JP2005196273A - Mesh generating system and mesh generating program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To efficiently retrieve nodal points when forming mesh, and also execute parallel processing by a plurality of processing elements. <P>SOLUTION: The respective processing elements 12 have a CDT processing part 16 for forming the mesh such as the respective elements become restrictive Deloney (CDT) division on the basis of a surface patch for defining the nodal point arranged inside an object and a surface shape of the object, and a quasi-restrictive Deloney division (SCDT) processing part 18 for selecting a new nodal point where a figure made of a nodal point of an element and a new nodal point does not cross with any surface patch and does not cross any of pre-formed elements, that is, the new nodal point where any nodal point does not exist inside the figure made of the nodal point of the element and the new nodal point, for retrieving a satellite nodal point for forming a nodal point of a certain element and a new nodal point when the element does not satisfy the CDT. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a mesh generation system and a generation program using a finite element method (FEM).

While the finite element method (FEM) has the advantage of excellent adaptability to complex shapes, it has a major drawback in that it requires a great deal of labor for mesh generation. At present, many excellent automatic element generation softwares have been put on the market, but most of them are based on a single CPU environment. Some software allows parallel processing, but the number of CPUs that can be used remains at a few levels. This is because many sequential processes are included in the element generation algorithm itself.
G. Y. Gagawa, T. Co-authored by T. Yamada, “Free mesh method”, A Newmeshless finite element method, Comp. Pp. 383-386 March 18, 1996 G. Y. Gagawa, T. Co-authored by T. Furukawa, “Recent developments of free mesh method”, Int. J. Numer. Meth. Engng., Pages 1419 to 1443, 2000 M.M. M. Tamegawa, T. Ogawa, N.M. Co-authored by N. Ogita, “A new algorithm for three-dimensional Voronoi tessellation”, Journal of Xomputational Physics 51, 191-207, 1983 R. A. RA Dwyer "Hither-dimensional Voronoi diagrams in linearexpected time", Discrete & Computational Geometry 6 (4), 343-367, 1991 L. P. LP Chew, “Constrained Delaunay triangulations”, Algorithmica4 (1), 97-108, 1989

  On the other hand, the free mesh method (FMM) is a calculation method that has been proposed for the purpose of reducing the labor of FEM mesh generation, and generates mesh generation locally around each node (for example, non-patented) Reference 1 and Non-Patent Document 2).

This local element generation can be processed independently in units of nodes, and high parallelization efficiency can be obtained even in parallel processing using a large number of processors. However, the conventional FMM has the following drawbacks.
(1) In the case of processing with a single processor, global element generation, that is, mesh generation on the premise of normal FEM, is overwhelmingly faster in calculation time.
(2) Only relatively simple shapes can be handled. It is difficult to apply to a shape having an acute angle such as a crack.

On the other hand, a technique called a packaging method (see Non-Patent Document 3 and Non-Patent Document 4) has been proposed as an algorithm for locally obtaining Deloni division. This method has the following problems although the average amount of computation is O (n) when the number of nodes is n.
(3) Since a uniform bucket is used for the search for adjacent nodes, the amount of computation increases rapidly in a node arrangement with a large density such as that used in FEM.

In addition, the Delaunay division is originally determined only by the nodes, but as a technique for performing Delaunay division while maintaining the geometric shape (Constrained Delaunay division: see Non-Patent Document 5), a correction algorithm for the packaging method Has been proposed, but has the following problems.
(4) The amount of calculation is O (n ³ ) and cannot be applied to a problem of practical scale.
(5) If the surface patch and node do not satisfy the 'Ridge-protected' condition, it is necessary to add the node. Here, the 'Ridge-protected' condition means that in the case of 3D, for each side of all triangles of the surface patch, a sphere that passes through two points at both ends, and other nodes on the inside and on the boundary. There is something that does not include.

  In order to solve the various problems described above, an object of the present invention is to provide a mesh generation system and program capable of efficient node search and capable of parallel processing with a plurality of processing elements.

An object of the present invention is to provide constrained Deloisian dividing means for generating a mesh in which each element is constrained Deloni (CDT) based on a node arranged inside an object and a surface patch that defines the surface shape of the object. A mesh generation system comprising:
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node A quasi-constrained Deloni partition (SCDT) means for selecting new nodes that do not
After the quasi-constrained Deloni dividing means obtains a continuous CDT boundary surface and isolates a region that is not CDT divided,
(A) In the isolated area, select a figure located on the CDT interface according to a predetermined order;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
This is achieved by a mesh generation system characterized in that elements such as CDT division are generated by repeating (a) and (b).

  According to the present invention, elements are generated in a predetermined order in an area isolated as an area that is not CDT divided, and are extracted from the isolated area. Thereby, an element is uniquely determined even when CDT division is not performed.

  Here, in the two-dimensional case, the element is a triangle, and a new figure, that is, a triangle is formed by the nodes at both ends of one side of the triangle and the new node. Become. In the three-dimensional case, the element is a tetrahedron, and a new figure, that is, a tetrahedron is formed by the nodes corresponding to the three vertices of the triangle forming one surface of the tetrahedron and the new nodes. If this is CDT, it becomes a new element.

  In a preferred embodiment, the apparatus further includes Deloni partitioning means for generating a mesh in which each element is Deloni partition, and when the element obtained by the Deloni partitioning means is not CDT, a new one is created by the constraint Deloni partitioning means. Element generation is performed.

  In a more preferred embodiment, the quasi-constrained Deloni dividing means generates the new figure in a sort order using as a key a number that uniquely identifies a node forming the figure.

In another preferred embodiment, the mesh generation system has a plurality of processing elements, each generating a mesh in an independent region into which the object is divided. Each processing element according to this embodiment is:
A constrained Deloni partitioning means for generating a mesh such that each element is a constrained Deloni (CDT) partition based on the nodes located within the object and the surface patches that define the surface shape of the object;
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node Quasi-constrained Deloni partition (SCDT) means for selecting new nodes that do not
After the quasi-constrained Deloni dividing means obtains a continuous CDT boundary surface and isolates a region that is not CDT divided,
(A) In the isolated area, select a figure located on the CDT interface according to a predetermined order;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
By repeating the steps (a) and (b), an element that is a CDT division is generated.

  More preferably, in each processing element, surface patch information is stored in advance in each storage device, and the processing element includes an internal node generating means for generating an internal node located inside the independent region. Yes.

It is also an object of the present invention to generate a mesh in which each element is a constrained Deloni (CDT) partition based on nodes located inside the object and surface patches that define the surface shape of the object. A mesh generation program that can be read by the computer to function as a constraint Delaunay dividing means,
Further, the computer
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node Function as a quasi-constrained Deloni partition (SCDT) means to select new nodes that do not
When functioning as the quasi-constrained Deloni dividing means, the computer is caused to perform a step of obtaining a continuous CDT boundary surface and isolating a region that does not become a CDT division.
(A) selecting a figure located on the CDT boundary surface according to a predetermined order in the isolated region;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
It is also achieved by a mesh generation program characterized by causing the computer to generate an element that becomes a CDT division by repeating (a) and (b).

In a preferred embodiment, the computer is further caused to function as a Delaunay dividing unit that generates a mesh in which each element is a Delaunay division.
If the element obtained when the computer functions as the Delaunay dividing means is not CDT, the computer is caused to function as the restrained Delaunay dividing means to generate a new element.

  According to this embodiment, it is possible to generate elements without communication between the processing elements substantially independently at each processing element.

  In a more preferred embodiment, when the computer is caused to function as a quasi-constrained Deloni dividing means, the new figure is generated in a sort order using a number uniquely identifying a node forming the figure as a key. Thus, the computer is operated.

  According to the present invention, it is possible to provide a mesh generation system and program capable of efficient node search and capable of parallel processing with a plurality of processing elements.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a block diagram showing an outline of a mesh generation system according to an embodiment of the present invention. In the present embodiment, the mesh generation system 10 includes N processing elements (PE) 12-1, 12-2,..., 12-N, which are connected by a bus or the like. The processing element 12 includes a DT processing unit 14 that performs Delaunay tetrahedron division (DT), a CDT processing unit 16 that performs constrained Delaunay tetrahedron division (CDT), and a CDT improvement. Sub-constrained Deloni (sub-Constrained)
Delaunay) includes an SCDT processing unit 18 that performs tetrahedral division (SCDT), and a storage device 20. The storage device 20 includes node information (for example, coordinates) 22 relating to nodes located in the object to be defined and mesh information 24 relating to the generated mesh.

  In the present embodiment, in order to define the object shape, each processing element performs processing locally without communication, and the tetrahedron defined by the mesh information is displaced. The shape of the entire object can be defined without causing

  Hereinafter, prior to the description of the mesh generation system, terms used in the present embodiment will be defined.

[node]
Objects that exist around us are continuums. In order to handle this with a computer, it is necessary to discretize it. Therefore, a finite number of points are generated in the object, and the object is expressed based on this. These points are called nodes.

[Surface patch]
A collection of triangles for defining the shape of an object is called a surface patch.
[mesh]
After connecting the nodes generated in the object to form a set of tetrahedrons, various processes are executed for each tetrahedron. The set of tetrahedrons is called a mesh. The mesh is not limited to a tetrahedron and may be a hexahedron.

[Deroni division]
When a set of nodes as shown in FIG. 2A is given, a triangle formed by dividing the convex hull region is called triangulation (see FIG. 2B). In FIG. 2B, consider a triangle bcd. Regarding the circumscribed circle of the triangle bcd, no other nodes a, e, f, g, h are present inside this circumscribed circle. Thus, if there is no node in the circumscribed circle of a triangle, the triangle is called a Delaunay triangle (DT). The example in FIG. 2 is two-dimensional, but in the case of three dimensions, the triangle is a tetrahedron.

  In the triangulation shown in FIG. 2B, if all the triangles constituting the triangulation are Delaunay triangles, the triangulation is called Delaunay triangulation (Deroni division: DT). Hereinafter, in the present specification, the term “triangle” includes “tetrahedron” unless two-dimensional and three-dimensional are distinguished.

[Packaging Act]
The packaging method is one of algorithms for obtaining Deloni division, and as shown in FIGS. 3A to 3D, it is the packaging method that obtains Delaunay triangles one by one. As shown in FIG. 4, in the packaging method, first, an appropriate node on the right side of the side ab connecting the nodes a and b is selected (step 401). Initially, the selected node is a candidate node. In the present embodiment, the right side of the side ab is considered to be the “right side” when the start point a is viewed from the end point b of the side.

  Next, it is determined whether or not the selected node exists within a circle passing through the nodes a and b and the previously set candidate nodes (step 402). If it is determined as Yes in step 402, the node selected in step 401 is set as a new candidate node (step 403).

  When the processing of Steps 401 to 403 is completed for all nodes located on the right side of the side ab (Yes in Step 404), the candidate node information at the last time point is a triangle located on the right side of the side ab. Is stored in the storage device as the nodes forming (step 405). This process is the same for the three-dimensional case (when a tetrahedron is formed). Here, instead of considering nodes for edges, nodes for tetrahedrons may be considered, and circumscribed spheres may be considered instead of circumscribed circles. A triangle obtained by such processing becomes a Delaunay triangle.

[Satellite node search]
A process of forming a Delaunay triangle by repeating a process of setting a certain node as a center node and surrounding nodes from this node as candidate nodes will be described. It is considered that nodes as shown in FIG. In this example, the central node is considered as node a.

  When searching for a satellite node, first, a node closest to the central node is searched (step 601). In the example shown in FIG. 5A, the node b is found (see FIG. 5B). The retrieved node is set as a satellite node (step 602). Next, the next satellite node is obtained by applying the algorithm of FIG. 4 to the line segment connecting the last-found satellite node and the central node (step 603). As for the line segment ab, the node c becomes a node constituting the Delaunay triangle, and this is a satellite node (see FIG. 5C). The process of step 603 is repeated until the satellite node obtained by the same process matches the first found satellite node (node b in the example of FIG. 5) (see step 604). As a result, the satellite nodes are determined as shown in FIGS. 5D and 5E, and the Delaunay triangle can be formed.

  The process shown in FIG. 6 is applied to a so-called internal node. Next, processing applied to boundary nodes including surface patches will be described. It is assumed that the nodes as shown in FIG. 7A to 7E, the broken line indicates a surface patch. In this case, the node on the surface patch is selected as the center node. In FIG. 7A, the central node is considered as node a.

  As shown in FIG. 8, first, a surface patch having a central node as a start point or an end point is searched (step 801). In the example of FIG. 7A, surface patches ea and ab are found, and thus nodes b and e are found. These surface patches include orientation. Next, the other node of the surface patch whose end point is the center node is set as the first satellite node (step 802). In FIG. 7A, the node e is the first satellite node.

  Thereafter, the next satellite node is obtained by applying the algorithm shown in FIG. 4 to the line segment connecting the last-found satellite node and the central node (step 803). As shown in FIG. 7B, for the line segment ea (side ae), the node d is set as a satellite node (see FIG. 7C). The process in step 803 is repeated until the last satellite node (node b in the above example) is reached (see step 804). From the state of FIG. 7C, the node c is set as the satellite node for the side ad (see FIG. 7D). FIG. 7E shows a state in which the final node b is set as a satellite node and the processing is completed.

  Next, the satellite node search in the three-dimensional case will be described. At the internal node, the first Deloni triangle (where triangle means a two-dimensional triangle) that is the seed for applying the packaging method is found, and the front and back surfaces of the triangle are registered in the list. A triangle is then removed from the list and the information is deleted from the list. For this triangle, an algorithm shown in FIG. 4 is applied to obtain a tetrahedron that touches the surface of the triangle. In FIG. 9, a triangle based on the triangle abc and a node d are newly obtained nodes. Of the four faces of the tetrahedron abcd, triangles other than the triangle based on the face including the central node, that is, the triangle adb and the triangle acd are registered in the list. Such a process is repeated until the list becomes empty.

  Next, the case of a boundary node will be described. First, a surface patch having a central node as a vertex is selected. Only the surface inside the triangular object of the surface patch is registered in the list. A triangle is then removed from the list and the information is deleted from the list. For this triangle, the algorithm in FIG. 4 is applied to obtain a triangle that touches the surface of the triangle. In FIG. 9, in FIG. 9, a triangle based on the triangle abc and a node d are newly obtained nodes. Of the four faces of the tetrahedron abcd, triangles other than the triangle based on the face including the central node and triangles that are not surface patches are registered in the list. Such a process is repeated until the list becomes empty.

[Constrained Delaunay split]
The region formed by the set of triangles (tetrahedrons) obtained when Delaunay is divided into a set of nodes coincides with the convex hull of the original set of nodes. However, the shape required as a mesh is a general arbitrary complicated shape including not only a convex but also a concave. Restrained Deloni (Constrained)
Delaunay) partitioning is used.

  Here, other nodes from the triangle are “visible” and “not visible” mean the following. For a given node A, for any node B inside the triangle, when line segment AB intersects any surface patch, node A is defined as “invisible” from that triangle.

A triangle is said to be a CDT (Constrained Delaunay Triangle) if there are no nodes visible from the triangle inside the circumscribed circle. Also, for a given triangulation, if all the triangles that make up the triangulation are CDTs, the triangulation is constrained Deloni (Constrained
Delaunay) Divided. An algorithm of a packaging method for performing CDT division will be described below. As shown in FIG. 10, a search is made for nodes that exist on the right side of a certain side, and the triangle formed by the node and the side does not intersect any surface patch (step 1001). If the target node exists in a circle passing through such a node and the nodes at both ends of the side (Yes in step 1002), the existing node is set as a new candidate node. (Step 1003). Step 1004 and step 1005 are the same as the algorithm of the packaging method for performing the DT division of FIG. The processes shown in FIGS. 6 and 8 can be applied to the satellite node search.

  Even in the three-dimensional case, “visible” and “not visible” can be defined as follows. If there is a point B inside the tetrahedron for a given node A and the line segment AB does not intersect with any surface patch, the node A is defined as “visible” from the tetrahedron. On the other hand, for a given node A, for any point B inside the tetrahedron, when line segment AB intersects any surface patch, node A is "not visible" from that tetrahedron. Define.

  For a tetrahedron, if there are no nodes visible from the triangle inside the circumscribed sphere, the tetrahedron is a CDT. For a given tetrahedron division, if all the tetrahedrons constituting the tetrahedron division are CDTs, the tetrahedron division is said to be a constrained Delaunay division.

  A packaging method algorithm for performing CDT division in the three-dimensional case will be described with reference to FIG. First, a node that is present in a half space of a surface space of a certain triangle and whose tetrahedron formed by three points (vertices) of the triangle and its nodes does not intersect any surface patch is searched (step 1101). ). Next, it is determined whether or not the target node exists inside the sphere passing through the three points of the triangle and the searched nodes (step 1102). If it is determined YES in step 1102, the existing node is set as a new candidate node (step 1103). Such processing is executed for all nodes existing in the half space (see step 1104), the candidate node at the last time point is set as a node existing in the half space, and necessary information is stored in the storage device. (Step 1105).

[SCDT]
In the present embodiment, an algorithm in which the CDT is corrected is introduced. For convenience, this is referred to as quasi-constrained Deloni division (Sub-CDT: SCDT). FIG. 12 is a flowchart showing an algorithm of a packaging method for performing SCDT division. The algorithm shown in FIG. 12 is the same as the process shown in FIG. 11 except for part of step 1201. In step 1201, a different point exists in a half space of a triangular surface space, and a tetrahedron composed of the node and three triangular points does not intersect any surface patch and has been created so far. Nodes that do not intersect any of the elements are searched. Here, the element refers to a triangle (a fixed tetrahedron surface) that has been created.

[Satellite node search using DT, CDT and SCDT]
FIG. 13 is a flowchart showing a satellite node search algorithm according to the present embodiment. In FIG. 13, step 1301 is executed by the DT processing unit 14 of FIG. 1, and step 1303 is executed by the SDT processing unit 16. Steps 1305 and 1306 are executed by the SCDT processing unit 18. The node information is stored in advance in the storage device, and the generated triangle and tetrahedron information is stored in the storage device as mesh information as the process proceeds.

  First, the DT processing unit 14 extracts information about a triangle from the mesh information in the storage device 20 and tries to obtain the next tetrahedron existing on the surface side of the triangle. Here, the next node is obtained by using a packaging method algorithm (see FIGS. 6 and 8) based on Delaunay division, thereby obtaining the next element (tetrahedron) (step 1301).

  Here, it is determined whether the obtained element is CDT (step 1302). This step may be executed by the DT processing unit 14 or may be executed by the CDT processing unit 16. If it is determined as Yes in step 1302, information regarding the new element is stored as mesh information in the storage device, and then the process proceeds to a process for obtaining the next element.

  On the other hand, when it is determined NO in step 1302, the CDT execution unit 18 obtains the next node using the packaging method algorithm (see FIG. 11) based on the constraint Delaunay division. An element is obtained (step 1303). Again, it is determined whether the determined element is CDT (step 1304). If it is determined as Yes in step 1304, information on the new element is stored in the storage device as mesh information, and the process proceeds to a process for obtaining the next element.

  If NO is determined in step 1304, the SCDT processing unit 18 obtains a continuous CDT boundary surface and isolates the region (step 1305). Next, the SCDT processing unit 18 takes out the tetrahedron having the original triangle as one surface, using the packing method algorithm (see FIG. 13) based on SCDT division, for the isolated region, and uses it as the next element (step 1306). ). Information on the extracted elements is stored in the storage device as mesh information.

  For example, whether or not it is a CDT may be checked by checking whether or not there is another node inside the circumscribed circle (circumscribed sphere) in accordance with the definition of CDT described above. In addition, since the nodes existing inside the circumscribed circle (the circumscribed sphere) are examined in the bucket when the packaging method is executed, the search is omitted by caching these nodes, and the processing speed is increased. be able to. The bucket will be briefly described later.

[Search for continuous CDT interface]
The continuous boundary surface in step 1305 will be described below. Here, only the three-dimensional case is targeted, and the two-dimensional case is not realized. However, for the sake of understanding, a two-dimensional diagram will be used for convenience.

  As shown in FIG. 14A, it is assumed that a set of nodes and surface patches is given. In the figure, black circles are nodes and broken lines are surface patches. When the surface patch satisfies a specific condition, the inside of the region can be completely divided by CDT as shown in FIG. The condition that this surface patch should satisfy is called the Edge-protected condition. At this time, the CDT is characterized in that there is only one CDT for a given node and surface patch.

  However, in general, not all surface patches satisfy the Edge-Protected condition from the beginning. In FIG. 14C, it is assumed that the portion indicated by the chain line in the surface patch does not satisfy the Edge-Protected condition. In that case, there is a region where CDT does not exist around the surface patch indicated by the chain line. This corresponds to a region indicated by hatching in the drawing. The boundary of the area indicated by hatching is called a CDT boundary surface. It should be noted that CDT is present in regions other than the region indicated by hatching, and there is only one type of set for a given node and surface patch.

  The SCDT processing unit 18 generates elements based on the above-described SCDT division algorithm for the area indicated by hatching in FIG. Note that the CDT has uniqueness, but the tetrahedron of the isolated region described above has no uniqueness as it is. As will be described later, uniqueness is required when each processing element 12 independently generates an element for a divided area. Therefore, in this embodiment, the following rules are introduced to obtain uniqueness.

  As shown in FIG. 15, one of the boundary triangles (a two-dimensional line segment in FIG. 14 schematically drawn in two dimensions) is selected according to a predetermined order (step 1501), and a tetrahedron that touches the triangle is created. (Step 1502). The created tetrahedron is removed from the isolated region, and the isolated region is updated so that the created tetrahedron is removed (step 1503). By repeating the processing of steps 1501 to 1503, the uniqueness of all elements of CDT and SCDT can be obtained.

  Here, in step 1501, in order to obtain uniqueness, a rule for ordering triangles constituting the boundary is determined, and an element is generated from the minimum or maximum triangle based on the order.

Examples of ordering include:
Consider the following four sets of boundary triangles:
{{0,9,7}, {9,7,2}, {2,7,0}, {0,2,9}}
Here, the numbers represent the node numbers constituting the triangle. First, for each triangle, the order is circulated so that the vertex having the smallest number among the three vertices constituting the triangle comes to the top. In the above example, the set is rewritten as follows.
{{0,9,7}, {2,9,7}, {0,2,7}, {0,2,9}}
Next, the triangles are ordered as follows.

For triangle A {a1, a2, a3} and triangle B {b1, b2, b3},
A <B if a1 <b2
If a1 = b1 and a2 <b2, then A <B
If a1 = b1 and a2 = b2 and a3 <b3, then A <B
If a1 = b1, a2 = b2, and a3 = b3, then A = B
In other cases, A> B

According to such an ordering, the set of exemplified triangles is rearranged as follows.
{{0,2,7}, {0,2,9}, {0,9,7}, {2,9,7}}
In the process of FIG. 15, the triangles may be selected in the order rearranged in this way.

[Bucket processing]
In the present embodiment, the DT processing unit 14 and the CDT processing unit 16 search for nodes using buckets. In the bucket process, a midpoint of a side is centered and nodes around it are searched in a spiral. More specifically, first, a first node existing on the right side of a certain side is set as a candidate node. Next, if the target node exists on the right side of the side and the target node exists inside a circle passing through the three nodes of both ends of the side and the candidate node, the node is set as a new candidate node. In the node search using the bucket, if the candidate node at that time and all the circles passing through the nodes at both ends of the side are searched, the process is terminated. The candidate node at the end is the node to be obtained. This process can be realized in the same manner in both the two-dimensional case and the three-dimensional case.

[Parallelization]
Next, parallelization by a plurality of processing elements 12-1, 12-2, ..., 12-N will be described. In the present embodiment, node generation and element (tetrahedron) generation can be realized substantially without communication between processing elements.

  In the present embodiment, the bounding box covering the object is divided by “N (= i × j × m)”, and only the surface patch of the divided three-dimensional region is defined, and the information is assigned to each processing element. It is stored in 12 storage devices. Each processing element 12 generates a node in a region other than the boundary of the region using a quadtree in the case of two dimensions and an octree in the case of three dimensions according to the node density field. In this process, only the upper part of the tree structure is communicated between the processing elements, and the assigned area of each processing element is determined. Thereafter, for the lower part, each processing element can generate a node independently.

  In addition, the generation of elements can be realized independently (without communication) by each processing element 12 for each area to be handled. As described above, the DT division, the CDT division, and the SCDT division, which are executed by the processing element according to the present embodiment, are generated by the packing method algorithm, and the satellite node search algorithm using these (see FIG. 13). Uniqueness can be ensured for each element. Therefore, even if each processing element generates an element independently, inconsistency at the boundary surface can be prevented.

[Virtual parallelization]
One feature of the generation of elements according to the present embodiment is that there is substantially no communication between processing elements. That is, it can be said that the calculation of each processing element is almost completely independent. Therefore, virtual parallelization can be realized by exchanging the operations of the processing elements with a single computer.

[Illustration]
The present inventors used this embodiment to generate elements in parallel processing for a pantheon consisting of 100 million elements. Here, the bouncing box covering the pantheon is divided into 262144 (= 64 × 64 × 64) cells. Each processing element is responsible for 64 (4 × 4 × 4) cells among the divided cells. Therefore, a total of 4096 processing elements generated the elements independently. Each processing element generates an internal element of the 64 cells in charge of the processing element, but the data has extra cell information, one in each of the vertical / horizontal / depth directions. That is, each processing element has 216 (6 × 6 × 6) pieces of data.

In the following, the results of operations performed by a single CPU using the virtual parallel technology described above are shown.
Model: Pantheon Number of nodes: about 21 million Number of elements: about 120 million hours: About 4 hours and 40 minutes (internal node generation and element generation)
CPU: Athron XP2100 + (1.73GHz)
Memory: 2GB
FIG. 16 is a diagram showing the generated mesh. The lower left diagram is an enlarged view of the pillar portion, and the lower right diagram is an enlarged view of the ceiling portion.

  The present invention is not limited to the above embodiments, and various modifications can be made within the scope of the invention described in the claims, and these are also included in the scope of the present invention. Needless to say.

FIG. 1 is a block diagram showing an outline of a mesh generation system according to an embodiment of the present invention. FIG. 2 is a diagram for explaining Deloni division. FIG. 3 is a diagram for explaining the packaging method. FIG. 4 is a flowchart showing a packaging method algorithm for performing DT division. FIG. 5 is a diagram for explaining a satellite node search with respect to an internal node. FIG. 6 is a flowchart showing a satellite node search algorithm for internal nodes. FIG. 7 is a diagram for explaining a satellite node search for a boundary node. FIG. 8 is a flowchart showing a satellite node search algorithm for boundary nodes. FIG. 9 is a diagram for explaining a three-dimensional satellite node search. FIG. 10 is a flowchart showing a packaging method algorithm for performing CDT division. FIG. 11 is a flowchart showing a packaging method algorithm for performing CDT division in the three-dimensional case. FIG. 12 is a flowchart showing a packaging method algorithm for performing SCDT division according to the present embodiment. FIG. 13 is a flowchart showing a satellite node search algorithm executed by the processing element according to the present embodiment. FIG. 14 is a diagram for explaining a search for continuous CDT boundary surfaces in the present embodiment. FIG. 15 is a flowchart showing selection of a triangle of an isolated area and generation of a tetrahedron in the present embodiment. FIG. 16 is a diagram showing a mesh generated using the mesh generation system according to the present embodiment, in which the upper center is an overall view, the lower left is a pillar portion, and the lower right is an enlarged view of a ceiling portion. It is.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Mesh generation system 12 Processing element 14 DT processing part 16 CDT processing part 18 SCDT processing part 20 Storage device

Claims (8)

A mesh generation system including a constraint Delaunay dividing unit that generates a mesh in which each element is a constraint Deloni (CDT) partition based on a node arranged inside the object and a surface patch that defines a surface shape of the object. There,
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node A quasi-constrained Deloni partition (SCDT) means for selecting new nodes that do not
After the quasi-constrained Deloni dividing means obtains a continuous CDT boundary surface and isolates a region that is not CDT divided,
(A) In the isolated area, select a figure located on the CDT interface according to a predetermined order;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
A mesh generation system characterized by generating an element that becomes CDT division by repeating (a) and (b). Furthermore, it has a Deloni dividing means for generating a mesh such that each element is divided by Deloni,
The mesh generation system according to claim 1, wherein when the element obtained by the Delaunay dividing unit is not CDT, a new element is generated by the constraint Delaunay dividing unit. 3. The mesh according to claim 1, wherein the quasi-constrained Deloni dividing unit generates the new figure in a sort order using a key that uniquely specifies a node forming the figure as a key. Generation system. A mesh generation system having a plurality of processing elements, each of the processing elements generating a mesh in an independent region obtained by dividing an object,
Each processing element
A constrained Deloni partitioning means for generating a mesh such that each element is a constrained Deloni (CDT) partition based on the nodes located within the object and the surface patches that define the surface shape of the object;
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node Quasi-constrained Deloni partition (SCDT) means for selecting new nodes that do not
After the quasi-constrained Deloni dividing means obtains a continuous CDT boundary surface and isolates a region that is not CDT divided,
(A) In the isolated area, select a figure located on the CDT interface according to a predetermined order;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
A mesh generation system characterized by generating an element that becomes CDT division by repeating (a) and (b). In each processing element, information on the surface patch is stored in advance in each storage device,
The mesh generation system according to claim 4, wherein the processing element includes an internal node generation unit configured to generate an internal node located inside the independent region. Causing the computer to function as a constrained Deloni partitioning means for generating a mesh such that each element is a Constrained Deloni (CDT) partition based on the nodes located within the object and the surface patches that define the surface shape of the object. A mesh generation program readable by the computer,
Further, the computer
When the generated element does not satisfy the CDT, in order to search for a node of an element and a satellite node that forms a new element, a figure formed by the node of the element and the new node is A new node that does not intersect with any surface patch and does not intersect with any of the elements created so far, and any node exists inside the element node and the figure created by the new node Function as a quasi-constrained Deloni partition (SCDT) means to select new nodes that do not
When functioning as the quasi-constrained Deloni dividing means, the computer is caused to perform a step of obtaining a continuous CDT boundary surface and isolating a region that does not become a CDT division.
(A) selecting a figure located on the CDT boundary surface according to a predetermined order in the isolated region;
(B) generating a new element in contact with the selected graphic, and then excluding the new element from the isolated region;
A mesh generation program characterized by causing the computer to generate an element that becomes a CDT division by repeating (a) and (b). Further, the computer is caused to function as a Delaunay dividing means for generating a mesh in which each element is a Delaunay division,
The generation of a new element is executed by causing the computer to function as the constraint Delaunay dividing unit when an element obtained when the computer functions as the Delaunay dividing unit is not CDT. Item 7. A mesh generation program according to item 6. When the computer is caused to function as a quasi-constrained Delaunay dividing means, the computer is operated so as to generate the new figure in a sort order with a key uniquely identifying a node forming the figure. The mesh generation program according to claim 6, wherein the mesh generation program is executed.