi-color contact determination method can be realized with the same discussion as in one dimension. That is, as shown in FIG. 5A, in the multi-color contact determination grid, there is still no relation between the grids assigned the value “1”. Similarly, there is no dependency between the grids with the value “2”, there is no dependency between the grids with the value “3”, and there is no dependency between the grids with the value “4”. There is no relationship. For this reason, parallel execution is possible with the same discussion as in the above one dimension.

  A method of assigning values to the contact determination grid will be described. First, FIG. 5A is divided into 2 × 2 unit cells (two-dimensional unit cells). FIG. 5B shows one of the two-dimensional unit cells (i is an integer of 1 or more). For each two-dimensional unit cell, the same value is assigned to the lattice at the same position in the unit cell. In the example of FIG. 5B, the value “1” is assigned to the lattice having the lattice number (2i-1, 2i-1). Also, the value “2” is assigned to the grid having the grid number (2i, 2i−1). Further, the value “3” is assigned to the grid having the grid number (2i-1, 2i). Further, the value “4” is assigned to the grid having the grid number (2i, 2i). This is performed for all two-dimensional unit cells. In this way, the multi-color contact determination grid shown in FIG. 5A can be defined.

A particle contact determination calculation method using the multi-color contact determination grids numbered as described above will be described with reference to FIG. First, the contact determination calculation is performed in parallel for the lattice having the lattice number (2i-1, 2i-1), that is, the lattice having the value “1” (step S202). Next, contact determination is performed on the lattice having the lattice number (2i, 2i-1), that is, the lattice having the value "2" (step S204). Next, contact determination is performed on the lattice having the lattice number (2i-1, 2i), that is, the lattice having the value “3” (step S206). Next, contact determination is performed on the lattice having the lattice number (2i, 2i), that is, the lattice having the value “4” (step S208). This processing can be executed as n = 2 and MAX_COLOR = 2 ² = 4 in the multi-color contact determination method program shown in FIG.

(3) Three-dimensional analysis target region Next, the three-dimensional analysis target region will be described with reference to FIGS. FIG. 7 is a diagram conceptually showing a three-dimensional multi-color contact determination grid. FIG. 7A shows a three-dimensional multi-color contact determination grid, and FIG. 7B shows a unit grid for applying multi-color. FIG. 8 is a diagram illustrating a flow of a three-dimensional multi-color contact determination method.

In order to extend the multi-color contact determination method to three dimensions, as shown in FIG. 7A, the multi-color contact determination grid is extended to three dimensions. As shown in FIG. 7 (a), in order to avoid data dependency on contact determination grid, color coded to 8 colors (2 ³ colors) color. Thus, a multi-color contact determination method can be realized with the same discussion as in one dimension and two dimensions. That is, as shown in FIG. 7A, in the multi-color contact determination grid, there is still no relation between the grids assigned the value “1”. Similarly, there is no dependency between the grids with the value “2”, there is no dependency between the grids with the value “3”, and there is no dependency between the grids with the value “4”. There is no dependency between the grids to which the value “5” is assigned, there is no dependency between the grids to which the value “6” is assigned, and there is no dependency between the grids to which the value “7” is assigned. There is no dependency relationship, and there is no dependency relationship between grids to which the value “8” is assigned. For this reason, parallel execution is possible in the same discussion as the one-dimensional and two-dimensional cases.

  A method of assigning values to the contact determination grid will be described. First, FIG. 7A is divided into 2 × 2 × 2 unit cells (three-dimensional unit cells). FIG. 7B shows one of the three-dimensional unit cells (i is an integer of 1 or more). For each three-dimensional unit cell, the same value is assigned to the lattice at the same position in the unit cell.

  In the example of FIG. 7B, the value “1” is assigned to the lattice having the lattice number (2i-1, 2i-1, 2i-1). Further, the value “2” is assigned to the lattice having the lattice number (2i, 2i-1, 2i-1). Further, the value “3” is assigned to the lattice having the lattice number (2i-1, 2i, 2i-1). Also, the value “4” is assigned to the grid having the grid number (2i, 2i, 2i−1). In addition, the value “5” is given to the lattice having the lattice number (2i-1, 2i-1, 2i). Also, the value “6” is assigned to the grid having the grid number (2i, 2i-1, 2i). Further, the value “7” is assigned to the grid having the grid number (2i-1, 2i, 2i). Also, the value “8” is assigned to the grid having the grid number (2i, 2i, 2i). This is performed for all three-dimensional unit cells. In this way, the multi-color contact determination grid shown in FIG. 7A can be defined.

  A particle contact determination calculation method using the multi-color contact determination grids numbered as described above will be described with reference to FIG. First, the contact determination calculation is performed in parallel for the lattice having the lattice number (2i-1, 2i-1, 2i-1), that is, the lattice having the value "1" (step S302). Next, contact determination is performed for the grid having the grid number (2i, 2i-1, 2i-1), that is, the grid having the value “2” (step S304). Next, contact determination is performed for the grid having the grid number (2i-1, 2i, 2i-1), that is, the grid to which the value “3” is assigned (step S306). Next, contact determination is performed for the grid having the grid number (2i, 2i, 2i-1), that is, the grid having the value “4” (step S308).

Similarly, the contact determination calculation is performed in parallel for the lattice having the lattice number (2i-1, 2i-1, 2i), that is, the lattice having the value "5" (step S310). Next, contact determination is performed on the grid having the grid number (2i, 2i-1, 2i), that is, the grid having the value “6” (step S312). Next, contact determination is performed for the lattice having the lattice number (2i-1, 2i, 2i), that is, the lattice having the value “7” (step S314). Next, contact determination is performed on the grid having the grid number (2i, 2i, 2i), that is, the grid assigned the value “8” (step S316). This process can be executed as n = 3 and MAX_COLOR = 2 ³ = 8 in the multi-color contact determination method program shown in FIG.

  The particle contact determination calculation method according to the present embodiment has been described above. The method of the present embodiment may be executed by a dedicated device (particle contact determination calculation device). Such a particle contact determination calculation device may include a particle contact determination calculation unit. The particle contact determination calculation unit can execute the particle contact determination calculation method described in this embodiment.

  In addition, a predetermined computer program may be incorporated into a general-purpose computer instead of a dedicated device so that the computer functions as the particle contact determination calculation device as described above. Such a computer program can be distributed in the market in the form of being stored in various storage media such as CR-ROM, DVD-ROM, and semiconductor media. Further, the market may be distributed by transmission via various networks, for example, download via the Internet.

  The multi-color contact determination method that is characteristic of the present embodiment has been described above. Next, performance evaluation will be described.

In this performance evaluation, evaluation was performed according to the following specifications.
Intel (R) Core (TM) i7-2600 processor (quad core / 3.40GHz / TB up to 3.80GHz / 8MB smart cache / HT compatible)
・ 8GB memory [4GB × 2 (DDR3 SDRAM PC3-10600) / Dual channel]
・ Windows (R) 7 Professional regular version (OEM) [64bit]

  In this performance evaluation, the particle size was set to 0.002, the number of particles was 62.5 million, and the number of steps was set to 20. In addition, each particle updates the information on the number of contacts at the time of determination. However, since a three-dimensional contact determination grid is used, the upper limit of the information on the number of contacts per particle is 12.

  In order to see the effectiveness of the multi-color contact determination method according to this embodiment, three programs are prepared as shown in Table 1 below. Table 1 shows the difference in the mounting method by Method.

  In Table 1, a program including a critical directive is referred to as method 1 in order to prevent data conflict when parallelizing the contact determination grid. In the contact determination grid parallel, a program that does not write the partner information and doubles the calculation amount is defined as method2. The above method 1 and method 2 are conventional methods. Finally, a program to be parallelized using the multi-color contact determination grid which is the method of the present embodiment is method3.

  The performance is evaluated for the calculation time and the number effect when one node is occupied and parallel execution is performed with a maximum of 8 threads by OpenMP. Here, the number effect is a general index indicating the effect of parallel processing. As expressed by equation (1), it is represented by the ratio of “execution time in parallel execution” to “calculation time in sequential execution”.

  S = Computation time required for sequential execution / Computation time required for parallel computation (1)

  In addition, the calculation time in Formula (1) refers to the total calculation time which totaled the calculation time required for contact determination calculation, and the contact force calculation time of particle | grains.

  In each method, the calculation time is compared between sequential calculation (number of threads 1) and parallel calculation (number of threads 2, 4, 6, and 8). Here, the calculation time is obtained by measuring the calculation time after the fifth step and averaging the values. The results of calculation time are shown in Table 2 below and FIG. Table 2 shows the execution time (seconds) of each method.

  From Table 2, the maximum multi-color contact determination method according to the present embodiment is used by using the multi-color contact determination method according to the present embodiment at 1.62 times (3.46 [seconds] of method3 with respect to 5.656 [seconds] of method1). It can be seen that an improvement in speed can be obtained.

  As described above, in the present embodiment, the multi-color contact determination method, which is a new thread parallel method using the multi-color contact determination grid, has been described in the contact determination calculation used in powder analysis and the like. In addition, performance evaluation for some conventional methods was performed. In the conventional method, lattice parallelism is used, but particle number renumbering is performed in order to improve calculation efficiency. In the multi-color contact determination method of this embodiment, in addition to this renumbering, the method of accessing the grid is devised to prevent data contention during thread parallelization. Therefore, higher parallelization efficiency can be expected than the conventional method. As described above, the multi-color contact determination method of the present embodiment obtained results superior to the conventional method in both the calculation time and the number effect.

  As mentioned above, although preferred embodiment of this invention was described referring an accompanying drawing, it cannot be overemphasized that this invention is not limited to this example. It will be apparent to those skilled in the art that various changes and modifications can be made within the scope of the claims, and these are naturally within the technical scope of the present invention. Understood.

  For example, in the above embodiment, the one-dimensional to three-dimensional space has been described as the analysis target space. However, the present invention is not limited to this, and can be applied to an analysis target space having an arbitrary number of dimensions.

  The present invention is applicable to a particle contact determination calculation method, a particle contact determination calculation device, and a computer program, and in particular, a particle contact determination calculation method performed using a contact determination grid in a predetermined analysis target region, It can be used for a particle contact determination calculation device and a computer program.

10 Contact determination grid 20 Particle 100 One-dimensional contact determination grid 110 Multi-color contact determination grid (one-dimensional)
120 One-dimensional unit cell 210 Multi-color contact determination cell (2D)
220 2D unit cell 310 Multi-color contact determination cell (3D)
320 3D unit cell

Claims (3)

A contact determination calculation method for particles performed by a contact determination calculation device using a contact determination grid in a three-dimensional analysis target region,
The contact determination calculation device includes a contact determination calculation unit that performs contact determination calculation of particles,
The contact determination calculation unit
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i-1, 2i, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i, 2i);
Are repeatedly performed in a predetermined order (i is an integer equal to or greater than 1 ). A particle contact determination calculation apparatus using a contact determination grid in a three-dimensional analysis target region,
Provided with a contact determination calculation unit that performs contact determination calculation of particles,
The contact determination calculation unit
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i-1, 2i, 2i-1);
Performing in parallel a particle contact determination calculation in a contact determination lattice with a lattice number of (2i, 2i, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i, 2i);
Are repeatedly performed in a predetermined order (i is an integer equal to or greater than 1 ). A computer program for causing a computer to function as a particle contact determination calculation device using a contact determination grid in a three-dimensional analysis target region,
The contact determination calculation device includes a contact determination calculation unit that performs contact determination calculation of particles,
The contact determination calculation unit
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i-1, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i-1, 2i, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i, 2i-1);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i, 2i-1, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice having the lattice number (2i-1, 2i, 2i);
Performing in parallel the particle contact determination calculation in the contact determination lattice with the lattice number (2i, 2i, 2i);
Are repeated in a predetermined order (i is an integer of 1 or more).