WO2000021003A9 - Method and system for mesh generation - Google Patents
Method and system for mesh generationInfo
- Publication number
- WO2000021003A9 WO2000021003A9 PCT/US1999/023576 US9923576W WO0021003A9 WO 2000021003 A9 WO2000021003 A9 WO 2000021003A9 US 9923576 W US9923576 W US 9923576W WO 0021003 A9 WO0021003 A9 WO 0021003A9
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- mesh
- image
- grid
- property
- correspondence table
- Prior art date
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
Definitions
- the present invention relates generally to a method for calculation and implementation of numerical simulation meshes in quasi-chaotic systems, and more particularly to mesh generation for systems containing a very large number of heterogeneous components.
- Chaotic geometry A geometry that cannot be described by simple mathematical means; Geometrical: Division of a domain into smaller "simple" sub-domains resulting in a discretization mesh or grid;
- Grid/Mesh A discrete geometric representation of a specific domain
- Image A mapping that defines what objects fill individual cells in a grid
- Quasi-chaotic geometry A geometry composed of a large number of regular and irregular sub-geometries.
- Finite element A numerical method for solving differential equations. 3. Description of the Available Art
- PDEs partial differential equations
- BVPs boundary value problems
- IBVPs initial boundary value problems
- FEA utilizes a mesh overlaid upon a representation of the subject matter
- the first step in FEA is dividing the domain of interest into many small and geometrically simple (e.g., triangles or squares, or their three- dimensional equivalents, pyramids and cubes), non-overlapping sub- domains (i.e., such that there is a one-to-one mapping of points contained in the representation of the global domain into the assembly of sub-domains). This process is referred to as "geometrical discretization” or “mesh construction.”
- each of these sub-domains a number of key points are selected. For example, if the sub-domain is contained in a three-dimensional space and has the shape of a brick, then a common choice is to select the eight corners of the brick as the key points. In finite element terminology, these key points are referred to as nodes.
- the geometry of the sub-domain is next determined by interpolation or approximation of the nodes. It is important to note that granularity begets precision —that is, the true geometry of a domain can be better approximated if the domain is divided into a larger number of smaller sub- domains, or if each sub-domain is allowed a more complex description, or if these two approaches are somehow combined.
- the values of the state variables of the process (e.g., temperature) at the nodes are interpolated as well.
- the interpolation is constrained to maintain a desired minimal degree of continuity across the elements' boundaries, in accordance with the governing PDEs.
- an infinitely dimensional problem is reduced to a finite dimensional one (i.e., a finite number of unknowns describes the entire process throughout the domain).
- the interpolation functions are known entities, it is possible to compute all the derivatives explicitly and at the element level. As a result, the problem is converted from solving PDEs into the solution of a finite system of algebraic equations.
- a repetition of this simple process can approximate a more complex global process. Again, just as with geometry, approximation may be improved if either the number of processes is increased, or the complexity of each simple process is allowed to increase, or a combination of the two.
- shape functions are typically constructed so that at every point within the domain they sum to 1 , ensuring a one-to-one mapping of points within the domain.
- GUIs graphical user interfaces
- the present invention addresses the shortcomings of the available art by providing an improved method for deriving a mesh from a picture, design, or any other image information source.
- the method comprises a) dividing the image into a grid of cells of arbitrary resolution; b) assigning to each cell in the mesh a property; c) creating a correspondence table relating a cell property found in the image to a specific information; and d) generating a heterogeneous mesh, reflecting the information in the correspondence table, the mesh being suitable for execution of a numerical procedure.
- a first advantage of the present invention is therefore the time savings allowed the user in generating a mesh suitable for a quasi-chaotic assemblage.
- Another advantage of the present invention is the enablement of rapid system modeling for quasi-chaotic assemblages.
- mapping of cell properties into modeling properties need not be one-to-one. For example, one could map a number of cell properties to the same material.
- FIG. 1 illustrates a quasi-chaotic two-dimensional mesh of a two-phase material.
- FIGs. 2 and 3 provide flowcharts illustrating the method of the present invention as it might be implemented as an executable software program.
- FIG. 1 there is illustrated a quasi-chaotic two- dimensional image of a two-phase material (a simplified asphalt image, in this case) including a few thousand objects.
- a two-phase material a simplified asphalt image, in this case
- To construct a mesh for this image using the method of the present invention requires only a few minutes of human effort, and a small amount of average-speed computer time.
- using the conventional methods found in commercial finite element packages today would require days of human time to construct a less efficient mesh.
- Applying the method of the present invention to the image of FIG. 1 involves, first, dividing the volume into a number of regions and matching adjacent regions at their shared boundary. This objective can be achieved by having the same division on the boundary, or using master-slave algorithms, or employing generalized contact algorithms, as will be understood by those skilled in the art.
- an image is generated, or an image source designated (in many instances the starting point for the mesh construction is either a picture, or the output of a CAD system).
- properties are assigned to each discrete image element, which are referred to as "pixels" in imaging terminology, and a correspondence table is created.
- a mesh is generated for each property.
- all meshes are joined using standard techniques, as will be understood by those skilled in the relevant art.
- a volume (area in two dimensions) mesh is generated only for those properties deemed above a certain threshold of interest. For properties considered to be of marginal importance, only the boundaries are modeled, preferably by boundary elements. Finally, all meshes are combined into a single global mesh using the standard techniques described above and known to those skilled in the relevant art. It should be noted that it is possible to perform this procedure in stages where after generating a number of sub-meshes, they are joined into combined sub-meshes, thus possibly reducing the amount of system resources required to carry out the mesh generation.
- the user need only specify the image source, identify the size of the image, and provide a relational table relating image properties (e.g., color) to a specified property type.
- image properties e.g., color
- the user need only repeat these steps, each time masking all but the relevant portion (i.e., only a fraction of the total mesh is generated with each pass).
- the user can be easily integrated into a single mesh using available mesh generation products.
- the contrast to the available art is clear.
- the user must delve into the details of the mesh to identify each component, which for quasi-chaotic assemblages may be in the millions. With the method and system of the present invention, this process is primarily performed by a computer through the construction of a correspondence table.
- One particular, and preferred, application of the method and system of the present invention is in the modeling of integrated circuit devices dies.
- a particular device die might include millions of individual components. Modeling such a device can be accomplished by one of two ways using the method and system of the present invention.
- an image source such as a three-dimensional ("3D") image of a chip, or a two-dimensional ("2D") image of a chip subsection if desired
- 3D three-dimensional
- 2D two-dimensional
- a relational mapping table is then created that maps each type of component (identified in the image by a color in our example) with a specified model. It should be noted that such mapping does not have to be one-to-one (for example many colors may be mapped to a single model).
- a second, more economical method may be preferred.
- a relational map is created.
- a mesh is generated for those components considered above a certain "importance" threshold.
- boundary elements are generated on the surface defining the less important components. These surfaces coincide with the boundaries of the important objects or the boundary of the chip itself.
- the chip may be subdivided into non- overlapping sub-components, and either of the two described processes would be repeated for each of the sub-components.
- the analysis phase could be carried out using sub-structuring techniques. This additional partitioning step reduces the amount of computer memory needed for building a complete mesh, thereby potentially reducing costs.
- the approach is somewhat more elaborate and requires more intensive computing resources.
- a uniform mesh is generated for the chip, where any subdivision is only geometrical, and not by component type.
- a mask is then used to "tunnel" the chip (that is, to define a set of elements that are eliminated). Relational maps are then used for doping and calculating metal deposits to add to materials, and to identify properties. Tunneling and mapping is repeated for every mask layer, and boundary elements are placed on the boundary of the "voids" left after tunneling.
- the included software code illustrates a complete system and method for generating a 2D mesh of 4-node quadrilateral elements.
- the generated meshes have arbitrary detail complexity, useful for modeling quasi-chaotic systems.
- the code returns a value of 1 . If a NULL pointer to the image file is received, the provided code returns a value of -1 . If the function failed to get requested memory from the system, the provided code returns a value of -2. In either case where the function failed to generate the mesh, the memory allocated will be released.
- Element and node numbers are not stored explicitly. Rather, they are obtained from the location of the node/element in the respective coor/elCont arrays. Therefore, to comply with "C" programming conventions, the element/node numbering starts with zero, and the node connectivity entries in elCont refer to the row number in the coor array.
- association vector "mat” which relates values in the image file to actual material models.
- the provided code does not check for errors in mapping, which may lead to an erroneous mesh generation and even to segmentation violation. Error checking could be easily added by one skilled in the relevant art. An error should occur only if the image file contains values larger than the dimension of the mat vector.
- a value of 0 entered in the mat vector indicates to the provided code that when a number corresponding to this entry on the image file is encountered, no element is generated.
- the provided code generates meshes bounded by a rectangular in an active coordinate system.
- a generalization of the exemplary method and system provided into nonrectangular meshes is straightforward, and can be obtained by simply replacing the linear interpolation used in the provided code in generation of the nodal coordinates, as will be understood by one skilled in the relevant art.
- the provided code is built around the assumption that the image file is first ordered by x, then by y (i.e., the image is stored row-wise).
- a mesh for the numerical procedure e.g., using a finite element method - the geometry of each element being fully defined by the geometry of each cell in the grid, and the material and type of element being defined by the correspondence table and cell property).
- elType an integer indicating the type of element (e.g., 1 isoparametric, 2 b-bar) fimage pointer to a file containing the image (an array of integers) mat array containing points correlating number in the image file with specific material models.
- mat[i] 0 indicates that no element should be generated.
- OUTPUT coor an array of nodal coordinates coor[0] node number coor[1 ] x-coordinate coor[2] y-coordinate elCont element connectivity array (nodes are numbered counter-clockwise) elCont[0] element material type elCont ⁇ number of node # 1 elCont[2] number of node # 2 elCont[3] number of node # 3 elCont[4] number of node # 5 numElmt number of elements generated numNode number of nodes generated
- int mesh2DQ4 (FILE *fimage, double * * *coor, double xRange[2][2], int *mat, int * * *elCont, int *numNode, int *numElmt, int xDiv, int yDiv) ⁇ double dx, dy, x, y; double * *ICoor; int I, j, k, m, n; int prop; int xDiv1 , yDiv1 ; int *INode, * *elC; int elNode[5];
- the inventive process begins by obtaining an image of the desired object, as illustrated in FIG. 2.
- the image is then discretized at a desired resolution, and each cell is assigned a property (e.g., color).
- Each property is assigned a priority, which can be as simple as "important" or "unimportant.”
- a table is then generated that relates the image property to mesh attributes such as element type, material model, and material constants.
- each property used in the image is visited. For each property, all the image cells are visited and each is meshed according to the priority assigned to the property. If the property is above a specified threshold, then each cell is represented by a volume or area element in accordance with the specifications in the correspondence table. If the property has a priority less than the threshold, only boundary elements are generated along the boundary of the sub-domain occupied by the current property in the discretized image. (The flowchart of FIG. 3 describes the process of identifying the boundary, as described below).
- the mesh associated with the current property After the mesh associated with the current property is generated, it is assembled into the global mesh, and the next property is addressed. When all properties have been addressed, the mesh is completed, and the procedure ends.
- the cells in the image are ordered in a vector, and they have been sorted by property.
- all cells in the image whose property is the current property are initialized by marking each edge of each cell with a zero.
- all cells of current property are traversed, and 1 is added to each of the edges.
- the system returns to the first cell (of the current property).
- a new traversal of the cells then begins, changing the edge values for those edges whose value is greater than 1 to zero.
- all boundaries of the sub-domain associated with the current property are composed of all cell edges that are marked with 1 .
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- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
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Abstract
Description
Claims
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AU13123/00A AU1312300A (en) | 1998-10-08 | 1999-10-08 | Method and system for mesh generation |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10363498P | 1998-10-08 | 1998-10-08 | |
US60/103,634 | 1998-10-08 |
Publications (2)
Publication Number | Publication Date |
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WO2000021003A1 WO2000021003A1 (en) | 2000-04-13 |
WO2000021003A9 true WO2000021003A9 (en) | 2000-09-08 |
Family
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Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
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PCT/US1999/023576 WO2000021003A1 (en) | 1998-10-08 | 1999-10-08 | Method and system for mesh generation |
Country Status (2)
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AU (1) | AU1312300A (en) |
WO (1) | WO2000021003A1 (en) |
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US11087038B2 (en) * | 2019-05-02 | 2021-08-10 | Suntracker Technologies Ltd. | Importance-directed geometric simplification system and method |
CN117574719A (en) * | 2023-11-21 | 2024-02-20 | 中国航空发动机研究院 | Periodic grid generation method and device, electronic equipment and storage medium |
Family Cites Families (2)
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US5751852A (en) * | 1996-04-29 | 1998-05-12 | Xerox Corporation | Image structure map data structure for spatially indexing an imgage |
US5877777A (en) * | 1997-04-07 | 1999-03-02 | Colwell; Tyler G. | Fluid dynamics animation system and method |
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1999
- 1999-10-08 WO PCT/US1999/023576 patent/WO2000021003A1/en active Application Filing
- 1999-10-08 AU AU13123/00A patent/AU1312300A/en not_active Abandoned
Also Published As
Publication number | Publication date |
---|---|
WO2000021003A1 (en) | 2000-04-13 |
AU1312300A (en) | 2000-04-26 |
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