JPH1153325A - Method for load distribution - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable parallel computation at a high speed by uniformly distributing an operation load to each processor of a parallel computer in an analysis area of a numerical value simulation. SOLUTION: In a method for distributing load to computers constituting a parallel computer, an analysis area, which is discritized in the space direction for a numerical value simulation and is divided into many odes and elements, is divided into almost uniform partial areas for the number of computers used for a parallel computation (102). Next, analysis area division information, which is independently given a node number and an element number, is generated in a node and element of each divided partial area and, moreover, the node numbers are redundantly given to the nodes existing on a boundary between the partial areas so that the become serial numbers of the whole analysis area (104). Then, a node number management table for indicating a correspondence between the node numbers for each partial area and the node numbers which becomes seal numbers in the entire analysis area is generated (105), and the analysis area division information and the node number management table are given to each computer which constitutes the parallel computers.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for distributing loads to computers constituting a parallel computer, and more particularly to a method for optimizing the load on each computer, which is used when a numerical simulation is performed by a parallel computer. The present invention relates to a load distribution method that makes it possible.

[0002]

2. Description of the Related Art As a prior art relating to a load distribution method,
For example, a "distribution / collection processing device for array data" described in JP-A-4-321158 and a paper "Multi Skyline Method for Distributed Memory Parallel Computer" described in IPSJ Research Report 96-HPC-63. Are known. The former prior art relates to a technique for efficiently distributing array data existing on a specific processor to a distributed memory, and the latter prior art relates to a technique for efficiently using a simultaneous linear equation solving system. The present invention relates to distribution of array data and a method of setting finite elements and node numbers.

[0003]

In the former prior art, the entire array data must be stored in a memory or a file of a specific processor. For this reason, this conventional technique requires a memory amount for storing the entire array data in a memory, and the problem that the scale of the problem that can be handled is limited by the memory amount of a specific processor is disadvantageous. Have. Further, in the conventional technique, when the entire array data is stored in a file, a time for inputting and outputting to and from the file becomes an overhead, thereby causing a problem that processing performance is reduced. .

The latter prior art relates to a method for setting finite elements and their node numbers used in finite element analysis, but can be applied to analysis of only a simple rectangular area. There is a problem that it is impossible to deal with a complicated analysis area.

An object of the present invention is to solve the above-mentioned problems of the prior art, and to use a differential grid and a finite element division used for discretization of an analysis region in a spatial direction in a numerical simulation for a parallel calculation. Another object of the present invention is to provide a load distribution method for computers constituting a parallel computer, which can divide the operation load so as to be uniform and improve the operation performance by parallelization.

Another object of the present invention is to divide the differential grid and the finite element division in advance so that the array data can be stored in a distributed memory without storing the entire array data in a memory and a file of a specific processor. It is an object of the present invention to provide a load distribution method for computers constituting a parallel computer capable of distribution.

[0007]

According to the present invention, an object of the present invention is to provide a method in which each of partial regions obtained by dividing an analysis region, which has been divided into a large number of nodes and elements by spatial discretization for numerical simulation, is In the load distribution method applied to each of the computers constituting the parallel computer, the analysis area is divided into sub-areas having a substantially uniform size corresponding to the number of computers used for the parallel computation, and the nodes for each of the divided sub-areas and Node numbers and element numbers are independently assigned to the elements, and further, node numbers existing on the boundary between the partial regions are overlapped with the node numbers so as to be serial numbers throughout the analysis region. This is achieved by generating a node number management table indicating the correspondence between the node numbers for each area and the node numbers that are serial numbers in the entire analysis area.

Further, the object is to provide each computer constituting a parallel computer with a partial region obtained by dividing an analysis region which has been discretized in a spatial direction for numerical simulation and divided into a number of nodes and elements. In the load distribution method, the analysis area is divided into sub-areas having a substantially uniform size corresponding to the number of computers used in the parallel calculation, and the entire analysis area is divided into nodes existing on the boundary between the sub-areas. This is achieved by assigning node numbers so that the numbers become serial numbers, and giving the node numbers and element numbers to the nodes and elements of the other partial areas independently for each partial area.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the load distribution method according to the present invention will be described below in detail with reference to the drawings.

FIG. 1 is a diagram for explaining the configuration and processing flow of a system for implementing a load distribution method according to an embodiment of the present invention. FIG. 2 is a diagram for explaining discretized information of an analysis area, which is an example of input information 106. FIG. 3 shows the input information 1 shown in FIG.
FIG. 4 is a diagram for explaining analysis region division information 107 for discretization information 06 and boundary information 108 for managing node numbers existing on the boundaries of the analysis region. FIG.
FIG. 2 is a diagram for explaining the configuration and processing flow of a second embodiment. 1 and 4, 101 is a load distribution processing unit, 102 is an analysis region division processing unit, 103 is an internal boundary determination processing unit, 104 is a node / element number assignment processing unit, 105 is a node number management table creation processing unit, Reference numeral 106 denotes input information, 110 denotes output information, 402 denotes an area size detection processing unit, 403 denotes a partial area division processing unit, and 404 denotes a partial area correction processing unit.

In FIG. 1, a load distribution processing unit 101 that divides array data and allocates it to a plurality of processors includes an analysis area division processing unit 102 that divides an analysis area into the number of processors, and a boundary surface generated by the division. , A node / element number assigning unit 104 for assigning a local node / element number to each of the divided areas, and a local And a node number management table creator 105 that creates a node number management table indicating the correspondence between a typical node number and a node number in the entire analysis area.

The input information 106 input to the above-mentioned load distribution processing unit 101 manages analysis area division information 107 which is information discretized in the spatial direction of the analysis area, and nodes existing on the boundary of the analysis area. It has boundary information 108 and the number of processors 109 used for parallel execution.
The output information 110 from the load distribution processing unit 101 is
The partial area division information 111 storing the discretization information in the spatial direction for each of the divided areas given to each processor constituting the parallel computer, the local node number for the boundary area generated by the division, and the entire analysis area Node number management table 112 indicating the correspondence with the node numbers
have. Then, the partial area division information 111 for each of the divided areas and the node number management table 11
2 is given to each processor constituting the parallel computer for operations such as numerical simulation.

An example of the input information 106 shown in FIG. 2 shows a discretization state in the spatial direction of the analysis area 201 which is the basis of the analysis area division information 107. The analysis area 201 as the input information is, for example, , The shape shown in FIG. 2 is a part of the water channel, and the processing performed by the parallel computer is, for example,
The water flow from the opening of the FA line at the top of the figure is the CD on the right side of the figure.
This is an example of calculating the flow velocity in each part of the area in the figure in the case where it flows out from the exit of the line.

In an example in which the analysis area 201 shown in FIG. 2 is discretized by finite element division, a line segment 204 and a line segment 20 are divided.
A number of nodes 202, which are intersections with 5, are assigned node numbers, and an element number is assigned to many regions 203 surrounded by line segments. In FIG. 2, element numbers are indicated by circled numbers.

Next, the analysis area division information 107 for the discretized information of the input information 106 shown in FIG. 2 and the boundary information 108 for managing the node number existing on the boundary of the analysis area will be described with reference to FIG. I do.

The analysis area division information 107 is composed of node information 302 storing node numbers and their coordinate positions, and finite element configuration information 303 managing node numbers constituting elements. The node information 302 is the input information 1 shown in FIG.
06, which are composed of the node numbers of all the nodes included in the entire analysis area 201 and the corresponding x and y coordinates. The finite element configuration information 303 is the input information 1 shown in FIG.
06, the element numbers of all the elements included in the entire analysis area 201 and four node numbers I1, I2, and I surrounding the element.
3 and I4. These node numbers I1, I
2, I3 and I4 are arranged counterclockwise from the lower left node of the element.

The boundary information 108 includes the boundary name 30
5, the number of nodes 306 forming the boundary and the number 307 of the nodes forming the boundary are stored. The boundary name 305 is shown in FIG.
Are the names defining the boundaries of all the analysis areas of the input information 106 shown in FIG. 3, and in the example shown in FIG.
A boundary indicated by two straight lines is created by the names of the points at both ends. FIG. 3 shows an example in which a name BC is given as a boundary of the bottom of the region shown in FIG. In the example shown in FIG. 2, “11” is stored as the number of nodes 306 in the example shown in FIG. Also, as the node number 307, the numbers of 11 nodes existing on this boundary are stored. In the case of the analysis area 201 shown in FIG.
The boundaries of E, EF, FA, and AB are created in the same format as described above.

Next, the configuration and processing flow of the analysis area division processing unit 102 shown in FIG. 1 will be described with reference to FIG.

The analysis area division processing section 102 includes an area size detection processing section 402, a partial area division processing section 403, and a partial area correction processing section 404. The region size detection processing unit 402 firstly performs the node information 3 described with reference to FIG. 3, which is one of the input analysis region division information 107.
02, the maximum value Xmax and the minimum value Xmin, Y in the X-axis direction
The maximum value Ymax and the minimum value Ymin in the axial direction are obtained. next,
By subtracting the minimum value from the obtained maximum value in the axial direction, the area width Xlen in the X direction and the area width Ylen in the Y direction are obtained.

The partial area division processing section 403 compares the area widths in the X and Y axis directions obtained by the area size detection processing section 402, and divides the analysis area in the longer axis direction by the number of processors. The divided partial areas are corrected by the partial area correction processing unit 404 as described later.

FIG. 5 is a diagram showing an example in which the analysis area 201 is divided into four partial areas 507 to 510 by the partial area division processing unit 403. In the example shown in FIG. 5, the X-axis is selected as the division axis direction, and the X-axis direction 505 of the analysis area 201 is equally divided by the number of processors. Here, a case where four processors are used is taken as an example. Note that a dotted line 506 in FIG. 5 represents a boundary of the partial area. In addition, 502 to 504 correspond to (Xmi
n, Ymin), (Xmax, Ymin) and (Xmin, Ymax).

FIG. 6 shows the partial area correction processing section 404 described above.
Is a flowchart for explaining the processing for correcting the size of the partial area in FIG. 7, and FIG. 7 is a diagram showing an example of an analysis area divided by the corrected partial area.

Since the partial area division processing unit 403 equally divides the specific axis direction by the number of processors, the number of elements in each partial area cannot be made uniform. Therefore,
The partial area correction processing unit 404 corrects the number of elements in each partial area. Hereinafter, this processing will be described with reference to FIG.

(1) First, the partial area correction processing unit 404 determines the number of elements from the number of elements in the analysis area and the number of processors 109 obtained from the finite element configuration information 303 of the analysis area division information 107 as input information. By dividing by the number of processors, the optimum number E of elements in one partial area
Mean is obtained (step 602).

(2) Next, in order to sequentially correct the number of elements for each partial area, the number of divisions of the analysis area, in this example, "4" is stored in the work register KK.
Is stored as the initial value "1" (steps 603 and 60).
4).

(3) The values stored in the registers KK and JJ are compared, and if JJ ≦ KK is not satisfied, ie, J
If J> KK, there is no partial area to be processed, so the process ends (step 605).

(4) If JJ ≦ KK in step 605, the number of elements in the partial area indicated by the register JJ is calculated. The value of the register JJ is, as shown in FIG.
It is assumed that values 1 to 4 are assigned to partial regions 507 to 510 from the right side of the partial region obtained by dividing the analysis region 201 into four. If JJ = 1, the number of elements in the partial area 507 shown in FIG. 5 is set as the number of elements to be obtained (step 606).

(5) Next, the number of elements in the partial area obtained in step 606 is subtracted from the optimum number of elements Emean obtained in step 602 to obtain a difference Ndiff.
The absolute value ABS (Ndiff) of ff is a predetermined allowable range Δ
It is checked whether it is larger than diff, and if it is within the allowable range, “1” is added to the value of the register JJ, and step 605 is performed.
Then, the processing of the next partial area is continued (steps 607 to 609).

(6) If ABS (Ndiff) is larger than the predetermined allowable range Δdiff in step 608, N
The value of diff is checked for positive or negative. If the value of Ndiff is a positive number, the coordinate Xdiv of the boundary surface of the partial area is moved in the minus direction by a predetermined correction amount ΔX, and the value of Ndiff is negative. If it is a number, it is moved in the plus direction by a predetermined correction amount ΔX (steps 610 to 612).

(7) After moving the coordinates of the boundary surface, the flow returns to the processing from step 606, and the number of elements existing in the corrected partial area corresponding to ΔX is obtained again. The processing is continued until the difference from the element number Emean falls within the allowable range Δdiff.

When the number of elements in the next partial area is obtained in the processing of step 606 described above, addition and subtraction are performed in consideration of the increase / decrease of the boundary surface of the previous partial area, and the number of elements in the partial area is calculated. Ask for.

By performing the above-described processing, the number of elements existing in each partial area can be made uniform.

The analysis area 201 divided into four partial areas 507 to 510 by the partial area division processing unit 403 is
The correction is made by the partial area correction processing unit 404, and the partial area is corrected as shown in FIG. FIG. 7 shows a state where the partial area 507 corrected as the partial area 1 by the partial area correction processing unit 404 is corrected. Partial area 50
7 and 508 are obtained from the boundary line 506 obtained by the partial area division processing unit 403 in step 61 described above.
It has moved to the boundary line 704 moved by ΔX in the process of 1.

FIG. 8 shows the internal boundary determination processing unit 1 shown in FIG.
FIG. 3 is a diagram illustrating detection of an internal boundary according to an embodiment 03.
Hereinafter, this will be described. Here, one partial area 1 obtained by the partial area correction processing unit 404 described above is used.
Is described as a rectangular partial area 801 having node numbers as shown in FIG.

First, the internal boundary determination processing unit 103 performs a boundary integration on each element 803 included in the partial area 801 by using an expression of ∫ads, where a is a constant, and performs the integration calculation at the node 80
Go for every 4 to find its value. The boundary here is
It includes a boundary that is in contact with a region outside the analysis region indicated by hatching, and an internal boundary that is a boundary with an adjacent partial region. The method of the boundary integration 802 will be described with reference to FIG. 8B in which a part 805 of the analysis area is enlarged.

In FIG. 8 (b), when an inner point 807, which is a node not in contact with the boundary surface, is subjected to line integration with four adjacent elements, it is well known that an inverse point indicated by an arrow is obtained. Since there is always an integral in the direction, the result of the boundary integral is always "0". On the other hand, a node 808 on the boundary line
When the line integration is performed with four adjacent elements, since there is only one integration with respect to the side on the boundary, the result of the boundary integration is always a value other than “0”.

Then, the internal boundary determination processing unit 103 performs the above-described boundary integration for all elements in the partial area 801 and collects nodes whose result is a value other than “0”. 8C, a table 809 is created for the partial area having the area name, the number of boundary nodes, and the boundary node number. Since the internal boundary and the boundary of the analysis area are mixed in this table 809, the internal boundary determination processing unit 103 sets the boundary information 10 in the input information 106.
8, the node number existing in the boundary information 108 is deleted from the table 809, and an internal boundary management table 810 having the number of internal boundary nodes and the node number as shown in FIG. I do.

FIG. 9 is a diagram for explaining the processing of the node / element number assigning section 104 shown in FIG. 1. This will be described below. Here, a description will be given assuming that the processing is performed on the partial area 801 described with reference to FIG.

The node / element number assigning section 104 first removes nodes existing in the internal boundary management table 810 created by the internal boundary determining section 103 in FIG.
Serial numbers are assigned to all nodes included in the area 902 shown in FIG. Next, the node / element number assignment processing unit 104 assigns a serial number to the node 903 existing in the internal boundary management table 810 by a number following the serial number assigned above, and assigns all nodes in the partial area 801. Have serial numbers. Also, the partial area 801
Are also assigned element numbers in order from the beginning so as to be serial numbers in the partial area 801. FIG. 9B shows the result of assigning the node numbers and the element numbers to the nodes and elements in the partial area 801 by the above-described processing. The above-described processing is executed for all of the partial areas.

FIG. 10 is a diagram for explaining the processing of the node number management table creation processing unit 105 shown in FIG.
Hereinafter, this will be described. Here, the entire analysis area 201 shown in FIG. 2 is divided into four uniform partial areas by the internal boundaries 1002 to 1004 by the processing described above, and the node number and the element number are serially numbered for each partial area. The description will be made assuming that the information has been given.

Node number management table creation processing unit 105
Assigns node numbers again to the nodes existing on the internal boundary lines 1002 to 1004 of the analysis area 201 so that the entire analysis area 201 has a serial number. At this time, the node numbers are given such that when all the nodes included in the analysis area 201 are assigned node numbers, they are serial numbers at the end. Therefore, the head of the node number existing on the internal boundary line is obtained as the head number = the number of nodes of the entire analysis area−the number of nodes on the internal boundary + 1.

For example, if the number of nodes in the entire analysis area 201 is 1
When the number of nodes existing on the internal boundary is 23 at 57 nodes, as shown in FIG. 10A, ascending order from the node number 135 to the nodes on the internal boundaries 1002, 1003, and 1004 Given to. Then, the node number management table creation processing unit 105 shows the correspondence between the newly assigned node number on the internal boundary line and the node number of the internal boundary management table 810 created by the node / element number assignment processing unit 103 (FIG. 10). A node number management table 112 as shown in b) is created.

The node number management table 112 shown in FIG. 10B is for the partial area 1005 shown as the partial area 1, and the same node number management table 112 is created for other partial areas. In that case, the correspondence of the node numbers on the two internal boundaries is registered in the node number management table of the partial area having the internal boundary with the two partial areas.

FIG. 11 is a view for explaining partial area division information 111 which is one of the output information 110. The partial area division information 111 includes, for each partial area, node information 1103 in which a node number unique to the partial area newly created in the processing described with reference to FIGS.
And finite element configuration information 1104 in which element numbers unique to the partial area are associated with node numbers I1 to I4 defining the elements. The example shown in FIG. 11 is for partial area 1, and partial area division information for other partial areas is created in the same manner as described above.

As described above, the partial area creation information 111 for each partial area and the node number management table 112 created as the output information 110 are given to each computer that performs parallel processing, and each computer Perform processing based on

According to the above-described embodiment of the present invention, the node number and the element number are independently assigned to the nodes and elements of each divided partial area having a uniform size, and the boundary between the partial areas is divided. Node numbers overlappingly give node numbers to the existing nodes so as to be serial numbers throughout the analysis area, and node numbers indicating the correspondence between the node numbers of each of the partial areas and the node numbers which are serial numbers throughout the analysis area. Although it has been described that the management table is generated, according to the present invention, for the divided uniform-sized partial areas, serial numbers are assigned to the nodes existing on the boundary between the partial areas and the entire analysis area. As described above, a node number may be assigned, and a node number and an element number may be assigned to each of the other partial regions independently of each other. Thereby, generation of the node number management table can be omitted.

FIG. 12 is a diagram for explaining the effect of performing a numerical simulation using the load distribution method according to the embodiment of the present invention.

In general, the numerical simulation simulates a physical phenomenon by discretizing a partial differential equation governing the physical phenomenon in the space and time directions, and solving the obtained simultaneous linear equation. . FIG.
(A) shows an example of the situation of the coefficient matrix of the system of linear equations when the present invention is not applied. In this example, since the protruding portions of the non-zero elements 1202 are scattered throughout, a lot of unnecessary calculations occur when solving the simultaneous linear equations.

On the other hand, FIG. 12B shows an example of the situation of the coefficient matrix when the present invention is applied. When the load distribution method according to the present invention is applied, the non-zero element 12
No. 04 assigns a serial number managed in the node number management table 112 to a node at an internal boundary, so that a portion 1205 where a non-zero element protrudes can be concentrated at the end of the coefficient matrix. Accordingly, when the present invention is applied, it is possible to solve a system of linear equations by separating a portion where a non-zero element protrudes from another portion and solve the system of linear equations at high speed. Will be possible.

[0050]

As described above, according to the present invention, the analysis load in the numerical simulation can be evenly distributed to the processors of the parallel computer, so that high-speed parallel calculation can be performed. Further, since the coefficient matrix to be created has a shape suitable for the skyline method, which is one of the simultaneous linear equation solving methods, high-speed simultaneous linear equation solving can be performed.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration and a processing flow of a system that implements a load distribution method according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating discretization information of an analysis area, which is an example of input information.

FIG. 3 is a diagram illustrating analysis region division information for discretized information of input information and boundary information for managing a node number existing on a boundary of the analysis region illustrated in FIG. 2;

FIG. 4 is a diagram illustrating the configuration and processing flow of an analysis region division processing unit.

FIG. 5 is a diagram illustrating an example in which an analysis region is divided into four partial regions by a partial region division processing unit.

FIG. 6 is a flowchart illustrating a process of correcting the size of a partial region in the above-described partial region correction processing unit.

FIG. 7 is a diagram illustrating an example of an analysis area divided by a corrected partial area.

FIG. 8 is a diagram illustrating detection of an internal boundary by an internal boundary determination processing unit illustrated in FIG. 1;

FIG. 9 is a diagram illustrating a process of a node / element number assignment processing unit illustrated in FIG. 1;

FIG. 10 is a diagram illustrating a process of a node number management table creation processing unit illustrated in FIG. 1;

FIG. 11 is a diagram illustrating partial area division information that is one of output information.

FIG. 12 is a diagram illustrating an effect when a numerical simulation is performed using the load distribution method according to the embodiment of the present invention described above.

[Explanation of symbols]

 Reference Signs List 101 load distribution processing unit 102 analysis region division processing unit 103 internal boundary determination processing unit 104 node / element number assignment processing unit 105 node number management table creation processing unit 106 input information 110 output information 402 region size detection processing unit 403 partial region division processing Unit 404 Partial area correction processing unit

 ──────────────────────────────────────────────────の Continuing on the front page (72) Inventor Satomi Hasegawa 5030 Totsuka-cho, Totsuka-ku, Yokohama-shi, Kanagawa Prefecture Inside the Software Development Division of Hitachi, Ltd. 81 Hitachi Software Engineering Co., Ltd.

Claims (3)

[Claims] 1. A load distribution method in which each of partial regions obtained by dividing an analysis region, which is divided into a number of nodes and elements by spatial discretization for numerical simulation, is provided to each computer constituting a parallel computer. Dividing the analysis region into sub-regions of substantially uniform size corresponding to the number of computers used for parallel computation, and independently giving node numbers and element numbers to nodes and elements of each of the divided sub-regions,
Furthermore, node numbers that overlap on the entire analysis region are assigned to nodes existing on the boundary between the partial region and the partial region so as to be serial numbers, and the node number for each of the partial regions and the serial number for the entire analysis region are assigned. A load distribution method characterized by generating a node number management table indicating a correspondence with a node number. 2. A load distribution method in which each of partial regions obtained by dividing an analysis region, which has been divided into a large number of nodes and elements by spatial discretization for numerical simulation, is provided to each computer constituting a parallel computer. The analysis area is divided into sub-areas having a substantially uniform size corresponding to the number of computers used for the parallel calculation, and the serial numbers are assigned to the nodes existing on the boundary between the sub-areas and the entire analysis area. A node number and a node number and an element number are independently assigned to nodes and elements of other partial areas for each partial area. 3. A load distribution method in which each of partial regions obtained by dividing an analysis region, which has been divided into a large number of nodes and elements by spatial discretization for numerical simulation, is provided to each computer constituting a parallel computer. For each partial area divided in advance by the number of computers used for parallel calculation, the node numbers are overlapped so that the serial numbers are assigned to the nodes existing on the boundary between the partial areas and the partial area so that the entire analysis area has a serial number. And generating a node number management table indicating a correspondence between the node number assigned to each partial area unit and the node number assigned so as to be a serial number in the entire analysis area.