JPH11260812A - System and method for mesh generation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a mesh generation system and a method for always making a simplified form into the same form and speeding up a simplification processing between areas after simplification, without an overlapped region and a gap. SOLUTION: A boundary segment construction means for removing a loop and an approximate mesh point from a boundary segment form, reconstituting a boundary segment so that the region can be decided uniquely and transferring it in a boundary segment storage part 31 and a boundary segment simplification means for setting a boundary mesh point which is out of the object of simplification as an inoperative mesh point, storing it in an inoperative mesh point storage part 32, dividing a boundary segment into blocks by using the inoperative mesh point stored in the inoperative mesh point storage part 32 and reducing the boundary mesh point by deleting the mesh points in order starting from the mesh point, whose simplification value is minimum in a means simplifying the boundary mesh constructed in the boundary segment construction means are installed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mesh generation method, and more particularly to a mesh generation method and method suitable for numerical simulation of oxidative deformation of a semiconductor process.

[0002]

2. Description of the Related Art A simplification used in a mesh generation method will be described with reference to a flowchart shown in FIG.
This will be described below using a specific example shown in FIG.

First, a boundary line segment for each area is obtained (FIG. 9).
Step F1). In FIG. 10, of the entire shape of G1,
The boundary line of the region B shown in G2 was taken up.

In step F2 of FIG. 9, the first boundary line segment to be simplified is determined. In FIG. 10, one mesh point of G2 is set as a mesh point of a line segment start point (referred to as “end point mesh point”).

Next, in step F3 of FIG. 9, a simplified value of a mesh point adjacent to the end point mesh point is calculated. FIG.
At 0, first, the simplified value of the 2 mesh points of G3 was calculated.

In step F4 of FIG. 9, the simplification value is determined. If the simplification value is smaller than the preset reference value, the mesh point is deleted, and the process is repeated from step F3. FIG.
Then, since the simplified value of 2 was less than the reference value, it was deleted.
Is evaluated. Since the simplification value of the mesh point 3 is also equal to or less than the reference value, it is deleted and the mesh point 4 is evaluated.

If the simplification value of the mesh point is larger than the reference value in step F4, an end determination is made, and if all the boundary line processes have been completed (step F6). Then, the simplification process ends. On the other hand, in step F6 of FIG.
In order to update the end point mesh points, the processing from step F2 is repeated.

Since the simplified value of the boundary mesh point 4 in FIG. 10 is equal to or larger than the reference value, the position of the end point mesh point is moved from 1 to 4 as shown by G4. Since mesh points that have not been evaluated remain, the same processing as when the end point mesh is 1 is performed. Finally, the shape is as shown in G5 (the broken line shows the original shape).

This method is a method in which simplification is completed by one scan.

[0010]

However, the above-mentioned prior art has the following problems.

The first problem is that simplification causes overlapping and gaps in areas. FIG. 11 shows a final shape including other regions A and C in the above example. As shown in FIG. 11, there is a gap between the regions A and B,
And C are overlapped.

[0012] The reason why such a problem occurs is that three or more regions are in contact with each other at one mesh point.
This is because mesh points inappropriate to be deleted are not set to be excluded from deletion.

A second problem is that the shape after simplification changes depending on the order of simplification.
For example, H2 and H3 in FIG.
The order of simplification is from the boundary mesh points 9 to 0, and conversely, the boundary mesh points 0 to 9
Respectively show the final shapes when going toward. The final shape changes depending on the direction of simplification.

The reason why such a problem occurs is that a local simplification method of performing simplification in a fixed order is used.

SUMMARY OF THE INVENTION Accordingly, the present invention has been made in view of the above problems, and an object of the present invention is to provide a mesh generation method and a mesh generation method capable of always making a simplified shape the same. It is in.

It is another object of the present invention to provide a mesh generation method and a mesh generation method in which overlapping areas and gaps do not occur between simplified areas.

Still another object of the present invention is to provide a mesh generation method and method for speeding up the simplification processing.

[0018]

In order to achieve the above object, according to the present invention, a loop or a neighboring mesh point is removed from a received boundary line shape so that a boundary line segment can be uniquely determined. And a means for simplifying the boundary mesh constructed by the boundary-segment constructing means, which are excluded from mesh point simplification. The boundary mesh points are set as immobile mesh points and stored in the immobile mesh point storage unit,
Using the fixed mesh points stored in the fixed mesh point storage unit, the boundary line segments are divided into blocks, and the simplified mesh values are sequentially deleted from the smallest mesh point, thereby reducing the boundary mesh points. And simplification means.

According to the mesh generation method of the present invention, a loop or a neighboring mesh point is removed from a given boundary line shape, and the boundary line is reconstructed so that a region can be uniquely determined, and the boundary line segment is stored. The boundary mesh points to be excluded from the object of mesh point simplification are set as immovable mesh points when the reconstructed boundary mesh is simplified, and stored in the immovable mesh point storage unit. Using the fixed mesh points stored in the mesh point storage unit, the boundary segments are divided into blocks, and the mesh points with the simplest values are deleted in order from the smallest, thereby reducing the number of boundary mesh points.

[0020]

Embodiments of the present invention will be described below. The present invention provides mesh points (referred to as “boundary mesh points”) on line segments (referred to as “boundary line segments”) generated at the Si / SiO2 boundary or SiO2 / ambient (ambient) boundary generated during oxidation deformation simulation. And a method and an effective method for removing the same.

In a preferred embodiment of the mesh generation method of the present invention, referring to FIG. 1, a boundary line segment construction section 21 receives a boundary line segment shape from the oxidation deformation calculation execution device 10, Remove points,
The boundary line segment is reconstructed so that the region can be uniquely determined, and is transferred to the boundary line storage unit 31 of the storage device.

The boundary line simplification unit 22 includes a boundary line structuring unit 2
Simplify the boundary mesh constructed in step 1. At this time, a boundary mesh point to be excluded from the simplification of the mesh points (referred to as “immobile mesh point”) is set, stored in the immobile mesh point storage unit 32, and stored in the immobile mesh point storage unit 32. The boundary mesh points are reduced by dividing the boundary line segments into blocks using points, and sequentially deleting the mesh points with the smallest simplification value.

In the embodiment of the present invention, by using a technique of setting immobile mesh points, gaps between areas and overlapping of areas due to deletion of mesh points where areas of three or more materials are in contact. Can be suppressed, and the method of deleting mesh points in ascending order of the simplification value can be used, so that the simplification result of the boundary line can be obtained regardless of the scanning direction of the line and the order of simplification. Can be uniquely determined.

[0024]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing an embodiment of the present invention;

[Embodiment 1] FIG. 1 is a diagram showing a configuration of an embodiment of the present invention. With reference to FIG.
Oxidation deformation calculation execution unit 1 executed by program control
0, a boundary line generation device 20 that is executed under program control, a storage device 30 that stores information, and a boundary line output device 40 that outputs the generated boundary line information.

The boundary line segment storage unit 31 stores identification numbers of boundary mesh points, position information, connection information, area information, and the like. These pieces of information are corrected, deleted, and added by the oxidation deformation calculation execution device 10 and stored in the storage unit 31.

The immobile mesh point storage unit 32 stores identification numbers of boundary mesh points which are not to be simplified when the boundary mesh points are simplified.

The boundary line segment generating device 20 includes a boundary line line segment construction unit 21 and a boundary line line segment simplification unit 22.

The boundary line segment construction unit 21 divides the boundary line segment information, which is created by the oxidative deformation calculation execution device 10 and includes an abnormal shape such as an intersecting line segment or a nearby mesh point or a mesh point, into a region division, The abnormal shape is corrected by, for example, combining and abolishing the neighboring mesh points, and is recorded in the boundary line recording unit 31.

The boundary line simplification unit 22 includes a boundary line structuring unit 2
The boundary line segment information corrected in step 1 is read from the boundary line segment recording unit 31, and among the boundary mesh points, immovable mesh points to be excluded from simplification are set.
To record. For example, in the case of two dimensions, a point where three or more materials are in contact at the same mesh point is registered as an immobile mesh point.

Next, the boundary line segment is divided by immobile mesh points, and the boundary line segment is blocked. A simplification value is calculated for each block, and mesh points having the minimum simplification value and having a value smaller than a preset simplification reference value are deleted.

The above operation is repeated until there is no boundary mesh point having a simplification value smaller than the simplification reference value.

Finally, the simplified boundary line information, the total moving area indicating the degree of simplification, the number of reduced mesh points, and the like are output to the boundary line output device 40.

FIG. 2 is a flowchart showing the overall processing flow of an embodiment of the present invention. The overall operation of one embodiment of the present invention will be described in detail with reference to FIGS.

The boundary line segment information accumulated in the boundary line segment storage unit 31 by the oxidation deformation calculation execution unit 10 is supplied to the boundary line segment construction unit 21.

The boundary line information supplied to the boundary line segment construction unit 21 includes, for example, the inversion of the triangular mesh, the loop or contact of the boundary line due to the entry into another material region, and the like, generated by the oxidation deformation calculation. There is a possibility that an abnormal mesh point or shape, such as an element in which the boundary line segment and the boundary mesh point are very close, is included.

In the boundary line segment construction section 21, the order of the material of the area,
For example, the boundary line segment is reconstructed by using a method of allocating regions in the order of hardness, and the adjacent boundary mesh points are integrated and abolished, and stored in the boundary line storage unit 31.

The boundary line segment simplifying section 22 deletes, in a fixed order, boundary mesh points that can be deleted from the boundary mesh points constructed by the boundary line segment constructing section 21 and stored in the storage section 31.

In the boundary line simplifying section 22, first, the storage section 3
A boundary line segment is obtained from No. 1 (step A1 in FIG. 2).

Next, mesh points (immobile mesh points) to be excluded from the simplification target of the boundary line are set. An immobile mesh point is set to a mesh point where three or more materials are in contact (step A2 in FIG. 2).

Then, in step A3, step A2
Select the block of the outline line divided by. The simplification is
It can be performed independently in block units.

Next, in step A4, the above-mentioned step A
The simplified value of the mesh point in the block selected in 3,
For example, the moving distance of a line segment when the boundary mesh point is deleted, the area of a region changed by the deletion, and the like are calculated.

Subsequently, in step A5, a boundary mesh point having the minimum simplification value in the block is selected.

In step A6, the simplification value of the selected boundary mesh point is determined. If the simplification value is equal to or less than the preset reference value, the process proceeds to step A7. On the other hand, if it is larger than the reference value, the simplification processing of the block is terminated, and the process proceeds to step A9.

In step A7, the grid is deleted.

In step A8, it is determined whether or not a boundary mesh point to be deleted remains in the block, and if so, the loop from A4 is repeated. If all the boundary mesh points have been deleted, the simplification of the block ends, and the process proceeds to step A09.

Last Step A of Boundary Segment Simplification Unit 22
In S9, it is determined whether the simplification processing of all blocks has been completed. If any unprocessed blocks remain, the loop from step A3 is repeated. on the other hand,
If all of them have been completed, the simplified boundary line information is transferred to the boundary line storage unit 31 in FIG.
2 is completed.

Finally, the completed boundary line shape, the area moved by simplification and the like are output to the boundary line output device 40.
Send to

Next, an embodiment of the present invention will be described with reference to FIG. 3 and FIG.

FIG. 3 is a diagram showing an example of the shape of the boundary line after the oxidation deformation calculation. An example of simplification of the boundary of the area B when three areas A, B, and C are present is shown.
(B01).

First, the area B shown in B2 in FIG.
Take out. The immobile mesh points (black circles in FIG. 3) in step A02 in FIG. 2 are set, and the boundary line segment is set to 12-1.
-2-3, 3-4, 4-5-6-7-8-9, 9-1
It is divided into five blocks of 0, 10-11-12.

Next, B3 in FIG. 3 is changed to 12-1-2-3 by selecting a block by the processing in step A3 in FIG.
The example when the line segment is selected is shown. Step A4
, The simplified value in the block (in the example shown in FIG. 3,
The result of calculating the distance traveled when simplifying)
It is shown on the right of B3 in FIG. Here, the moving distance for simplification is indicated by the size of a circle. The broken line is a simplification reference value, and the determination in step A6 of FIG. 2 means that mesh points below this value are to be deleted. in this case,
As a result of the search for the minimum deletion point in step A5, since the simplified value of the boundary mesh point 1 is the minimum, the boundary mesh point 1
Is deleted in step A7.

B4 in FIG. 3 shows the result of recalculation of the simplified value after deleting the boundary mesh point 1. Boundary mesh point 2
The simplification value becomes larger than the simplification reference value, and is therefore not excluded. As a result, line segment 12-1-
The simplification of 2-3 ends with a line segment 12-2-3.

The other groups also perform the processing from step A3, and finally have the shape of B5 in FIG.

FIGS. 4 and 5 illustrate in detail an algorithm (method) for simplification in one embodiment of the present invention.

This is a case where the shape of the boundary line segment of the group selected in step A3 in FIG. 2 is the shape shown in C1 in FIG. The calculation result of the simplified value is shown by the size of the circle on the right of C2. The broken line is the deletion reference value. At this point, all boundary mesh points are to be deleted.

Steps A4 to A7 in FIG. 2 are repeated,
The mesh points on the boundary segment are deleted in ascending order of the simplification reference value.

The shape after the boundary mesh points 3 to 6 have been deleted is C3 in FIG. Due to the deletion of the boundary mesh points 3 to 6, the calculation results of the simplified values of the boundary mesh points 2 and 7 change.

Similarly, when the boundary mesh point 8 having the minimum simplification value in C3 in FIG. 4 is deleted as shown in C4 in FIG. 5, the simplification value of the boundary mesh point 7 exceeds the reference value. Become like

When the boundary mesh point 1 having the minimum simplification value is deleted at C4 in FIG. 5, the result becomes as shown at C5, and the remaining boundary mesh points 2 and 7 both exceed the simplification reference value. The simplification of the main line is completed by the determination in step A8 in FIG. The final shape is the solid line of C6 in FIG. 4 (the broken line is the shape before simplification).

According to step A9 in FIG. 2, the process is repeated until the simplification of all other block segments is completed.

Embodiment 2 Next, a second embodiment of the present invention will be described. In the second embodiment of the present invention, a search for a mesh point having the minimum simplification value is performed not by each block but by using all boundary mesh points. The system configuration is the same as the configuration of the first embodiment described with reference to FIG.

The step of calculating and setting the fixed mesh points from the connection state of the areas and the step of simplifying (deleting the mesh points) the mesh points that come into contact with or intersect with other areas. Is calculated and set in two places. The setting of the fixed mesh point, which depends only on the connection state of the area and has no relation to the change in the outer shape,
This is performed outside and forward of the mesh deletion loop. The setting of an immobile mesh point that needs to be updated with a change in shape is performed in a mesh point deletion loop. As described above, the point that the setting of the fixed mesh points is divided according to the role is different from the first embodiment.

FIG. 6 is a flowchart showing the processing flow of the second embodiment of the present invention. FIG. 6 is a diagram for specifically explaining the second embodiment of the present invention.

In step D1 of FIG. 6, a boundary line segment is obtained. A case where the shape of the boundary line at that time has a step-like shape as shown by E1 in FIG. 7 will be described as an example.

At step D2 in FIG. 6, a fixed mesh point is set. The immobile mesh points set here are mesh points where regions of three or more materials intersect. 1, 6, 7, 12, 13, 1 indicated by black squares (■) in E1 of FIG.
Eight points 7, 18, and 19 are points set as immobile mesh points.

At step D3 in FIG. 6, an immobile mesh point is also set. The immobile mesh points set here are set to points which may intersect with other regions by deleting them from the boundary mesh points other than the immobile mesh points set in step D2.

When a thin region is uneven as shown in FIG. 7, the simplified reference value of the minimum width abnormality of the region is used.
The deletion of the boundary mesh points may cause the boundary line to enter another area. For example, if the point 9 of E2 in FIG. 7 is deleted, the line segment 8-10 of the area B enters the area A. Therefore, in step D3, a mesh point such as point 9 is set as an immobile mesh point, and is excluded from simplification.

In FIG. 7, E2 shown by black circles (●)
Six points 4, 8, 9, 10, and 16 are mesh points that are excluded from simplification by the process of step D3 in the first simplification loop.

Next, in step D4 of FIG. 6, simplified values of mesh points other than the fixed mesh points are calculated.

Then, in step D5 of FIG. 6, the smallest mesh point is selected from the simplified values calculated in step D4. In FIG. 7, point 5 is the minimum.

Subsequently, in step D6 of FIG. 6, the simplification value of the selected mesh point is compared with the reference value. If the simplification value is equal to or smaller than the reference value, the flow advances to step D7 to delete the mesh point. Is repeated. If the value is equal to or more than the reference value, the simplification has been completed, and the simplification process ends.

E3 in FIG. 7 is the shape after the boundary mesh points 5 have been deleted in step D7 in FIG. E4 in FIG. 8 is a result of resetting the immobile mesh points because the outer shape has changed by deleting the boundary mesh points 5 (the boundary mesh points 4 and 8 are the following.
Changes to normal boundary mesh points).

By repeating the processing from step D3 to step D6 in FIG. 6, finally, the shape is simplified to the shape represented by the solid line E5 in FIG. 8 (the original shape is a broken line).

In the first embodiment, if the simplification reference value is not set smaller than the minimum width of the area, the area line segment may enter another area. In this case, even when the simplification reference value is larger than the minimum width of the region, the simplification can be performed without intersecting with another region.

[0076]

As described above, according to the present invention, the following effects can be obtained.

The first effect of the present invention is that the simplified shape can always be made the same.

The reason is that, in the present invention, since the mesh points are deleted in ascending order of the simplification value in the block,
This is because there is no direction for simplification.

The second effect of the present invention is that no overlap region or gap is generated between the simplified regions.

The reason for this is that the present invention uses immovable mesh points, which exclude mesh points in contact with regions of three or more materials from simplification.

A third effect of the present invention is that simplification can be performed at high speed.

The reason is that, in the present invention, since the simplification processing is independent for each block, it is possible to parallelize the simplification processing.

A fourth advantage of the present invention is that any simplified reference value can be used.

The reason for this is that, in the present invention, by performing simplification, mesh points where a line segment enters another area are excluded from deletion as needed.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of an embodiment of the present invention.

FIG. 2 is a flowchart showing a processing flow of an embodiment of the present invention.

FIG. 3 is a diagram for specifically explaining one embodiment of the present invention.

FIG. 4 is a diagram (part 1) for specifically explaining a simplification process according to an embodiment of the present invention;

FIG. 5 is a diagram (part 2) for specifically explaining the simplification processing according to the embodiment of the present invention;

FIG. 6 is a flowchart showing a processing flow of another embodiment of the present invention.

FIG. 7 is a diagram (part 1) for specifically explaining another embodiment of the present invention.

FIG. 8 is a diagram (part 2) for specifically explaining another embodiment of the present invention.

FIG. 9 is a flowchart illustrating a simplification process in a conventional mesh generation method.

FIG. 10 is a diagram for specifically explaining a simplification process in a conventional mesh generation method.

FIG. 11 is a diagram for illustrating a problem of a simplification process in a conventional mesh generation method.

FIG. 12 is a diagram for illustrating a problem of a simplification process in a conventional mesh generation method.

[Explanation of symbols]

 REFERENCE SIGNS LIST 10 Oxidation deformation calculation execution device 20 Boundary segment generation device 21 Boundary segment construction unit 22 Boundary segment simplification unit 30 Storage device 31 Boundary segment storage unit 32 Fixed mesh point storage unit 40 Boundary segment output device

Claims (7)

[Claims] (1) A loop or a neighboring mesh point is removed from a given boundary line shape, and a boundary line is reconstructed so that a region can be uniquely determined, and is transferred to a boundary line storage unit. (B) means for simplifying the boundary mesh constructed by the boundary line construction means, wherein the boundary mesh points to be excluded from the mesh point simplification are referred to as “immovable meshes. Point)), stored in the fixed mesh point storage unit, and using the fixed mesh points stored in the fixed mesh point storage unit, the boundary line segment is divided into blocks, and the mesh with the simplest value is minimized. And a boundary line simplification means for reducing boundary mesh points by sequentially deleting points from the points. 2. A boundary component generation unit that receives a boundary line segment shape from an oxidation deformation calculation execution unit and generates a boundary line segment includes: (a) removing a loop or a nearby mesh point from the boundary line segment segment; Boundary segment construction means for reconstructing a boundary segment so that an area can be uniquely determined and transferring the boundary segment to a boundary segment storage unit; and (b) means for simplifying a boundary mesh constructed by the boundary segment construction means. Registering the fixed mesh points in the fixed mesh point storage unit, using the fixed mesh points stored in the fixed mesh point storage unit, dividing the boundary line by the fixed mesh points into blocks, and for each block Boundary line simplification means for calculating a simplification value and sequentially deleting mesh points having a minimum simplification value and having a value smaller than a preset simplification reference value; To be Mesh generation scheme. (A) From a given boundary line shape, loops, adjacent mesh points, and the like are removed, the boundary line is reconstructed so that a region can be uniquely determined, and transferred to a boundary line storage unit. (B) when simplifying the reconstructed boundary mesh, a boundary mesh point to be excluded from mesh point simplification is set as an immobile mesh point and stored in an immobile mesh point storage unit; Using the fixed mesh points stored in the mesh point storage unit, the boundary line segment is divided into blocks, and the simplified mesh values are sequentially deleted from the smallest mesh point to reduce the number of boundary mesh points. Mesh generation method. 4. An immobile mesh point is calculated and set from a connection state of a region, and a mesh point that contacts or intersects another region is calculated and reset as an immobile mesh point, so that a simplified value is minimized. 4. The mesh generation method according to claim 3, wherein the search for the mesh points is performed using all the boundary mesh points instead of each block. 5. A step of removing loops, adjacent mesh points, and the like from the received boundary line segment shape, reconstructing the boundary line so that an area can be uniquely determined, and transferring the boundary line to a boundary line storage unit. (B) a step of acquiring a boundary line segment from the boundary line segment storage unit; (c) setting immovable mesh points to be excluded from a target of simplification of the boundary line segment to block the boundary line segment (D) selecting a block of the divided outline, (e) calculating a simplified value of a mesh point in the selected block, (f) calculating a minimum simplified value in the block. (G) determining a simplification value of the selected boundary mesh point; (h) if the simplification value is equal to or less than a preset reference value, the boundary mesh point And in the block, It is determined whether the boundary mesh points to be deleted remain, and if so, the processing from the step (e) is repeated. On the other hand, if all the boundary mesh points have been deleted, the block is simplified. Ending and proceeding to the process of the next step (i); and (i) in the step (g), when the simplified value of the selected boundary mesh point is larger than a reference value,
It is determined whether the simplification processing of the block has been completed and whether the simplification processing of all the block lines has been completed. If unprocessed blocks remain, control is performed to repeat the processing from step (d). A mesh generation method, comprising: 6. A step of removing loops, adjacent mesh points, and the like from the received boundary line segment shape, reconstructing a boundary line so that an area can be uniquely determined, and transferring the boundary line to a boundary line storage unit. (B) a step of acquiring a boundary line segment from the boundary line segment storage unit; (c) a step of setting a mesh point where three or more material regions intersect as an immovable mesh point; (d) the step (c). (E) mesh points other than the fixed mesh points, among the set boundary mesh points other than the fixed mesh points, points that may possibly intersect with other areas when deleted. (F) a step of selecting the minimum mesh point among the calculated simplification values, and (g) comparing the simplification value of the selected mesh point with a reference value, If less than the reference value, the mesh point And delete, the repeating the process from step (d), if less than the reference value mesh generation method characterized by comprising the steps of controlling so as to terminate the process of simplification. (A) A loop or a neighboring mesh point is removed from a given boundary line shape, the boundary line is reconstructed so that a region can be uniquely determined, and the boundary line is stored in a boundary line storage unit. Means for storing; and (b) means for simplifying the constructed boundary mesh, wherein the fixed mesh points are stored in a fixed mesh point storage unit, and the fixed mesh points stored in the fixed mesh point storage unit are stored. Means for reducing the boundary mesh points by dividing the boundary line segments into blocks and sequentially deleting the mesh points with the smallest simplification value, using the above-mentioned means (a) and (b) A recording medium on which a program for causing a computer to function is recorded.