JPH08297654A - Method and device for ordering mesh node - Google Patents

Abstract

PURPOSE: To reduce storage capacity and to improve arithmetic efficiency when solving a simultaneous linear equations. CONSTITUTION: An input device 101 sends the data of a mesh-divided structure through a CPU 102 to a storage device 103 as a graph. A directional priority deciding device 104 receives the graph from the storage device 103 through the CPU 102, passes it through a priority deciding device 105 for the respective directions of the graph and sends this information through the CPU 102 to the storage device 103. A node numbering device 106 receives the information from the storage device 103 through the CPU 102, numbers the nodes of a group and sends this information through the CPU 102 to the storage device 103. The graph, for which all the nodes are completely numbered by ordering, is sent from the storage device 103 through the CPU 102 to an output device 107 together with the number table of respective nodes.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a coefficient matrix of simultaneous linear equations in order to reduce memory capacity and improve calculation efficiency when solving simultaneous linear equations that appear in the process of analyzing the structure of an object. The present invention relates to a method and an apparatus for performing pretreatment.

[0002]

2. Description of the Related Art In structural analysis, a structure to be analyzed is divided into meshes by drawing mesh lines in a direction parallel to one or more lines or planes that characterize the shape of an object, and intersection points of mesh lines ( Hereinafter, such a point will be represented by a graph constituted by a segment and a mesh line intercept (hereinafter, such a line segment will be referred to as a branch). Then, the relationship between the displacement (change in position) of each node and the external force (force applied from outside) is formulated into a simultaneous linear equation Ax = b using the coefficient matrix A and the right side vector b, and the solution x is obtained. The skyline matrix is generally found in the field of structural analysis. As shown in Fig. 2, most of the elements are zero and non-zero elements are concentrated near the diagonal of the matrix, and each element of the matrix is the same with the diagonal line as the axis of symmetry. It is a matrix with the characteristic that it is a value. The skyline method uses the characteristics of the skyline matrix to store only non-zero element regions near diagonal elements involved in the operation when solving simultaneous linear equations.
This is a matrix solution method that executes an operation for this, and aims to reduce the storage capacity and improve the operation efficiency. Therefore, the performance of the skyline method is improved when the non-zero elements are gathered near the diagonal elements in the coefficient matrix.

In order to concentrate the non-zero elements of the coefficient matrix near the diagonal elements in order to improve performance, the rows and rows and the columns and columns of the coefficient matrix are exchanged before solving the simultaneous linear equations. It is necessary to perform pre-processing. This preprocessing is called ordering, and the graph (FIG. 3B) corresponding to the structure of the coefficient matrix (FIG. 3A): the column numbers and nonzero elements of the coefficient matrix correspond to nodes and branches, respectively. Yes) corresponds to the operation of changing the number assigned to each node. Further, concentrating non-zero elements near the diagonal elements of the coefficient matrix corresponds to reducing the number difference between any two adjacent nodes in the graph corresponding to the coefficient matrix.

The prior art of the ordering method is Reverse
The Cuthill-Mckee method (hereinafter abbreviated as RCM method. Matrix calculation software: Maruzen Co., Ltd., Oguni Riki Ed. Murata Kenro et al., 1991) is generally used. The outline of the execution procedure of the RCM method will be described below in association with FIG. In the following description, the line segment distance means the minimum number of branches for connecting any two nodes on the graph.

(1) In the graph, the number of branches extending from each node is calculated, the node having the smallest number of branches is selected as the reference node, and the node number is set to 1.

(Corresponding to the node 1 in FIG. 4A) (2) The line segment distance from the reference node is calculated at each node, and all nodes are numbered in ascending order of the line segment distance.

(Numbers attached to the respective vertices in FIG. 4A are node numbers) (3) At the time of (2), the numbers of the nodes attached to all the nodes are renumbered in reverse order. (The number attached to each vertex in FIG. 4B is a node number.) In the RCM method which is a conventional technique, an index regarding the numbering of nodes when the line segment distance from the reference node to each node is equal is clarified. Since it is not determined, if the numbers of these nodes are arbitrarily set, there is a problem in that the maximum value of the difference between the numbers of two adjacent nodes may not become small. For example, when the RCM method is applied to the graph of FIG. 5 (b) corresponding to the structure of the torus-shaped object of FIG. 5 (a), if the numbers are added as shown in FIG. The maximum value of the number difference between the two nodes (for example, the node number 15 and the node number 28) is 13, but when the numbers are assigned as shown in FIG. 6B, the two nodes connected by one branch are connected. The maximum value difference (for example, node number 14 and node number 35) is 21
Therefore, the maximum value of the number difference between two adjacent nodes becomes large. Therefore, when the target of the structural analysis is a torus-shaped object, the RCM method is not always effective in realizing the reduction of the storage capacity and the improvement of the calculation efficiency.

[0008]

SUMMARY OF THE INVENTION The object of the present invention is that the maximum value of the difference between the numbers of two adjacent nodes may increase when the line segment distances from the reference node to each node are equal. In order to solve the problem, in order to reduce the maximum value of the number difference between two adjacent nodes, an ordering method having a clear setting standard for the numbering of nodes is provided.

Further, in the present invention, in order to give an index for grouping the nodes in the process of ordering, an index for determining the priority of each direction of the graph is given.

Further, in the present invention, in order to number the nodes stepwise for each group in the process of ordering, an index for determining the priority order between groups in an arbitrary direction is given.

Further, according to the present invention, in order to keep the number difference of two adjacent nodes between groups within a certain value in the process of performing ordering, when numbering the nodes in each group, Gives an index of the numbering of nodes at.

Further, according to the present invention, in order to make the number difference between two adjacent nodes between groups always smaller than a certain value in the process of performing ordering, when grouping the nodes for each group, Give mutual connection.

Further, in order to automatically realize the ordering method according to the present invention by an apparatus, data relating to a structure for applying the ordering method according to the present invention is input, or the present invention is used by using these data. A device must be constructed which can process the data according to the method according to. Therefore, the present invention simultaneously provides such a device configuration.

[0014]

In order to solve the above problems, in the present invention, when a simultaneous linear equation that appears in the process of structural analysis is solved, a graph corresponding to the coefficient matrix of the simultaneous linear equation is calculated. The ordering method determines priorities in each direction of the graph, and the nodes located in the direction are grouped in order from the direction having the higher priority, and the priorities among the groups in the direction are determined. However, it is characterized in that the nodes of the mesh are numbered for each group in order from the group having the higher priority determined above, and when determining the priority of each direction in the graph, it is counted along each direction. The first means for giving a higher priority in the order of increasing number of nodes and the priorities among the groups by grouping the nodes located in any direction on the graph. At the time of determination, a second means for selecting an arbitrary group in the direction as a reference group, and determining the order between the groups in the order of shortest line segment distance from the reference group, and the node number in each group When the group is a reference group selected by the second means when determining, a node as a reference in the group is arbitrarily set, and if the group is other than the reference group, from the group, A third means for selecting a node closest to the reference node in the reference group as the reference node, and determining node numbers in the order of increasing line segment distance from the reference node in the group, and any means other than the reference group. When deciding the node number in the group, the highest node number in the group with the immediately preceding order and the node number of the reference node in the arbitrary group are consecutive numbers. The fourth was in so that
And means.

A mesh node ordering device for implementing the method according to the present invention comprises an input device, a direction priority determining device, a group priority determining device, a node number determining device, an output device, a central processing unit and a storage device. It is characterized by

[0016]

By applying the ordering method according to the present invention to a graph, it is possible to reduce the maximum value of the number difference between any two adjacent nodes in the graph. Therefore, the simultaneous linear equation that appears in the process of structural analysis of an object It can contribute to reduction of storage capacity and improvement of calculation efficiency when solving the equation using the skyline method.

Further, in the ordering method according to the present invention,
By giving a high priority in the order of the number of nodes counted along each direction of the graph, the priority of each direction of the graph is determined, and an index for grouping is obtained.

Further, in the ordering method according to the present invention,
By selecting any group on each direction of the graph as the reference group and determining the priority order between the groups in the ascending order of the line segment distance from this reference group, the node numbering can be performed step by step for each group. Is ready to do.

In the ordering method according to the present invention,
As a reference node of each group, if the group is the reference group, any node in the group, and if the group is a group other than the reference group, the node closest to the reference node in the reference group from the group And select the nodes in the group in ascending order from the reference node in the group.
An index for the numbering of the nodes within each group that allows the number difference of the nodes to be kept below a certain value is determined.

In the ordering method according to the present invention,
When assigning numbers within an arbitrary group, make sure that the highest node number in the group with the immediately preceding priority and the reference number within an arbitrary group are consecutive numbers The connection relation between the groups is obtained such that the difference between the numbers of the two adjacent nodes is less than a certain value.

The input device sends the data of the mesh-divided structure as a graph to the storage device via the central processing unit. The direction priority determining device receives the graph from the storage device via the central processing unit, determines the priority of each direction of the graph, and sends this information to the storage device via the central processing unit. The group priority determining device receives information about the graph and the priority of each direction of the graph from the storage device via the central processing unit (CPU), and groups the nodes according to the priority of each direction to group each node. Priorities are determined and this information is sent to the storage device via the central processing unit. The node numbering device receives information from the storage device via the central processing unit about the graph and the priority of each group, numbers the nodes of the group, and transfers this information to the storage device via the central processing unit. To send. With the above-described ordering method, the graph in which all the nodes have been numbered is sent from the storage device to the output device via the central processing unit together with the number table of each node. With the above device configuration, the ordering method according to the present invention can be automatically realized.

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a mesh node ordering method according to the present invention will be described below with reference to the drawings. In addition, as a target to which the ordering is applied, as shown in FIG.
An example is a graph of a two-dimensional torus-shaped object with n rows and two columns. Here, the node on the i-th row and the j-th column is set to the node (i,
j). For the sake of simplicity, graphs with values of m and n of 6 and 8 are used in the following description of the embodiments.

FIG. 7 is a flow chart showing the ordering method according to the present invention. In step 701 of inputting the data of the graph of FIG. 7, the graph to be ordered is input.

In step 702 of determining the priority order of each direction of the graph of FIG. 7, since the graph is expressed in two dimensions, the two directions of the row direction and the column direction are the objects for determining the priority order. , The row direction or the column direction has a higher priority. Here, when the number of nodes is counted along the two directions of the row and column of the graph, it is m and n in each direction. (1) If m <n, the priority in the column direction is set to the row direction. Set higher than.

(2) If m ≧ n, the priority in the row direction is set higher than that in the column direction.

In the graph of FIG. 5B, since the values of m and n are 6 and 8, respectively, the priority in the column direction is set higher than that in the row direction according to the above (1).

In step 703 for determining the priority order between the groups in FIG. 7, nodes are grouped as follows based on the priority order in the two directions determined in the step for determining the priority order in each direction. , Determine priorities among the groups. Here, grouping of nodes is performed as follows based on the priority in the column direction.

(1) If the priority in the column direction is higher than that in the row direction, the nodes are grouped in each column, and (2) if the priority in the row direction is higher than that in the column direction, the nodes are grouped in each row. Turn into. In the graph of the example, since the priority in the column direction is higher than that in the row direction, the nodes are grouped for each column according to (1). In the graph of FIG. 5B, for example, the fourth column is selected as the reference group, and the shorter the distance from the reference group, the higher the priority order becomes.
When the priority order of each group is determined, an example of determining the priority order of each group is as shown in FIG.

An embodiment of step 704 for numbering nodes for each group in FIG. 7 will be described with reference to the drawings. When node (1, 4) is selected as the reference node in the reference group in the graph of FIG. 5 (b) and numbers are assigned in the order of increasing distance from the reference node, the number of each node in the reference group is It is obtained as the node number in the fourth column of 8 (b). After that, in the second to eighth groups, set the reference node in each group to the closest one to the reference node in the reference group, and number the nodes in each group. , The number of each node is as shown in FIG. 8 (b).

Step 705 for outputting the execution result of FIG.
Outputs the result as shown in FIG.

A configuration example of the mesh node ordering device according to the present invention will be described below with reference to FIG. In the present embodiment, the input device 101 uses the central processing unit 102 as a graph to draw the data of the structure divided into meshes by drawing a mesh line in a direction parallel to one or more lines or surfaces that characterize the shape of the object. Via the storage device 103. The direction priority determination device 104 counts the number of nodes along each direction of the graph by referring to the data of the graph of the storage device 103 via the central processing unit 102, and the direction having the greater number of nodes has the higher priority. The priority of each direction is determined to be higher, and this information is sent to the group priority determination device 105 via the central processing unit 102. The group priority determination device 105 refers to the data in the graph of the storage device 103 and the priority information in each direction,
The nodes are grouped in order from the direction with the highest priority, the priorities among the groups in the direction are determined, and the information on the priorities between the groups is sent to the node numbering device 106 via the central processing unit 102. Send to. The node numbering device 106 refers to the data in the graph of the storage device 103 and the priority information among the groups, and targets the highest priority group among the groups to which the node numbers have not yet been assigned. And number all the nodes in the group. In addition, when assigning the node numbers, the node number assigning device 106 selects an arbitrary node in the reference group as the reference node when assigning the node numbers, and selects a node other than the reference group in the group. Select the node closest to the reference node in the reference group as the reference node with. Also, the node numbering device 106
When numbering the nodes within each group, the nodes within the group are numbered in ascending order of the line segment distance from the reference node within the group within the group, and information about this number is centrally processed. Storage device 10 via device 102
Send to 3. After the numbers of all the nodes in the graph are sent from the node numbering device 106, the storage device 103 sends the graph and the node numbers to the output device 107 via the central processing unit 102.

[0032]

When solving the simultaneous linear equations that appear in the process of analyzing the structure of an object, by changing the structure of the coefficient matrix of the simultaneous linear equations by using the mesh node ordering method and apparatus according to the present invention, When solving simultaneous linear equations, it is possible to realize reduction of storage capacity and improvement of calculation efficiency.

[Brief description of drawings]

FIG. 1 is a block diagram of a mesh node ordering device according to the present invention.

FIG. 2 is an explanatory diagram showing the structure of a skyline matrix.

FIG. 3 is an explanatory diagram of a coefficient matrix of simultaneous linear equations.

FIG. 4 is an explanatory diagram of a conventional ordering method.

FIG. 5 is an explanatory diagram of an example to which ordering is applied.

FIG. 6 is an explanatory diagram of prior art ordering.

FIG. 7 is a flowchart of a mesh node ordering method according to the present invention.

FIG. 8 is an explanatory diagram of an embodiment of determining the priority order of groups according to the present invention.

[Explanation of symbols]

101 ... Input device, 102 ... Central processing unit, 103 ... Storage device, 104 ... Direction priority determination device, 105 ... Group priority determination device, 106 ... Node numbering device, 1
07 ... Output device.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Yasuhiro Kobayashi 7-2-1, Omika-cho, Hitachi-shi, Ibaraki Hitachi, Ltd.

Claims (6)

[Claims] 1. A structure in which a mesh is divided by drawing a mesh line in a direction parallel to one or more lines or planes that characterize the shape of an object, priority of each direction is determined, and the determined priority is determined. , The nodes located in the direction are grouped in order from the highest direction to determine the priority order among the groups in the direction, and the nodes existing in each group in the descending order of priority. A mesh node ordering method which is characterized by numbering. 2. The mesh node ordering method according to claim 1, wherein, when determining the priority order of each direction, the priority order becomes higher as the direction having a larger number of nodes counted along each direction. 3. The method according to claim 1, wherein when determining a priority order between groups in an arbitrary direction, an arbitrary group in the direction is selected as a reference group, and a group having a shorter distance from the reference group is selected. A mesh node ordering method that decides higher priorities. 4. When numbering the nodes existing in each group according to claim 1, if the group is the reference group according to claim 3, an arbitrary node in the reference group is In the case other than the above-mentioned reference group, among the nodes in the group, the node closest to the reference node in the reference group is selected as the reference node of the group, and in the order of increasing distance from this reference node, within the group. A mesh node ordering method for numbering existing nodes. 5. The numbering of the node having the highest number in the group having the priority immediately before the numbering of the nodes in the arbitrary group according to claim 4, and in the arbitrary group. A mesh node ordering method that numbers the nodes so that the node number with the smallest number becomes a continuous integer value. 6. An input device for inputting data of the mesh-divided structure according to claim 1, a direction priority determining device for determining priority in each direction, and grouping of nodes in each direction. A group priority order determination device that determines the priority order between each group, a node numbering device that numbers the nodes existing in each group, and an output device that outputs the graph data of the ordered structure And a central processing unit for controlling these devices, and a storage device for storing input / output data and data necessary for processing performed by each device.