JP5046222B2 - Finite element analysis apparatus, finite element analysis method, and computer program - Google Patents

Description

  The present invention maintains a high convergence of the analytical solution while reducing the load of grid generation by the user at the time of finite element analysis in which the grid constituting the finite element is analyzed in units of side elements using the multigrid method. The present invention relates to a finite element analysis apparatus, a finite element analysis method, and a computer program.

  In recent years, with the rapid development of computer technology, it has become practically possible to perform response analysis of nonlinear problems, transient problems, etc. that handle more detailed phenomena by computer simulation. In such computer simulation, various physical phenomena can be handled and the range of application is wide, so the Finite Element Method (FEM) is often used as an analysis method, and the analysis accuracy is mesh. It is thought to depend on the density of the division.

  When mesh division is made finer to increase the accuracy of computer simulation, for example, when solving using an iterative method such as the ICCG (Incomplete Cholesky Conjugate Gradient Method) method, the computation time increases exponentially and the computation processing time is shortened. It becomes difficult. In order to solve such a problem, for example, Patent Document 1 uses a multigrid method that is considered to be able to solve faster than the ICCG method.

In the multigrid method, an approximate solution is obtained by using an iterative solution method such as a Gauss-Seidel method for simultaneous equations for the finest mesh among a plurality of meshes of different coarse and dense. For example, the Gauss-Seidel method has the property that the spatial high-frequency component of the error converges quickly at the initial stage of the iteration, while the convergence of the low-frequency component is very slow. Therefore, the error included in the approximate solution obtained by truncating several iterations is only the low frequency component. Next, the residual for the approximate solution is projected onto a coarse mesh. Since an error that appears as a low frequency when viewed from a fine mesh also appears as a high frequency when viewed from a coarse mesh, the remaining error can be quickly removed by obtaining an approximate solution in the same manner for the coarse mesh.
JP-A-5-324696 Kanahori and 2 others, “Application of Algebraic Multigrid Method to Electromagnetic Field Finite Element Analysis”, 2000 China Federation of Electrical and Information Related Associations, 457 (2000) Kameari, “Application of Geometric Multigrid Method to Numerical Analysis of Electromagnetic Fields”, Joint Study Group for Static and Rotating Machine, SA-01-9, RM-01-79 (2001)

  The multigrid method is roughly classified into an algebraic multigrid method and a geometric multigrid method. In the algebraic multigrid method, since the coefficient matrix for each hierarchy required in the multigrid method is created inside the solver, the user does not need to consider the mesh node distribution and has a low burden. However, it has a demerit that a stable convergence solution cannot always be obtained (see Non-Patent Document 1).

  On the other hand, in the geometric multigrid method, a mesh for analysis is prepared in advance for each layer, and a coefficient matrix for each grid is created based on the prepared mesh information. Therefore, since the shape function of a finite element is used, the error vector can be continuously approximated by a mesh between layers, and a convergent solution can be obtained more stably than the algebraic multigrid method in many cases. . However, the convergence of the solution depends on the mesh prepared in each layer, and has a demerit that the burden on the user is large (see Non-Patent Document 2).

  In thermal analysis and structural analysis that can be discretized with nodal elements, there are cases where a convergent solution can be obtained when using an algebraic multigrid method or a geometric multigrid method. In the electromagnetic field analysis that is discretized, there is a problem that it is difficult to stably obtain a convergent solution regardless of which method is used.

  The present invention has been made in view of such circumstances, and a finite element analysis apparatus and finite element that realize grid generation capable of stably obtaining a convergent solution even in electromagnetic field analysis discretized by side elements An object is to provide an analysis method and a computer program.

In order to achieve the above object, a finite element analysis apparatus according to a first aspect of the present invention is a finite element analysis apparatus that performs a finite element analysis for analyzing a grid constituting a finite element in units of side elements using a multigrid method. A geometric model receiving means for receiving a geometric model to be analyzed, a fine grid generating means for generating a node of a grid of the highest hierarchy of the received geometric model based on a predetermined rule, and a geometry relating to an edge connecting the node and the node Importance calculation means for calculating the importance related to the connection relationship between one node and other nodes based on scientific information, and the importance set for the node itself, and the connection relationship between the calculated one node and other nodes If the importance related to is greater than the value calculated from the importance of one node itself and the importance of the other node itself, the other node is assigned a lower rank relative to the one node. The node selection means for selecting as a node at the time of grid generation, the first course grid generation means for generating a lower hierarchy grid using the selected node, and the importance of the nodes of the generated lower hierarchy grid, Importance recalculation means that recalculates based on the geometric information, and when the recalculated importance is greater than the value recalculated from the importance of one node itself and the importance of another node itself A node reselecting means for reselecting the other node as a node at the time of generating a grid of a further lower layer for the one node, and a second node for generating a grid of a further lower layer using the reselected node A course grid generation means and a determination means for determining whether or not the generation of the grid has been completed, and if the determination means determines that the generation of the grid has not been completed, The importance of the nodes of the layer grid is recalculated based on the geometric information, and if the determination means determines that the generation of the grid is completed, the operator between the grid layers is estimated. Thus, the solution is calculated.

  Further, in the finite element analysis apparatus according to the second invention, in the first invention, the importance calculation means and the importance recalculation means are such that the nodes where the errors projected onto the grid in the lower hierarchy are concentrated become larger. The importance is calculated on the basis of geometric information on the nodes and the sides connecting the nodes.

Further, in the finite element analysis apparatus according to the third invention, in the first or second invention, the node selection means and the node reselection means have an importance degree related to the connection relation between the calculated one node and another node, If it is greater than the value calculated from the importance of one node itself and the importance of the other node itself and is not adjacent to the already selected node, the other node It is characterized in that it is selected as a node at the time of grid generation .

  In the finite element analysis apparatus according to a fourth aspect of the present invention, in any one of the first to third aspects of the invention, the determination means includes means for counting the number of hierarchies that generated the grid, and the number of hierarchies counted is predetermined. Means for determining whether or not the number has been exceeded, and when the means determines that the predetermined number has been exceeded, it is determined that generation of the grid has been completed.

  In the finite element analysis apparatus according to a fifth aspect of the present invention, in any one of the first to third aspects, the determination means includes means for counting the total number of generated grids, and the total number of counted grids is predetermined. Means for determining whether or not the number has been exceeded, and when the means determines that the predetermined number has been exceeded, it is determined that generation of the grid has been completed.

A finite element analysis method according to a sixth aspect of the invention is a finite element used for finite element analysis by a finite element analysis apparatus including a processor that analyzes a grid constituting a finite element in units of side elements using a multigrid method. In the analysis method, the finite element analysis device generates, based on a predetermined rule, a shape model reception step of receiving a shape model to be analyzed by the processor based on a predetermined rule. Step for generating a fine grid, importance level calculating step for calculating the importance level related to the connection relationship between one node and another node, and the importance level set for the node itself, based on geometric information about the nodes and the edges connecting the nodes The importance related to the connection relation between one node and other nodes calculated is the importance of one node itself and the importance of other nodes themselves. A node selection step of selecting another node as a node when generating a lower layer grid for the one node, and generating a lower layer grid using the selected node. A first course grid generation step, an importance recalculation step for recalculating the importance of the nodes of the generated lower hierarchy grid based on the geometric information, and the recalculated importance is determined by the one node itself A node reselecting step of reselecting the other node as a node when generating a grid of a further lower hierarchy with respect to the one node when the importance is greater than a value recalculated from the importance of the other node itself , A second course grid generation step for generating a grid of a further lower layer using the reselected nodes; a judgment for determining whether or not the generation of the grid is completed; If it is determined that the generation of the step and the grid is not completed, the importance of the nodes of the generated lower-level grid is recalculated based on the geometric information, and it is determined that the generation of the grid is completed. If so, the step of calculating the solution by estimating the operator between the grid layers is performed.

In the finite element analysis method according to a seventh aspect of the present invention, in the sixth aspect of the invention, the importance level calculation step and the importance level recalculation step are performed by the processor that projects the finite element analysis device onto a lower-level grid. The importance is calculated on the basis of the geometric information about the nodes and the edges connecting the nodes so that the errors are concentrated at the nodes where the errors are concentrated.

The finite element analysis method according to an eighth aspect of the present invention is the sixth or seventh aspect, wherein the node selection step and the node reselection step are performed by the finite element analysis apparatus using one processor and the other calculated by the processor. If the importance related to the connection relationship of one node is greater than the value calculated from the importance of one node itself and the importance of another node, and is not adjacent to the already selected node, A node is selected as a node at the time of grid generation of a lower hierarchy with respect to the one node .

The finite element analysis method according to a ninth aspect is the method according to any one of the sixth to eighth aspects, wherein the determination step counts the number of layers in which the finite element analysis device has generated a grid by the processor. steps, and the step number counted hierarchy determines whether exceeds a predetermined number, Yes so as to run, that determine the formation of the grid is completed when it is determined that the ratio exceeds a predetermined number Features.

Furthermore, finite element analysis method according to a tenth invention, in any one of the sixth to eighth aspects, wherein the determination step, the finite element analysis device counts the total number of by the processor, to generate the grid step, wherein the total number of counted grid are so as to perform the step of determining the formation of the grid is completed when it is determined that the ratio exceeds the steps and a predetermined number to determine whether more than a predetermined number And

A computer program according to an eleventh aspect of the invention is a computer program that can be executed by a computer that executes a finite element analysis that analyzes a grid constituting a finite element in units of side elements using a multigrid method. , A shape model receiving step for receiving a shape model to be analyzed, a fine grid generating step for generating a node of a grid in the highest hierarchy of the received shape model based on a predetermined rule, a side connecting the node and the node Importance calculation step to calculate the importance related to the connection relationship between one node and other nodes based on geometric information about the node, and the importance set for the node itself, connection of the calculated one node and other nodes The importance of the relationship is calculated from the importance of one node itself and the importance of another node itself A node selection step for selecting the other node as a node when generating a lower layer grid for the one node, and a first course grid for generating a lower layer grid using the selected node. A generation step, an importance recalculation step for recalculating the importance of the nodes of the generated lower hierarchy grid based on the geometric information, and the recalculated importance is the importance of one node itself and other importance Node reselection step that reselects the other node as a node at the time of grid generation of a further lower layer for the one node when the value is larger than the value recalculated from the importance of the node itself , the reselected node A second course grid generation step for generating a grid of a further lower layer using the step, a determination step for determining whether the generation of the grid is completed, and the step If the number of layers in the cross-sectional step is determined not to exceed a predetermined number, wherein the function as the step of the returning to the importance recalculation step.

In the computer program according to a twelfth aspect of the present invention, in the eleventh aspect, the importance calculation step and the importance recalculation step increase the computer at a node where errors projected on a grid in a lower hierarchy are concentrated. As described above, the method is characterized in that it functions as a step of calculating the importance based on the geometric information regarding the nodes and the sides connecting the nodes.

The computer program according to a thirteenth aspect of the invention is the computer program according to the eleventh or twelfth aspect, wherein the node selection step and the node reselection step are performed according to the importance of the computer relating to the connection relationship between the calculated one node and the other nodes. Is greater than the value calculated from the importance of one node and the importance of the other node itself, and if it is not adjacent to the already selected node, the other node is subordinate to the one node. It is made to function as a step of selecting as a node when generating a grid of a hierarchy .

The computer program according to a fourteenth aspect of the present invention is the computer program according to any one of the eleventh to thirteenth aspects, wherein the determining step includes the step of counting the number of hierarchies that generated the grid, It is configured to function as a step for determining whether or not a predetermined number has been exceeded, and a step for determining that generation of a grid is completed when it is determined that the predetermined number has been exceeded.

The computer program according to a fifteenth aspect of the present invention is the computer program according to any one of the eleventh to thirteenth aspects, wherein the determining step includes the step of counting the total number of grids generated by the computer, It is characterized by functioning as a step of determining whether or not a predetermined number has been exceeded, and a step of determining that generation of a grid has been completed when it is determined that the predetermined number has been exceeded.

  In the first invention, the sixth invention, and the eleventh invention, when performing the finite element analysis for analyzing the grid constituting the finite element by the side element unit using the multi-grid method, the top layer of the accepted shape model The nodes of the grid are generated based on a predetermined rule, and the importance of the nodes is calculated based on the geometric information about the nodes and the sides connecting the nodes. A node having a calculated importance greater than a predetermined value is selected as a node when the lower layer grid is generated, and a lower layer grid is generated using the selected node. Recalculate the importance of the nodes of the generated lower layer grid based on geometric information, and reselect the nodes whose recalculated importance is greater than the specified value as the nodes when generating the grid of the further lower layer. Then, use the reselected nodes to generate a further lower level grid. Determine whether the grid generation is complete, and if it is determined that the grid generation is not complete, recalculate the importance of the nodes of the generated lower layer grid based on the geometric information. When it is determined that the generation of the grid has been completed, an operator between the grid layers is estimated to calculate a solution. As a result, when generating a course grid in a lower hierarchy, select nodes that are judged to be likely to concentrate errors based on geometric information used in the geometric multigrid method, that is, nodes having high importance, and select them. It is possible to generate a course grid that connects the nodes and has a different form from the fine grid. Therefore, the spatial high-frequency component of the error can be quickly converged, and the solution can be solved by estimating the operator between hierarchies in the same way as in the geometric multigrid method, while leaving the simplicity of grid generation in the algebraic multigrid method. It becomes possible to maintain stable convergence.

  In the second invention, the seventh invention, and the twelfth invention, the importance is calculated based on the geometric information about the nodes and the edges connecting the nodes so that the errors projected onto the lower-level grids become larger as the nodes are concentrated. To do. This makes it possible to quickly converge the spatial high-frequency component of the error by selecting nodes that have strong connections between nodes and are projected with concentrated errors, making it easy to generate grids in the algebraic multigrid method. It is possible to maintain stable convergence of the solution in the geometric multigrid method while leaving

  In the third invention, the eighth invention, and the thirteenth invention, each node is adjacent to the selected node, and the other node forming the side with the node as one end is excluded, and the selected node is connected to each other. A generated grid. This makes it possible to select coarsely projected nodes with strong connections between nodes and generate coarse coarse grids, and to quickly converge spatial high-frequency components of errors. It becomes.

  In the fourth invention, the ninth invention, and the fourteenth invention, when the number of hierarchies that generated the grid is counted, it is determined whether or not the counted number of hierarchies exceeds a predetermined number, and when it is determined that the predetermined number is exceeded. It is determined that grid generation is complete. In the fifth, tenth, and fifteenth inventions, the total number of generated grids is counted, whether or not the total number of grids counted exceeds a predetermined number, and is determined to have exceeded the predetermined number. In this case, it is determined that the generation of the grid is completed. As a result, the course grid generation process can be appropriately terminated, and it is possible to execute a finite element analysis that performs analysis in units of side elements using the multigrid method while maintaining solution convergence.

  According to the first invention, the sixth invention, and the eleventh invention, it is determined that errors are likely to be concentrated based on geometric information used in the geometric multigrid method when generating a course grid in a lower hierarchy. It is possible to select a node, that is, a node having high importance, and to generate a course grid having a form different from that of the fine grid in which the selected nodes are connected. Therefore, the spatial high-frequency component of the error can be quickly converged, and the solution can be solved by estimating the operator between hierarchies in the same way as in the geometric multigrid method, while leaving the simplicity of grid generation in the algebraic multigrid method. It becomes possible to maintain stable convergence.

  According to the second invention, the seventh invention, and the twelfth invention, it is possible to quickly converge the spatial high-frequency component of the error by selecting a node that is strongly connected between the nodes and in which errors are concentrated and projected. Therefore, it is possible to maintain the stable convergence of the solution in the geometric multigrid method while maintaining the simplicity of grid generation in the algebraic multigrid method.

  According to the third invention, the eighth invention, and the thirteenth invention, it is possible to generate a coarse grid with coarse meshes by selecting nodes that are strongly linked and have errors concentrated and projected. It is possible to quickly converge the spatial high-frequency component.

  According to the fourth invention, the fifth invention, the ninth invention, the tenth invention, the fourteenth invention, and the fifteenth invention, the course grid generation process can be properly terminated while maintaining the convergence of the solution. Then, it becomes possible to execute finite element analysis in which analysis is performed in units of side elements using the multigrid method.

  Hereinafter, the present invention will be specifically described with reference to the drawings showing embodiments thereof. FIG. 1 is a block diagram showing a configuration of a finite element analysis apparatus 1 to which a grid generation method according to an embodiment of the present invention is applied. In FIG. 1, a finite element analysis apparatus 1 includes at least a CPU (Central Processing Unit) 11, a storage unit 12, a ROM 13, a RAM 14, a communication unit 15 connected to a communication line, an input unit 16 such as a mouse and a keyboard, a display, and the like. It comprises output means 17 and auxiliary storage means 18.

  The CPU 11 is connected to the above-described hardware units of the finite element analysis apparatus 1 via the internal bus 19, and controls the above-described hardware units, and a control program or auxiliary storage unit 18 stored in the ROM 13. Various software functions are executed according to a control program introduced into the storage means 12 using a (portable) recording medium 2 such as a CD-ROM or DVD. The storage unit 12 is a fixed storage medium such as a hard disk, and stores data necessary for processing in addition to the control program described above.

  The RAM 14 is composed of SRAM, flash memory, etc., and stores temporary data generated when software is executed. The communication unit 15 is connected to the internal bus 19 and transmits / receives data acquisition from the outside, operation control data of the external device, and the like.

  The input means 16 is an input medium such as a keyboard or a mouse provided with character keys, numeric keys, various function keys and the like necessary for operating the finite element analysis apparatus 1. The output means 17 is a display device such as a liquid crystal display device or a CRT display, displays the operation state of the finite element analysis device 1, displays a screen for prompting the user to input an operation, and graphically displays the analysis result. For example, image data for display is displayed. It should be noted that the output means 17 can be substituted for some or all of the various function keys of the input means 16 by using the output means 17 as a touch panel system.

  The finite element analysis apparatus 1 may be in a form in which a computer program according to the present invention is downloaded from an external computer connected to the communication means 15 and processing is executed by the CPU 11.

  Hereinafter, the procedure of electromagnetic field analysis processing using the finite element analysis apparatus 1 having the above-described configuration will be described. In the present embodiment, a method used when finding a solution using a multigrid method when analyzing a grid constituting a finite element, such as electromagnetic field analysis, in units of side elements will be described.

  FIG. 2 is a flowchart showing a processing procedure of the CPU 11 of the finite element analysis apparatus 1 according to the embodiment of the present invention. The CPU 11 of the finite element analysis apparatus 1 receives a two-dimensional shape model or a three-dimensional shape model to be subjected to electromagnetic field analysis from the input means 16 operated by an operator or from an external computer via the communication means 15 ( Step S201). The CPU 11 generates a relatively fine mesh grid (hereinafter referred to as a fine grid) that is discretized by the side elements for the received shape model (step S202). The fine grid is generated algebraically by a method similar to the conventional algebraic multigrid method.

  CPU11 calculates | requires a solution using a finite element method with respect to the produced | generated fine grid. The matrix equation to be solved by the CPU 11 is as shown in (Equation 1). In (Equation 1), K1 is a system matrix in a fine grid discretized by edge elements, A is a solution vector in a fine grid discretized by edge elements, and f is discretized by edge elements. The external force vectors in the fine grid are shown respectively.

  The CPU 11 determines the connection strength with respect to the importance of the node, for example, a predetermined node i (i is an arbitrary integer), created based on the geometric information about the node of the fine grid configured in the uppermost layer. The auxiliary matrix K2 having the connection information shown is received (step S203), and a node having an importance greater than a predetermined value is selected as a node for generating a coarse mesh (hereinafter referred to as a course grid) in a lower layer (step S204).

  The CPU 11 generates a course grid by connecting the selected nodes with sides (step S205). The CPU 11 determines whether or not the generation of the grid has been completed (step S206). If the CPU 11 determines that the generation of the grid has not been completed (step S206: NO), the CPU 11 moves the process to step S203. The information about the importance of the node is received again for the generated course grid, and the above-described processing is repeated.

  That is, it has information on the importance of the node created based on the geometric information about the node of the generated course grid, for example, connection information indicating the connection strength with a predetermined node i (i is an arbitrary integer). The auxiliary matrix K2 is received again, and a node having an importance greater than a predetermined value is reselected as a node for generating a coarse grid having a coarser mesh. The CPU 11 generates a new course grid using the selected node, and determines whether the generation of the grid is completed (step S206).

  When the CPU 11 determines that the generation of the grid has been completed (step S206: YES), the CPU 11 ends the course grid generation process and generates the operator P between the generated grid layers (step S207). In the algebraic multigrid method, the course grid is generated by specifying the operator P, whereas in the finite element analysis apparatus according to the present embodiment, the course grid of each layer is first, as in the geometric multigrid method. And the convergence of the solution is ensured by generating an operator P between the layers. The CPU 11 calculates a solution vector A by solving (Equation 1) using the generated operator P (step S208).

  The method for determining whether or not the generation of the grid is completed is not particularly limited. For example, the number of hierarchies for course grid generation is set in advance, and the number of hierarchies is incremented by 1 each time a course grid is generated. If the number of hierarchies exceeds the preset number of hierarchies, it may be determined that the grid generation is completed. Of course, the number of hierarchies set in advance may be sequentially decremented by 1 to determine whether the number of hierarchies has become 0 (zero).

  In addition, the total number of generated grids is set in advance, and the grid number is added each time a course grid is generated. If the total number of grids exceeds the preset limit, the grid It may be determined that the generation is completed. Of course, the number of newly generated grids may be sequentially subtracted from the preset limit number to determine whether the limit number has become 0 (zero).

Specifically, the node selection process by the CPU 11 is as follows. A set Ni of nodes adjacent to the node i is defined as shown in (Expression 2). In (Expression 2), ω _h represents a set of all nodes in the fine grid, and k _ij represents a coefficient of the auxiliary matrix K2.

In (Expression 2), the node j adjacent to the node i means that the node k is connected when the coefficient k _ij of the auxiliary matrix K2 is not 0. The CPU 11 uses, at the time of course grid generation, a node whose connection relationship indicating the importance of the node is equal to or greater than a predetermined value, that is, a node whose coefficient k _ij of the auxiliary matrix K2 is equal to or greater than the multiplication average value multiplied by the coefficient value θ. Select as a node. A set Si of nodes to be selected is defined as (Equation 3).

  The coefficient value θ is a coefficient indicating the spread of the diagonal term of the square matrix. When θ is 0 (zero), the diagonal term itself, that is, all other nodes adjacent to the node i are selected. It means that. The selected node i is a node on which errors are concentrated when projected onto a lower-layer grid.

  The operator P is generated by the following procedure. In the present embodiment, the unknowns are assigned to the sides, and the operator P becomes a matrix indicating the relationship between the fine grid sides and the unknown numbers assigned to the course grid sides. When the number of sides of the fine grid is I and the number of sides of the coarse grid is L, the size of the operator P is I × L.

FIG. 3 is an exemplary diagram when the sides of the course grid are generated across a plurality of elements of the fine grid. For example, when the side E of the coarse grid crosses three elements of the fine grid, the side E is divided into three line segments E1, E2, and E3 by the element side of the fine grid. When generating operator P _E related sides E, generates operator P _E1, P _E2, P _E3 for each line segment E1, E2, E3, the operator P _E obtained by summing these operators _{(= P E1 + P E2 +} P E3) Will be calculated.

Specifically, the side vectors for the line segments E1, E2, and E3 are defined as l ₁ , l ₂ , and l _3, and the vector shape function of the side that forms the fine grid including the line segments E1, E2, and E3 is represented by N _1. , N ₂ and N ₃ . The operator P _Ek related to the line segment Ek (k = 1, 2, 3) is calculated as shown in ( _Expression 4).

In (Expression 4), the symbol “·” indicates the inner product of the vectors, and ND is the number of sides of the fine grid including the line segment Ek. Moreover, e _m (m is a natural number) indicates the edge included in each of the grid. That is, the correspondence between each side of the grid and the side crossing the grid is calculated. The operator P _Ek for each calculated line by linear addition (5), it is possible to generate an operator P _E related edges E. In yet (number 5), Ne represents the number of division by the elements side of the fine grid edge E.

  Therefore, compared to the case of generating a grid using a purely algebraic multigrid method, it is possible to prepare a grid with high solution convergence as in the case of using the geometric multigrid method, and use an operator for the grid. By applying the multigrid method, the solution can be converged stably.

  FIG. 4 is a diagram schematically illustrating the course grid generation process described above. As shown in FIG. 4A, in a fine grid having a plurality of sets I1, I2,..., Nodes Q1, which are adjacent to each other by side elements of the fine grid, centered on a node P1 representing the set I1, Q2, ..., Q6 exist.

  When selecting the nodes used in the course grid, as shown in FIG. 4B, the nodes Q1, Q2,..., Q6 that are adjacent to the node P1 by the side elements are excluded from the nodes constituting the course grid. To do. Then, the geometric information included in the auxiliary matrix, that is, a node at which it is determined that errors are likely to concentrate is searched. When the node P2 is selected as shown in FIG. 4C, the same process as described above is repeated with the node P2 as the center, for example, the nodes forming the course grid as shown in FIG. 4D. P1, P2, P3,... Are selected.

  Thus, at the time of generating the course grid, the other node that is adjacent to the selected node and forms a side with the node as one end is excluded from the nodes used in the course grid. By doing this, the connection between the nodes is strong, and it is possible to select a node that is projected with concentrated errors, and to generate a coarse grid of the mesh, and to quickly converge the spatial high-frequency component of the error This makes it possible to ensure the convergence of a stable solution.

  As described above, according to the present embodiment, when generating a course grid in a lower hierarchy, nodes that are determined to have errors easily concentrated based on geometric information used in the geometric multigrid method, that is, important It is possible to select a node having a high degree and generate a course grid having a different form from that of the fine grid in which the selected nodes are connected. Therefore, the spatial high-frequency component of the error can be quickly converged, and it is possible to maintain the stable convergence of the solution in the geometric multigrid method while retaining the simplicity of grid generation in the algebraic multigrid method. Become.

It is a block diagram which shows the structure of the finite element analysis apparatus to which the grid generation method which concerns on embodiment of this invention is applied. It is a flowchart which shows the process sequence of CPU of the finite element analysis apparatus which concerns on embodiment of this invention. It is an illustration figure in case the side of a course grid is generated ranging over a plurality of elements of a fine grid. It is a figure which shows a course grid production | generation process typically.

Explanation of symbols

1 Finite Element Analyzer 11 CPU
12 storage means 13 ROM
14 RAM
15 Communication means 16 Input means 17 Output means 18 Auxiliary storage means

Claims (15)

A finite element analysis device that performs a finite element analysis using a multigrid method to analyze a grid constituting a finite element in units of side elements,
A shape model receiving means for receiving a shape model to be analyzed;
Fine grid generation means for generating the nodes of the grid of the highest hierarchy of the received shape model based on a predetermined rule;
An importance calculation means for calculating the importance related to the connection relationship between one node and another node based on geometric information about the nodes and the edges connecting the nodes, and the importance set for the node itself;
If the importance related to the connection relationship between the calculated one node and the other nodes is greater than the value calculated from the importance of the one node itself and the importance of the other nodes, the other node A node selecting means for selecting as a node when generating a grid of a lower hierarchy for one node;
First course grid generation means for generating a lower hierarchy grid using the selected nodes;
Importance recalculation means for recalculating the importance of the nodes of the generated lower hierarchy grid based on the geometric information;
If the recalculated importance is greater than the importance of one node itself and the importance of the other nodes themselves, the other nodes are generated as grids of further lower layers for the one node. A node reselection means to reselect as a node of time,
Second course grid generation means for generating a further lower-level grid using the reselected nodes;
A determination means for determining whether or not the generation of the grid is completed,
When it is determined that the generation of the grid is not completed by the determination means, the importance of the nodes of the generated lower layer grid is recalculated based on the geometric information,
A finite element analysis apparatus characterized in that, when it is determined by the determination means that generation of a grid is completed, an operator between grid hierarchies is estimated to calculate a solution.   The importance calculating means and the importance recalculating means calculate importance based on geometric information about nodes and edges connecting the nodes so that the nodes where errors projected on the lower layer grid are concentrated become larger. The finite element analysis apparatus according to claim 1, wherein the finite element analysis apparatus is configured as described above. The node selection means and the node reselection means are:
The importance related to the connection relationship between the calculated one node and other nodes is greater than the value calculated from the importance of one node itself and the importance of other nodes, and is adjacent to an already selected node 3. The finite element analysis apparatus according to claim 1 , wherein, if not, the other node is selected as a node at the time of grid generation of a lower hierarchy with respect to the one node . 4. The determination means includes
Means for counting the number of layers that have generated the grid;
Means for determining whether or not the counted number of hierarchies exceeds a predetermined number,
The finite element analysis apparatus according to any one of claims 1 to 3, wherein when the means determines that the predetermined number has been exceeded, it is determined that the generation of the grid has been completed. The determination means includes
Means for counting the total number of generated grids;
Means for determining whether the total number of grids counted exceeds a predetermined number,
The finite element analysis apparatus according to any one of claims 1 to 3, wherein when the means determines that the predetermined number has been exceeded, it is determined that the generation of the grid has been completed. A finite element analysis method used for finite element analysis by a finite element analysis apparatus including a processor that analyzes a grid constituting a finite element in units of side elements using a multigrid method,
The finite element analysis device uses the processor to
A shape model reception step for receiving a shape model to be analyzed;
A fine grid generation step for generating the nodes of the grid of the highest hierarchy of the received geometric model based on a predetermined rule;
An importance calculation step for calculating the importance related to the connection relationship between one node and another node based on the geometric information about the nodes and the edges connecting the nodes, and the importance set for the node itself;
If the importance related to the connection relationship between the calculated one node and the other nodes is greater than the value calculated from the importance of the one node itself and the importance of the other nodes, the other node A node selection step for selecting a node for generating a lower-level grid for one node,
A first course grid generation step of generating a lower hierarchy grid using the selected nodes;
Importance recalculation step of recalculating the importance of the nodes of the generated lower hierarchy grid based on the geometric information,
If the recalculated importance is greater than the importance of one node itself and the importance of the other nodes themselves, the other nodes are generated as grids of further lower layers for the one node. Node reselection step to reselect as the node of time,
A second course grid generation step of generating a further lower level grid using the reselected nodes;
A determination step for determining whether or not the generation of the grid is completed; and when it is determined that the generation of the grid is not completed, the importance of the nodes of the generated lower layer grid is determined based on the geometric information. And calculating the solution by estimating the operator between the grid layers when it is determined that the generation of the grid is completed. In the importance calculation step and the importance recalculation step, the finite element analysis device uses the processor to
7. The finite element analysis according to claim 6, wherein the importance is calculated based on geometric information relating to the nodes and the edges connecting the nodes so that the nodes where the errors projected onto the lower layer grid are concentrated become larger. Method. In the node selection step and the node reselection step, the finite element analysis apparatus uses the processor to
The importance related to the connection relationship between the calculated one node and other nodes is greater than the value calculated from the importance of one node itself and the importance of other nodes, and is adjacent to an already selected node 8. The finite element analysis method according to claim 6 or 7 , wherein, if not, the other node is selected as a node at the time of grid generation of a lower hierarchy with respect to the one node . In the determination step, the finite element analysis device is configured to be executed by the processor.
Step step for counting the number of hierarchical generated grid, and the number counted hierarchy determines whether exceeds a predetermined number
And run
The finite element analysis method according to any one of claims 6 to 8, wherein it is determined that the generation of the grid is completed when it is determined that the predetermined number is exceeded. In the determination step, the finite element analysis device is configured to be executed by the processor.
The step of counting the total number of generated grid,
The step of the total number of counted grid determines that generation of the grid is completed when it is determined that exceeds the steps, and the predetermined number to determine whether more than a predetermined number
The finite element analysis method according to claim 6, wherein the finite element analysis method is executed . A computer program that can be executed by a computer that executes finite element analysis that analyzes a grid constituting a finite element in units of side elements using a multigrid method,
The computer,
A shape model reception step for receiving a shape model to be analyzed;
A fine grid generation step for generating the nodes of the grid of the highest hierarchy of the received geometric model based on a predetermined rule;
An importance calculation step for calculating the importance related to the connection relationship between one node and another node based on the geometric information about the nodes and the edges connecting the nodes, and the importance set for the node itself;
If the importance related to the connection relationship between the calculated one node and the other nodes is greater than the value calculated from the importance of the one node itself and the importance of the other nodes, the other node A node selection step for selecting a node for generating a lower-level grid for one node,
A first course grid generation step of generating a lower hierarchy grid using the selected nodes;
Importance recalculation step of recalculating the importance of the nodes of the generated lower hierarchy grid based on the geometric information,
If the recalculated importance is greater than the importance of one node itself and the importance of the other nodes themselves, the other nodes are generated as grids of further lower layers for the one node. Node reselection step to reselect as the node of time,
A second course grid generation step of generating a further lower level grid using the reselected nodes;
A determination step for determining whether or not the generation of the grid is completed, and a step for returning to the importance recalculation step when the determination step determines that the number of hierarchies does not exceed a predetermined number. A computer program. The importance calculation step and the importance recalculation step include the computer,
12. The function of calculating importance based on geometric information about nodes and sides connecting the nodes so that the nodes where errors projected onto the lower layer grid are concentrated becomes larger. Computer program. The node selection step and the node reselection step include the computer,
The importance related to the connection relationship between the calculated one node and other nodes is greater than the value calculated from the importance of one node itself and the importance of other nodes, and is adjacent to an already selected node 13. The computer program according to claim 11 or 12, wherein if not, the computer is caused to function as a step of selecting the other node as a node at the time of grid generation of a lower hierarchy with respect to the one node . In the determining step, the computer is
Counting the number of hierarchies that generated the grid;
And functioning as a step for determining whether or not the counted number of hierarchies exceeds a predetermined number, and a step for determining that generation of a grid is completed when it is determined that the predetermined number is exceeded. The computer program according to claim 11, wherein the computer program is characterized by the following. In the determining step, the computer is
Counting the total number of generated grids;
A step of determining whether or not the total number of grids counted exceeds a predetermined number, and a step of determining that the generation of the grid is completed when it is determined that the predetermined number has been exceeded. The computer program according to any one of claims 11 to 13.

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