CN112989673B - Discrete grid point fast re-regularization method based on binary tree model - Google Patents
Discrete grid point fast re-regularization method based on binary tree model Download PDFInfo
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Abstract
The invention relates to a discrete grid point fast renormalization method based on a binary tree model, which comprises the steps of obtaining the number and the serial number of grid points connected with each grid point; removing repeated points in the grid points connected with each grid point, and updating the number of the connected grid points; classifying the grid points; determining a root node of the binary tree model; determining a second layer of nodes of the binary tree model, and constructing left and right child nodes of the root node; adding subsequent layer nodes of the binary tree model to complete the construction of the binary tree model; based on a binary tree model, the row and column information of the grid points is reconstructed, and the grid point coordinates after structured sorting are output according to the row and column sequence, so that the data of the grid points is re-normalized. The invention abstracts dense point problems into a binary tree, and the operation flow is clear; the row and column information is structurally stored, the algorithm efficiency is high, and the rapid structural ordering of the grid point data is realized; the method has clear layers and modular writing, and has strong robustness and reusability.
Description
Technical Field
The invention relates to the field of discrete grid generation in CAE (computer aided engineering) numerical simulation, in particular to the field of automatic grid generation in finite element numerical simulation, and specifically relates to a binary tree model-based method for quickly re-normalizing discrete grid points.
Background
Finite element numerical simulation techniques have been widely used in many fields over the past decades and have become powerful numerical analysis tools for industry to explore future potential. However, the generation of the finite element mesh for the industrial products with complex shapes is still challenging, and the generation of the high-quality finite element mesh not only needs rich experience accumulation, but also wastes time and labor. The grid full-automatic generation can reduce difficulty and improve generation efficiency, but in special problems of design optimization, reliability evaluation and the like, the risk that an uncertain numerical value discrete error covers a calculation truth value can be brought. Although the mesh deformation technology can avoid the introduction of uncertainty numerical value discrete errors, the problems of some complex conditions cannot be dealt with, such as the case of intersecting lines introduced by surface punching.
The idea of mixed use of the structured grid generation method and the unstructured grid generation method can solve the problems, namely, the introduction of new discrete errors can be avoided, and automatic grid generation under various conditions can be realized. The mixed thinking divides the whole simulated calculation domain into an area with an unchanged shape and an area with a changed shape, firstly generates meshes of the area with the unchanged shape by using a non-structural method, then extracts the boundaries of the area of the non-structural meshes, generates meshes of the area with the changed shape by using a structural method, and finally assembles the two parts of meshes to form the integral finite element analysis mesh. When the shape of the calculation domain is changed, only the coordinates of the grid points of the structured grid part are reconstructed and updated, the connection relation between the grid points is maintained unchanged, and the grid points are reassembled with the unstructured grid of the unchanged area to generate a new finite element analysis grid.
The hybrid grid generation concept also brings new problems, such as matching and transformation of grid point data at interface positions of structured grids and unstructured grids. Structured grids employ grid point data in an ordered arrangement, while unstructured grids employ grid points in an unordered arrangement. In the process of converting grid point data from unstructured sorting to structured sorting, the missing of information of grid rows and columns can cause disorder of grid point connection relation, so that the converted grid point data cannot be used by a structured grid generation method, and the structured grid generation fails. Therefore, it is necessary to re-normalize the unstructured discrete grid points arranged in a disordered manner, recover the row and column information of the grid data, and form a data structure that can be recognized and used by the structured grid generation algorithm.
Currently, there is no relevant research aiming at the special problem, and authors and others have previously proposed a method [ CN202011490658.7] for restitution of spatial discrete grid points, which implements reordering of interface grid data points by means of recursive search, but the method of the patent emphasizes that the technique implementation has the disadvantages of low search efficiency, complex flow and the like in the actual use process. Inspired by the similarity of the binary tree data structure and the interface quadrilateral meshes, the inventor expects further beneficial improvements to the existing spatial discrete grid point renormalization method.
Disclosure of Invention
The invention provides a fast re-regularization method of discrete grid points based on a binary tree model, which is characterized in that the connection relation among the discrete grid points is utilized, and the row and column information of discrete grid point data is reconstructed by constructing the binary tree model describing interface grid data, so that the fast structured ordering of the grid point data is realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
a discrete grid point fast renormalization method based on a binary tree model is realized by executing the following steps:
the method comprises the following steps: acquiring the number and serial number of grid points connected with each grid point;
step two: removing repeated points in the grid points connected with each grid point, and updating the number of the connected grid points;
step three: classifying the grid points;
step four: determining a root node of the binary tree model;
step five: determining a second layer of nodes of the binary tree model, and constructing left and right child nodes of the root node;
step six: adding subsequent layer nodes of the binary tree model to complete the construction of the binary tree model;
step seven: and reconstructing row and column information of discrete grid points based on a binary tree model, and outputting grid point coordinates after structured sorting according to the row and column sequence to realize the rescripurization of the discrete grid point data.
In one embodiment, the first step is specifically:
number n of grid points connecting each grid pointlinkInitially defined as zero;
traversing all quadrilateral mesh cells formed by the mesh points, if any mesh point (Xs, Ys, Zs) exists in the quadrilateral cell, the grid point (Xs, Ys,zs) number of connected grid points nlinkAdd 2 and add the numbers of two grid points connected to the grid point (Xs, Ys, Zs) to the connected grid point number array of the grid points (Xs, Ys, Zs).
In one embodiment, the second step is specifically:
and for each grid point (Xs, Ys and Zs), circularly traversing the connected grid point number array, and eliminating repeated grid point numbers until all connected grid points of the grid points (Xs, Ys and Zs) are subjected to duplicate checking and updating.
In one embodiment, the step three is specifically:
according to the number n of connected grid pointslinkThe values of (2) divide the grid points into 3 types of corner points, boundary points and interior points, where the number of connected grid points nlinkThe grid points 2 are divided into corner points, nlinkThe grid points 3 are divided into boundary points, nlinkThe grid point of 4 is divided into interior points.
In one embodiment, the step four is specifically:
determining a root node of the binary tree, namely a grid corner point, according to a mapping relation between the binary tree model and grid data; if no angular point is designated, selecting any angular point as a root node of the binary tree model; if a corner point is designated, the corner point is selected as a root node.
In one embodiment, step five is specifically:
and 2 grid points connected with the root node are boundary points, any point is selected as a left child node, and the other point is selected as a right child node.
In one embodiment, step six specifically is:
for the node of the ith (i >2), successively traversing each parent node of the upper layer (i-1);
acquiring all grid points connected with each father node according to the connection relation of the grid points, removing the grid points added with the binary tree model, and leaving the grid points which are not added;
adding the non-added grid points to the binary tree model according to the number and the type of the non-added grid points;
and repeating the process until all the grid points are added into the binary tree.
Further, if the number of the grid points which are not added is 2, adding the corner points or boundary points which are not added into the grid points as left child nodes of the corresponding father nodes, and adding another grid point as right child nodes of the father nodes;
if the number of the mesh points which are not added is 1, the mesh points which are not added are directly added as right child nodes of the corresponding father nodes;
and if the number of the grid points which are not added is 0, adding no child node.
In one embodiment, the step seven is specifically:
in the binary tree model, all left subtrees started by a root node form a 1 st row of grid data, and all right subtrees started by each node in the 1 st row form each column of the grid data;
traversing the left and right subtrees of the binary tree model, and outputting the grid data according to the sequence of first row and second row to realize the renormalization of the discrete grid point data.
Compared with the prior art, the invention has the following beneficial effects: the invention abstracts the dense point problem into a binary tree, adopts a binary tree model to describe the interface discrete grid point data, reconstructs the row and column information of the discrete grid point data, and has clear operation flow; the row and column information is structurally stored, the algorithm efficiency is high, and the rapid structural ordering of the grid point data is realized; the method has clear layers and modular writing, and has strong robustness and reusability.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so that those skilled in the art can understand and read the present invention, and do not limit the conditions for implementing the present invention, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the functions and purposes of the present invention, shall fall within the scope covered by the technical contents disclosed in the present invention.
FIG. 1 is a schematic diagram of an exemplary 4-row by 5-column grid in accordance with one embodiment of the present invention;
FIG. 2 is a schematic diagram of unstructured storage of mesh data according to one embodiment of the invention;
fig. 3 is a diagram illustrating the number of connected grid points and the number array according to an embodiment of the present invention;
fig. 4 is a diagram illustrating the number and number array of connected grid points after deduplication according to an embodiment of the present invention;
fig. 5 is a schematic diagram of mesh point classification according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating a root node and a second level node of a binary tree model according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating a process of adding nodes in the fourth layer of the binary tree model according to an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating a whole process of adding nodes of a binary tree model according to an embodiment of the present invention;
FIG. 9 is a diagram of a binary tree model for a 4 row by 5 column trellis according to an embodiment of the present invention;
fig. 10 is a schematic diagram of data storage of grid points after structured sorting according to an embodiment of the present invention.
Reference numerals:
1-grid point, 2-quadrilateral grid cell, 3-grid point number, 4-number of connected grid points, 5-number array of connected grid points.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention are described in further detail below with reference to the embodiments and the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
In the present invention, the terms "comprises/comprising," "consisting of … …," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a product, apparatus, process, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such product, apparatus, process, or method if desired. Without further limitation, an element defined by the phrases "comprising/including … …," "consisting of … …," or "comprising" does not exclude the presence of other like elements in a product, device, process, or method that comprises the element.
The present invention will be described in further detail with reference to a specific grid of 4 rows by 5 columns and the accompanying drawings, which are illustrative only and not limiting, and are not to be construed as limiting the invention.
The method comprises the following steps: the number and number of connected grid points for each grid point are obtained.
First, the value n of the number 4 of connected grid points 1 of each grid point 1 in the 4-row × 5-column grid illustrated in fig. 1linkInitially defined as zero and traverses all quadrilateral mesh cells 2 (the list of mesh cells in fig. 2) formed by all mesh points 1. If any grid point (X)s,Ys,Zs) Existing in the quadrilateral elements 2, grid points (X)s,Ys,Zs) Of the number 4 of connected grid points 1, nlinkAdd 2 and will be compared with grid point (X)s,Ys,Zs) The number 3 of the connected two grid points 1 is added to the grid point (X)s,Ys,Zs) The final result is shown in fig. 3 in the number array 5 of connected grid points.
Step two: duplicate points in the connected grid points of each grid point are removed and the number of connected grid points is updated 4.
For each discrete grid point (X)s,Ys,Zs) And circularly traversing the serial number array of the connected grid points and eliminating the serial number of the repeated grid points. Detailed description of the preferred embodimentIs the m (m) th grid point>1) Phase connected grid point PmTraversing the 1 st to m-1 st connected grid points, if any, and the grid point PmOf the same number of grid points, PmIs deleted from the array of numbers of the connected grid points, while the number n of the connected grid points of this grid point is takenlinkSubtract 1, and exit the traversal. Repeating the above traversal process until the grid point (X)s,Ys,Zs) All connected grid points complete the duplicate checking and updating. For example, grid point number 14 in fig. 3, having 4 networking grid points, the number values being 16, 4 and 8, respectively, cycles through the number values, finding that the 3 rd networking grid point number value 4 is the same as the 2 nd networking grid point number value 4, and thus deleting the 3 rd networking grid point. After the last removal of the duplicate points, grid points numbered 14 have 3 connected grid points, numbered 16, 4 and 8, respectively. The number and number array after the deduplication of the connected grid points of all the grid points is shown in fig. 4.
Step three: the discrete grid points are classified.
According to the number n of connected grid pointslinkThe values of (2) divide the grid points into 3 types of corner points, boundary points and interior points, where the number of connected grid points nlinkDivision of grid points equal to 2 into corner points, nlinkThe grid points equal to 3 are divided into boundary points, nlinkGrid points equal to 4 are divided into interior points. Thus points numbered 5, 13, 16, 20 are divided into corner points, points numbered 1, 2, 3, 8, 10, 14, 15, 17, 18, 19 are divided into boundary points, and points numbered 4, 6, 7, 9, 11, 12 are divided into interior points. The final classification results are shown in fig. 5.
Step four: a root node of the binary tree model is determined.
According to the mapping relation between the binary tree model and the grid data, the root node of the binary tree is known to be the grid corner point at the same time, and the root node can be selected from all the corner points at will. Different angle points have no influence on model construction, but different row and column directions can be generated, and the overall adjustment can be performed according to the original grid information after the information of the rows and columns is reconstructed. Therefore, if no corner point is specified, any corner point can be selected as a root node of the binary tree model; if a corner point is designated, the point is selected as a root node. The grid point numbered 20 is designated here in the 4 row by 5 column grid example as the root node of the binary tree model.
Step five: and determining the second layer of nodes of the binary tree model, namely constructing the left child node and the right child node of the root node.
As can be seen in fig. 4, there are 2 grid points, numbered 19 and 15 respectively, connected to the root node (numbered 20). As can be seen from fig. 5, the grid points numbered 19 and 15 are both boundary points, and therefore either one point can be selected as the left child node, and the other point can be selected as the right child node. Different node selections can exchange row and column information, for example, a grid point with the number of 15 is selected as a left child node, a grid with 5 rows and 4 columns is generated, a grid point with the number of 19 is selected as a left child node, a grid with 4 rows and 5 columns is generated, and the whole transformation adjustment can be carried out after the renormalization, and the construction of a binary tree model is not influenced. The grid point number 19 is selected as the left child node of the root node and the grid point number 15 is selected as the right child node of the root node in the 4 row by 5 column example here, as shown in fig. 6.
Step six: and adding subsequent layer nodes of the binary tree model to complete the construction of the binary tree model.
And for the node of the ith (i >2), successively traversing each father node of the last layer (i-1), acquiring all grid points connected with each father node according to the connection relation of the grid points, removing the grid points added with the binary tree model, and leaving the grid points which are not added. If the number of the mesh points which are not added is 2, adding the angular points or boundary points which are not added into the mesh points as left child nodes of the corresponding father nodes, and adding the other mesh points as right child nodes of the father nodes; if the number of the mesh points which are not added is 1, the mesh points which are not added are directly added as right child nodes of the corresponding father nodes; and if the number of the grid points which are not added is 0, adding no child node. And repeating the process until all the grid points are added into the binary tree. For example, fig. 7 illustrates a detailed adding process of the nodes in the fourth layer of the binary tree model, in which a solid circle indicates that the grid point of the number has been added into the binary tree model, and a dashed circle indicates that the grid point of the number is to be added into the binary tree model. The binary tree model level 3 has added 3 points numbered 18, 11 and 10 in sequence. The grid point numbered 18 is accessed and from figure 4 it can be seen that this point is connected to 3 grid points numbered 9, 17, 19. Where point number 19 has been added to level 2 of the binary tree model, so there are 2 grid points numbered 9, 17 with point number 17 being the boundary point, added to the left child node of 18, and the remaining 9 added to the right child node of 18. Next, the grid point with the number 11 is accessed, and from fig. 4, it can be found that the point is connected with 4 grid points with the numbers 7, 9, 15, and 19, wherein 3 points with the numbers 9, 15, and 19 have been added to the binary tree model, and the non-added grid points are only 1 with the number 7, and are directly added with the right child node with the number 11. And finally, accessing the grid point with the number of 10, and finding that the grid point is connected with 3 grid points with the numbers of 5, 7 and 15, wherein 2 points with the numbers of 7 and 15 are already added into the binary tree model, and the non-added grid points are only 1 grid point with the number of 5 and are directly added with the right child node with the number of 10. The process of adding the nodes of the whole binary tree model is shown in FIG. 8.
Step seven: and reconstructing row and column information of discrete grid points based on a binary tree model, and outputting grid point coordinates after structured sorting according to the row and column sequence.
FIG. 9 illustrates a binary tree model of an example 4 row by 5 column trellis in which all left sub-trees starting with the root node constitute row 1 of the trellis data and all right sub-trees starting with each node of row 1 constitute each column of the trellis data. By traversing the left and right subtrees of the binary tree model, the grid data can be output according to the sequence of first row and second row, and the data of the discrete grid points can be rearranged. For example, with the root node (number 20) of the binary tree model as the starting point of traversal output, the grid point (number 20) is output first, then the right child node (number 15) of the number 20 node is output, then the right child node (number 10) of the number 15 node is output, then the right child node (number 5) of the number 10 node is output, and the right child node does not exist in the number 5 node, and the output of column 1 of the mesh data is completed. Then, the left child node (number 19) of the 20-numbered nodes is output, and all right child nodes ( numbers 11, 7, 1, respectively) of the 19-numbered grid points are sequentially output according to the aforementioned method, thereby completing the output of the second column of grid data. The above process is repeated to complete the output of all the column data, and the ordering of the grid points after the final renormalization in the output file is shown in fig. 10.
Thus, it should be understood by those skilled in the art that while exemplary embodiments of the present invention have been illustrated and described in detail herein, many other variations and modifications can be made, which are consistent with the principles of the invention, from the disclosure herein, without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.
Claims (9)
1. A fast re-regularization method of discrete grid points based on a binary tree model is used for automatically generating grids in finite element numerical simulation and is characterized by comprising the following steps:
the method comprises the following steps: acquiring the number and serial number of grid points connected with each grid point;
step two: removing repeated points in the grid points connected with each grid point, and updating the number of the connected grid points;
step three: classifying the grid points;
step four: determining a root node of the binary tree model;
step five: determining a second layer of nodes of the binary tree model, and constructing left and right child nodes of the root node;
step six: adding subsequent layer nodes of the binary tree model to complete the construction of the binary tree model;
step seven: and reconstructing row and column information of discrete grid points based on a binary tree model, and outputting grid point coordinates after structured sorting according to the row and column sequence to realize the rescripurization of the discrete grid point data.
2. The binary tree model-based method for rapidly renormalizing discrete grid points according to claim 1, wherein the first step is specifically:
networking each mesh pointNumber of grid pointsn linkInitially defined as zero;
traversing all quadrilateral grid units formed by grid points, if any grid point: (X s, Y s, Z s) Present in quadrilateral cells, will be associated with grid pointsX s, Y s, Z s) Number of connected grid pointsn linkAdding 2, and will be compared with grid pointX s, Y s, Z s) The numbers of two grid points connected to each other are added to grid pointX s, Y s, Z s) In the array of connected grid point numbers.
3. The binary tree model-based method for rapidly renormalizing discrete grid points according to claim 1, wherein step two is specifically:
for each grid point: (X s, Y s, Z s) Circularly traversing the connected grid point number array, and eliminating repeated grid point numbers until the grid points (X s, Y s, Z s) All connected grid points complete the duplicate checking and updating.
4. The method according to claim 1, wherein the third step is specifically:
according to the number of connected grid pointsn linkThe values of (2) divide the grid points into 3 types of corner points, boundary points and interior points, where the number of connected grid pointsn linkThe grid points of =2 are divided into corner points,n linkthe grid points of =3 are divided into boundary points,n linkthe grid point of =4 is divided into interior points.
5. The method according to claim 1, wherein the fourth step is specifically:
determining a root node of the binary tree, namely a grid corner point, according to a mapping relation between the binary tree model and grid data; if no angular point is designated, selecting any angular point as a root node of the binary tree model; if a corner point is designated, the corner point is selected as a root node.
6. The method according to claim 1, wherein the step five is specifically:
and 2 grid points connected with the root node are boundary points, any point is selected as a left child node, and the other point is selected as a right child node.
7. The method for rapidly renormalizing discrete grid points based on a binary tree model according to claim 1, wherein step six specifically includes:
for the firstiThe nodes of the layer are connected with each other,i>successively go through the upper layer (i-each parent node of 1);
acquiring all grid points connected with each father node according to the connection relation of the grid points, removing the grid points added with the binary tree model, and leaving the grid points which are not added;
adding the non-added grid points to the binary tree model according to the number and the type of the non-added grid points;
and repeating the process until all the grid points are added into the binary tree.
8. The binary tree model-based method for fast renormalization of discrete grid points according to claim 7, wherein:
if the number of the mesh points which are not added is 2, adding the angular points or boundary points which are not added into the mesh points as left child nodes of the corresponding father nodes, and adding the other mesh points as right child nodes of the father nodes;
if the number of the mesh points which are not added is 1, the mesh points which are not added are directly added as right child nodes of the corresponding father nodes;
and if the number of the grid points which are not added is 0, adding no child node.
9. The method according to claim 1, wherein the seventh step is specifically:
in the binary tree model, all left subtrees started by a root node form a 1 st row of grid data, and all right subtrees started by each node in the 1 st row form each column of the grid data;
traversing the left and right subtrees of the binary tree model, and outputting the grid data according to the sequence of first row and second row to realize the renormalization of the discrete grid point data.
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