JPH07182310A - Method and device for structure analysis - Google Patents

Abstract

PURPOSE:To provide a method and device for structure analysis which increase the convergence speed of a solution in the repeating process of analytic processing and shorten the computation time. CONSTITUTION:The initial value of an approximate solution is set in an area to be analyzed, and stored in an external storage device 4 (steps S1 and S2) while divided into plural partial structures. In this example, an (i)th partial structure has areas 2i-2, 2i-1, and 2i, and the data in the respective areas are read out of the external storage device 4 and stored in a main storage part. In steps S4-S8, an approximate solution is found as to the (i)th partial structure. Specially, acceleration processing using acceleration coefficient is performed in a step S6. And, the processing is completed as to all the partial structures, decision on convergence is made, and the processing is repeated until the approximate solution is converged.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a structural analysis method and apparatus for dividing an analysis region into partial structures, executing an analysis for each partial structure, sequentially correcting the obtained solutions, and obtaining the solutions of the entire structure. It is about.

[0002]

2. Description of the Related Art Partial differential equations are solved in order to calculate various fields such as structural analysis and electric field analysis. As a method for solving these problems, a numerical calculation method such as a finite element method or a difference method is generally used. These numerical calculation methods lead to simultaneous linear equations by discretizing partial differential equations, and ultimately it is necessary to solve simultaneous linear equations.

Methods for solving simultaneous linear equations are roughly classified into a direct method and an iterative method. A typical direct method is the Gaussian elimination method, but it has a drawback that the storage capacity for storing the coefficients of simultaneous linear equations increases when the bandwidth is widened.

On the other hand, examples of the iterative method include the SOR method and the CG method. Unlike the direct method, the iterative method needs to store only the coefficients of simultaneous linear equations, and therefore has the advantage that the required storage capacity does not depend on the bandwidth and can be smaller than the direct method.

By the way, when the scale of simultaneous linear equations becomes large to some extent, the storage capacity of a computer for processing operations becomes insufficient. Therefore, in order to solve an equation of a larger scale, it is necessary to use an external storage device, that is, a storage device such as a disk memory, which requires a long access time. However, when an external storage device is simply used, compared to a main storage device (that is, a semiconductor storage device),
The access time increases so much that it cannot be compared. for that reason,
Since the time required for processing becomes enormous, the processing cannot be completed within a realistic time. Therefore, the method of solving the equation is modified to reduce the number of inputs and outputs to and from the external memory. However, such an improvement method has been proposed for the direct method, but no such improvement method has been known for the iterative method.

Therefore, the partial structure method has been proposed as an efficient method that can use the iterative method and can also use external storage. In this partial structure method, the analysis region is divided into a plurality of partial structures, analysis is performed for each partial structure, and the process is repeated until the obtained solution converges. Here, the scale of the partial structure is set to a range in which the storage capacity required when the calculation is performed by the partial structure alone can be stored in the main memory of the computer that processes the operation. Therefore, in the present partial structure method, the arithmetic processing in each partial structure can be executed in the main memory.

As described above, in the partial structure method, since the arithmetic processing is performed in the main memory having a short access time, the processing is fast. Further, since input / output with the external storage is intensively performed for each partial structure, the number of accesses to the external storage is small and efficient. Further, there is an advantage that both the direct method and the iterative method can be used to solve the simultaneous linear equations in each substructure.

[0008]

However, the above general substructure method has a problem in the convergence of the solution. That is, in the calculation procedure by the partial structure method,
The calculation of substructures is sequentially repeated, and a solution that satisfies the equation is obtained for each subimage. However, a large amount of iterations may be required to obtain a solution that satisfies the equation over the entire analysis region. is there.

FIG. 11 is a diagram showing an example of the relationship between the number of iterations and solution convergence by a general substructure method. In the figure, the horizontal axis represents the number of iterations and the vertical axis represents the value of the approximate solution. In this example, a value close to the true value is set as the initial value of the solution, but there is a tendency that it deviates from the true value once with iteration, and then approaches the true value, but the speed of approaching the true value is extremely high. slow. From the figure, it is expected that a solution that is close enough to the true value can be obtained by repeating the calculation.
This requires a large number of iterations, is impractical and unusable in practice.

Naturally, the convergence speed varies depending on the given analysis conditions, but generally shows the tendency shown in FIG. Needless to say, it is desirable to converge faster even in the case where the convergence is relatively fast.

As described above, in the general substructure method, the solution converges slowly and may require a large number of iterations depending on the given analysis conditions. Time) is long and not efficient. It is useless because the calculation time is too long to get a solution in a practical time range. There is a problem.

The present invention has been made in view of the above problems, and provides a structural analysis method and apparatus capable of accelerating the solution convergence speed in the iterative process of analysis processing and shortening the calculation time. The purpose is to do.

[0013]

A structural analysis method according to the present invention for achieving the above object is a structural analysis method for generating an approximate solution to an analysis condition given for a region to be analyzed and performing a numerical analysis. Then, for each of the input step of performing the setting input of the acceleration coefficient and the approximate solution, and each of the partial areas obtained by dividing the area to be analyzed into a plurality of areas,
A generating step for independently generating an approximate solution based on the analysis conditions and the set approximate solution, and a convergence direction of the solution based on the acceleration coefficient input in the input step for the approximate solution generated in the generating step. Update step and a setting step of newly setting the value obtained by the updating step as an approximate solution, and repeating the generating step, updating step and setting step until the approximate solution converges within a predetermined range. It is characterized by doing.

Further, the structural analysis apparatus of the present invention which achieves the above object is a structural analysis apparatus which generates an approximate solution to an analysis condition given to a region to be analyzed and carries out a numerical analysis. Input means for setting and inputting an approximate solution, and for each of the partial areas obtained by dividing the area to be analyzed into a plurality of areas, an approximate solution is independently obtained based on the analysis condition and the set approximate solution. Generating means for generating, updating means for updating the approximate solution generated by the generating means in the convergence direction of the solution based on the acceleration coefficient input by the input means, and a value obtained by the updating means for updating Setting means for setting as an approximate solution, and the processing by the generating means, updating means and setting means is repeated until the approximate solution converges within a predetermined range.

[0015]

With the above structure, an approximate solution is repeatedly generated for each partial region, and the generated approximate solution is further updated in the convergence direction of the solution by the set acceleration coefficient, thereby improving the convergence speed of the solution. .

[0016]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT A preferred embodiment of the present invention will be described below with reference to the accompanying drawings.

<Embodiment 1> FIG. 1 is a block diagram showing a schematic control configuration of a structural analysis apparatus of Embodiment 1. In the figure, 1 is a CPU, which performs various controls in the present structural analysis apparatus. A ROM 2 stores various control programs and data executed by the CPU 1. The control program represented by the flowchart described later with reference to FIG.
Stored in 2. A RAM 3 provides a work area when the CPU 1 executes various controls. RAM3
Has a main memory 3a, a counter 3b, and an acceleration coefficient 3c. The function of each unit will be described later.

An external storage device 4 is composed of, for example, a hard disk. The external storage device 4 stores data regarding the partial structure. 5 is an input unit, a CPU
Various commands and data are input to 1. Reference numeral 6 denotes a display unit, which performs various displays under the control of the CPU 1.

Next, a processing procedure for structural analysis in the first embodiment will be described. FIG. 2 is a flowchart showing the procedure of the structural analysis of the first embodiment. FIG. 3 is a diagram showing an example of a state in which the analysis area is divided into partial structures. In the figure,
Although shown two-dimensionally, the same applies to a three-dimensional region. Further, although the same drawing shows the case where the number of partial structures is three, even if the number of partial structures is different, the processing can be performed in the same manner as the procedure described below.

First, as an issue to be analyzed, it is assumed that an equation within the area of ablk-a shown in FIG. 3 is defined. In solving this equation, the analysis region is divided into multiple substructures. In the example of the analysis region in FIG. 3, it is composed of three partial structures, and each partial structure is composed of a region + region, a region + region + region, and a region + region. Of these, regions and regions are overlapping portions between partial structures. The scale of one substructure is
The storage capacity required when the partial structure is calculated independently is determined so that it falls within a predetermined range.

Next, the process of solving the equation given to the analysis area will be described with reference to the flowchart of FIG.

First, in step S1, an initial value of a solution is set in the entire analysis area. The initial value may be one that satisfies the fixed boundary condition. In the subsequent step S2, these initial values are stored in the external storage device 4.
It should be noted that each initial value is divided and stored in each of the areas in FIG.

In step S3, the counter 3b of the RAM 3 is reset and the content is set to 1. Incidentally, FIG.
, The content of the counter 3b is indicated by i. After that, the analysis for each partial structure is performed in the processing from step S4.

In step S4, the data of the i-th partial structure is read from the external storage device 4, and the read data is stored in the RAM 3
It is stored in the main storage unit 3a. In the configuration of the partial structure as shown in FIG. 3, the region 2i-2 and the region 2i are provided for the i-th partial structure.
-1 and the data of the area 2i are required. For example i = 2
If so, the second partial structure is subjected to analysis, and the area, the area, and the data of the area are read out and stored in the main storage unit 3a.

In step S5, with respect to the i-th substructure, a fixed boundary (c-i, d-j in the case of the second substructure in FIG. 3) and a boundary between substructures (also c.
-D, i-j) The value on is fixed, an equation is made, and a new approximate solution is obtained. In step S6, the previous step S5
Acceleration processing is performed on the solution obtained in. Then, the solution that has been subjected to the acceleration processing is stored in the external storage device 3, and the stored contents of each area are rewritten. The acceleration process in step S6 will be described later.

In step S8, i (counter 3
Update b). Then, in step S9, it is determined based on the value of i whether or not the processes of steps S4 to S7 have been completed for all the partial structures. If processing has not been completed for all partial structures, the process returns to step S4 to process the next partial structure. On the other hand, if the processing has been completed for all the partial structures, the process proceeds to step S10 to make a convergence determination. In the convergence determination, the obtained solutions are all the analysis regions (a-b-l-k- in FIG. 3).
It is to determine whether or not a, that is, the region ~) satisfies the equation without contradiction. For example, the result of the previous iterative calculation and the result of the current iterative calculation determine whether or not the variation of the approximate solution has converged within a predetermined range. And
If it has not converged, the process returns to step S3, and the process from the first partial structure is repeated again. In this repetition, the value of each area stored in the previous step S7 is used. On the other hand, if the solution has converged in step S10, this processing ends. At this point, the data stored in the external storage device 3 becomes the solution.

In the above method, since the partial structure is divided into the main memory and the processing is performed, the processing can be performed with a small main memory capacity, and the processing time can be shortened by the efficient access to the external storage device. Is achieved. Furthermore, in the first embodiment, the acceleration processing accelerates the convergence of the solution and shortens the calculation time. The acceleration process will be described below.

In the i-th substructure, when the newly obtained approximate solution is v ⁽ⁿ⁾ and the approximate solution after the acceleration processing is V ⁽ⁿ⁾ , the relationship between the two is V ⁽ⁿ⁾ = V ^(n-1) + α (v ⁽ⁿ⁾ -V ^(n-1) ) (1) where V ^{(n-1) is the} previously stored value α is the acceleration coefficient Given.

According to the equation (1), the general partial structure method corresponds to the case of α = 1. Here, in order to accelerate the convergence, the acceleration coefficient α is set to a value larger than 1. That is,
The acceleration coefficient is input using the input unit 5, and the acceleration coefficient 3 is input.
Store in c.

FIG. 4 is a diagram for explaining the effect of the first embodiment. The convergence tendency shown in FIG. 4 is obtained by applying the method of this embodiment to the same problem as that used in FIG. 11 described above. In FIG. 4, the acceleration coefficient α is 1.5.
The number of iterations and the change in the solution are shown for two types of 1 and 1.8. It is clear that both of them converge faster than the conventional example of FIG. Further, when the acceleration coefficient α is 1.8, the true value is once exceeded, but finally it converges in the same number of iterations as when α = 1.5.

FIG. 5 is a view showing numerical values of the convergence tendency shown in FIGS. 11 and 4. Although the acceleration coefficient α is 1.0, that is, in the general substructure method, there is an error of nearly 2% even when the number of iterations is 50, but in the present embodiment, the error is 0.5% or less after 30 times. It can be confirmed that the convergence speed is improved. In particular, it should be noted that the general substructure method requires a large number of iterations when trying to further improve the solution from the state where the error is 2%. This is because the solution converges slowly as shown in FIG. Therefore, when trying to obtain an approximate solution with an error level that is rather small, the amount of calculation and the time required for calculation by the general method increase extremely. Therefore, the difference between the general method and the method of the first embodiment is larger than the difference between the errors shown in FIG. That is, it should be noted that the acceleration effect in the first embodiment is extremely large.

Next, the value of the acceleration coefficient will be further described. Naturally, the acceleration effect obtained by the first embodiment depends on the acceleration coefficient. In the example shown in FIG. 2, α =
There is a difference in effect between 1.5 and α = 1.8. Generally, the acceleration coefficient must be larger than 1 in order to obtain the acceleration effect. The larger the acceleration coefficient is, the larger the acceleration effect is. However, when the acceleration coefficient is larger than a certain level, the solution is overcorrected like the acceleration coefficient 1.8 in FIG. If this overshoot is too large, the solution will not be corrected well, and the number of iterations required to obtain a converged solution will rather increase, or in some cases it will not converge. As described above, there are restrictions on the desirable range of the acceleration coefficient, and in particular, 1.0 ≦
It is desirable that α <2.0. Particularly, in the analysis example of FIG. 4, it is estimated that the optimum acceleration coefficient is in the range of 1.5 ≦ α ≦ 1.8. As a method for setting the acceleration coefficient, trial calculation may be performed for several kinds of acceleration coefficients, a value considered to be the most appropriate among them may be adopted, and this may be input from the input unit 5.

<Second Embodiment> Next, a second embodiment will be described. The configuration and processing procedure of the partial structure analysis apparatus according to the second embodiment are similar to those of the first embodiment (FIGS. 1 and 2). Example 1
However, the same acceleration coefficient is used for all the partial structures, but the second embodiment is different in that a separate acceleration coefficient is used for each partial structure. If the acceleration coefficients determined for each partial structure are all set to the same value, it is the same as that of the first embodiment. However, if at least two or more different acceleration coefficients are used, it is different from the first embodiment. The effect can be obtained, and the convergence can be further speeded up.

That is, the example of the analysis result of FIG. 4 shows that the way of convergence differs depending on the value of the acceleration coefficient, but the relationship between the acceleration coefficient and the way of convergence differs depending on the field conditions and the like. The relationship between the acceleration coefficient and the way of convergence depends on many conditions, but the relationship between the distribution of the field to be obtained and the connected portion of the substructure has a great influence. Therefore, the optimum value of the acceleration coefficient for each partial structure is often different. Therefore, when the acceleration coefficient value suitable for each substructure is used, the convergence becomes faster than when the same acceleration coefficient values are used for all the substructures. That is,
The second embodiment has the effect of further improving the convergence as compared with the first embodiment.

Here, the method of obtaining the acceleration coefficient used in the first and second embodiments will be described.

The acceleration coefficient has an optimum value in the range of 1.0 to 2.0. When the value of this acceleration coefficient is small apart from the optimum value, the acceleration effect becomes small. On the contrary, if the value of the acceleration coefficient is too large, the solution is modified too much and the number of iterations required to obtain the solution increases. And
In some cases, it takes an extra time, or the solution vibrates and the correct solution cannot be obtained. Therefore, it is necessary to set the value of the acceleration coefficient to the optimum value or its vicinity.

As one method of obtaining the optimum value of the acceleration coefficient, there is a method of performing an iterative calculation for some values of the acceleration coefficient and selecting a value with the best result.

Alternatively, the acceleration coefficient may be automatically obtained by using the Gauss-Seidel method. According to this method,
First, the simultaneous one-time equations to be solved are expressed in matrix. That is, (-[E] + [D]-[F]) {x} = {b} (2) where-[E]: lower triangular matrix of coefficient matrix [D]: of coefficient matrix To triangular matrix − [F]: It is an upper triangular matrix of the coefficient matrix. Further, the calculation procedure of the Gauss-Seidel method is shown in the matrix display as follows. That is, {x} ^{(k + 1)} = [D] ^-1 ({b} + [E] {x} ^{(k + 1)} + [F] {x} ^(k) ) (3), where And the subscripts (k + 1) and (k) of {x} are
Indicates that {x} is the value at that iteration (eg, {x} ^(k) is the value at the kth iteration).

The acceleration procedure using the acceleration coefficient is {x} ^{(k + 1)} = {x} ^(k) + α ({X} ^{(k + 1)} -{x} ^(k) ) ( 4) where α is an acceleration coefficient {X} ^{(k + 1)} : a value obtained by iterative calculation {x} ^{(k + 1)} : an accelerated value.

At this time, in obtaining the acceleration coefficient α, the relationship between {x} ^{(k + 1)} and {x} ^(k) is derived as follows: {x} ^{(k + 1)} = ([D] -α [E]) ⁻¹ {(1-α) [D] + α [F]} {x} ^(k) + α ([D] −α [E]) ⁻¹ {b} (5)

The above formula (5) is a recurrence formula for {x}. The convergence speed is faster as the absolute value of the coefficient of {x} ^(k) is smaller. Therefore, the optimum value of the acceleration coefficient α is
This is to minimize the absolute value of the coefficient of {x} ^{(k) in} the above equation. That is, such α may be obtained and used as the acceleration coefficient.

Further, in the first and second embodiments described above, the value of the acceleration coefficient is 1.0 or more.
Values less than 1.0 can also be used. In this case, the acceleration factor slows down the convergence speed. Therefore, the acceleration effect cannot be obtained. However, there are cases where the system to be calculated is unstable or is hypersensitive to substructure repetition. In such a case, even if the acceleration coefficient is 1.0, the calculation process becomes unstable, and a convergent solution may not be obtained in some cases. Therefore, by setting the acceleration coefficient to 1.0 or less, the calculation process is stabilized, and as a result, a convergent solution can be obtained quickly. Considering such a case, the acceleration coefficient α is 0 <
It is desirable that α be in the range of 2.0.

As described above, in the first and second embodiments described above, by adding the acceleration process to the analysis process for each partial structure, the number of iterations required to obtain a solution with a predetermined accuracy can be reduced. Therefore, the amount of calculation and the calculation time can be greatly reduced. Since the calculation time is too long in the conventional method, the calculation accuracy that could not be achieved can be realized by the method of the first and second embodiments. Acceleration in the first and second embodiments The process is not complicated and the amount of calculation required for this process is negligible. In addition, the processing procedure of the general structural analysis method can be applied as it is, and the effect that the calculation time can be remarkably shortened by a slight change can be obtained.

<Third Embodiment> In the first and second embodiments described above, the acceleration process is performed by setting the acceleration coefficient obtained in advance. The method of calculating the optimum acceleration coefficient has been described above, but in the method of obtaining the optimum acceleration coefficient by executing the iterative method using several acceleration coefficients, iterative calculation is performed multiple times for one calculation. In some cases, the goal of finding a solution quickly is not met.

The method using the Gauss-Seidel method as an example requires a complicated calculation procedure and a large calculation time. As a countermeasure, a simple approximation method may be used, but the equation to be solved is limited to one having a specific property, and the amount of calculation itself does not decrease so much. Furthermore, the above-mentioned method can be applied only to a method in which the process of iterative calculation can be expressed in the form of a recurrence formula. However, in the iterative methods such as the partial structure method, it is often difficult to express the calculation procedure by a recurrence formula.

That is, at present, the calculation procedure of the iterative method is limited to that which can be expressed by the recurrence formula. Except for equations having specific properties, the amount of calculation for obtaining the optimum value becomes enormous and the optimum value of the acceleration coefficient Even if there is a simple method for obtaining the optimum value of the acceleration coefficient, there are problems that the calculation procedure for that is still complicated and the amount of calculation may be large. Therefore, in the third embodiment, a structural analysis apparatus will be described in which the value of the coefficient for improving the convergence speed of the solution in the analysis processing is automatically set appropriately and the calculation time can be further shortened.

The structural analysis apparatus according to the third embodiment sets a certain value as the initial value of the acceleration coefficient, and increases or decreases the acceleration coefficient based on the change of the approximate solution by the subsequent iterative calculation. As a result, the value of the acceleration coefficient is set to the optimum value in the process of iterative calculation. The structural analysis apparatus of the third embodiment is also the same as the first embodiment (FIG. 1).
Since it has the same configuration as that, detailed description thereof is omitted here.

FIG. 6 is a flow chart showing the structural analysis procedure of the third embodiment. This procedure incorporates the automatic setting procedure of the acceleration coefficient in the process described in the first embodiment. In FIG. 6, the counter 3d provided in the RAM 3 stores the number of approximate solutions whose values have increased at least in the previous and current processes in the course of the iterative process.

In step S21, a predetermined initial value is set as the acceleration coefficient. Next, in step S22, the content N of the counter 3d provided in the RAM 3 is set to zero (N = 0). This counter (N) counts the number of solutions in which the newly obtained value (referred to as a new value) has increased from the previous value (referred to as a previous value) during the iterative process.

In step S23, the solution is calculated. That is, the value of the solution stored in the external storage device 4 ^(a new solution x ^{(k + 1)} is ^obtained according to the procedure of the iterative method using the solution x ^(k) obtained in the previous calculation. The calculation content of the method depends on the type of iterative method used.
The acceleration process is performed as in the first embodiment. Therefore, the previous value x of the solution
^{From (k)} , the new value X ^{(k + 1)} and the acceleration coefficient α, the accelerated corrected solution x ^{(k + 1)} is x ^{(k + 1)} = x ^(k) + α (X ^{(k + 1)} −x ^(k) ) (5) Then, in step S24, the corrected solution x ^{(k + 1 )} thus obtained is stored in the external storage device 4,
Rewrite the previous value x ^(k) . The iterative calculation method used in steps S23 and S24 may be performed separately for each partial structure as in the first embodiment, or iterative calculation may be performed for all analysis regions.

In step S25, it is determined whether the obtained corrected solution is increasing or decreasing with respect to the previous value, and if the solution is increasing, the count value N of the counter 3d is incremented. In this way, the number of increased solutions for all unknowns is counted and stored in the counter 3d. The counting process is executed when the corrected solution x ^{(k + 1)} is stored in the external storage device 4 in step S24.

Next, in steps S26 to S28, the acceleration coefficient setting is updated based on the value of the counter N. First, in step S26, the value of the counter (referred to as the previous value of the counter) N0 in the previous processing is read and the amount of change of the value N of the current counter with respect to N0 is evaluated (step S27). Then, the acceleration coefficient α is newly set based on this evaluation (step S2).
8). Here, the acceleration coefficient α is reset by αn = α if | (N−N0) /N|≧0.1
-0.1 | (N-N0) / N | <0.1, αn = α
+0.1 However, if αn ≧ 1.99, αn = 1.99 If αn <1.0, αn = 1.0.

At step S29, the current count number N
Is stored in the counter 3d as N0. Then, the convergence of the solution in the iterative calculation is determined. Here, if the solution has not converged, the process returns to step S22 and the above processing is repeated. If the solution is convergent, the iterative calculation ends.

According to the processing described above, in the third embodiment, even if an acceleration coefficient distant from the optimum value is set as the initial value, it is close to the optimum value after the above-mentioned processing is repeated several times. The speed factor is set automatically.

The effect of the third embodiment will be described with reference to FIGS. 7 and 8. 7 and 8 show the relationship between the number of iterations and the solution correction amount when the substructure method is used as the iterative method. In the partial structure method, it is generally difficult to express the iterative process in the form of a recurrence formula.

First, FIG. 8 is a diagram showing the relationship between the number of iterations of processing and the amount of correction of the solution when the acceleration coefficient α is fixed to 1.0 (that is, when iterative calculation by a general method is used). is there. The correction amount of the solution gradually decreases with the number of iterations, and the degree is about -0.35 dB / time.

On the other hand, FIG. 7 is a diagram showing the relationship between the number of iterations of the processing according to the third embodiment and the correction amount of the solution. Here, the initial value of the acceleration coefficient is 1.0. According to the figure, the correction amount is large at the initial stage of the iteration, but the correction amount greatly decreases after the number of iterations exceeds 10. This indicates that the acceleration coefficient was close to the optimum value around that time. In the second half, the degree of decrease in the correction amount is −
It is 2 dB / time, and it can be seen that the solution converges at a speed of 5 to 6 times as compared with the case where the acceleration coefficient is fixed to 1.0.
From the above, according to the third embodiment, it can be confirmed that the acceleration coefficient is appropriately set.

However, the accuracy of the solution cannot be directly evaluated only by the correction amount of the solution. Therefore, the result of comparing the solution values is shown in FIG. FIG. 9 is a diagram showing the error of the approximate solution after 30 times of iterative processing. According to this, when the acceleration coefficient is fixed at 1.0 (when a general method is applied without performing the acceleration process), there is an error of 13%, but the acceleration coefficient is set to 1.5 and 1.8. When fixed (method of Example 1), the error is very small. Therefore, it is considered that the optimum value of the acceleration coefficient exists around this. The result of the iterative processing in the third embodiment also has an error similar to these,
It is confirmed that the acceleration coefficient is set appropriately.

In the resetting of the acceleration coefficient in step S28 described above, the acceleration coefficient is increased / decreased based on whether or not the change in the number of increasing solutions exceeds 10%. However, this criterion is not limited to this and depends to some extent on the problem to be analyzed. Therefore, this criterion will be further explained.

First, the basic idea of the third embodiment is as follows.
In the iterative calculation, the solution should change monotonically in the process that the solution converges smoothly. " That is, what is modified in the increasing direction continues to increase toward the upper solution, and what is modified in the decreasing direction continues to decrease toward the lower solution. However, as a result of introducing the acceleration coefficient in this process, if the solution is accelerated too much, the solution goes too far and the solution starts to go back. That is,
The number of solutions that increase or decrease the value changes. In such a case, it is necessary to reduce the acceleration coefficient. vice versa,
It is considered that there is room for further acceleration when monotonous conversion is continued.

Based on such a concept, it is sufficient that the amount of change in the unknown number that increases or decreases, which is the criterion for increasing or decreasing the acceleration coefficient, is zero. However, in reality, this condition is too strict. FIG. 10 is a diagram showing the ratio of the approximate solution whose value has increased in the iterative process, in which the horizontal axis represents the number of iterations and the vertical axis represents the rate of change in the unknown count increase. However, the acceleration coefficient is fixed at 1.0. As shown in FIG. 10, the rate of change in the increasing unknowns is in the range of 1 to 10%, although the acceleration is not accelerated at all. From this result, if the rate of change is about 10% or less, it can be considered that the convergence process is good. Of course, since these tendencies depend on the problem, it is generally desirable to set the criterion in the range of 2 to 15%. For problems that have a significant adverse effect on the convergence of acceleration, the acceleration factor should be set to a small value.

The amount of change in the acceleration coefficient is also set to 0.1 in this embodiment, but this also depends on the problem. If the change amount is reduced, the accuracy of adjusting the acceleration coefficient is improved, but the correction takes time. The amount of change in the acceleration coefficient is from 0.05 to
It is desirable to set it in the range of 0.2. Here, if importance is placed on certainty, the change amount should be set small.

Further, although it is the initial value of the acceleration coefficient, it is desirable to set it small. This is because the convergence process is not stable at the beginning of the iteration and may be temporarily accelerated too much, which may delay the convergence. The convergence result shown in FIG. 9 when the initial value is 1.5 indicates this.

As described above, according to the third embodiment, since the acceleration coefficient is automatically set to the optimum value, the convergence is fast and the calculation is efficient. The calculation procedure required to automatically set the acceleration factor is simple and the amount of calculation required for it is extremely small. Since it can be applied regardless of the type of iterative method, it can be applied to the case where the procedure of the iterative method cannot be expressed by a recurrence formula. Does not require any particular property in the equation. The effect is obtained. That is, the third embodiment can be easily applied to the iterative method such as the degree, and the effects as described above can be obtained.

Although the iterative method based on the partial structure method described in the first embodiment is used in the third embodiment, the present invention is not limited to this, and any other iterative method can be applied. Furthermore, by combining with the method of the second embodiment, different α may be automatically set for each partial structure.

<Embodiment 4> Next, Embodiment 4 will be described as a modification of Embodiment 3 described above. The calculation process of the present embodiment is the same as that of the third embodiment (FIG. 6), and therefore detailed description is omitted here, and only the characteristic part of the fourth embodiment will be described.

The fourth embodiment is different in the method of resetting the acceleration coefficient in step S28. The resetting of the acceleration coefficient in the fourth embodiment is as follows: | (N−N0) /N|≧0.1 ωn = ω−0.
1 If 0.1> | (N-N0) /N|≧0.05, then ωn
= Ω 0.05> | (N-N0) / N |, then ωn = ω +
0.1 However, if ωn ≧ 1.99 then ωn = 1.99 if ωn <1.0 then ωn = 1.0 where N: the number of unknowns whose solution value has increased in this iteration N0: last time The number of unknowns for which the solution value increased in the iteration of ω: The value of the current acceleration coefficient ωn: The value of the reset acceleration coefficient.

In the resetting of the acceleration coefficient in step S28 of the third embodiment, the acceleration coefficient is either increased or decreased, but in the fourth embodiment, the acceleration coefficient is not changed. In the third embodiment, the acceleration coefficient is reset by either increasing or decreasing the acceleration coefficient. Therefore, even if the acceleration coefficient is near the optimum value, the value of the acceleration coefficient must always change. I had to do it.
Therefore, especially when the correction range of the acceleration coefficient is large,
In some cases, the convergence is not smooth and the convergence speed is hindered. On the other hand, according to the fourth embodiment, smoother convergence is realized and the certainty of convergence is improved.

<Fifth Embodiment> A fifth embodiment will be described as another modification of the third embodiment. Also in the fifth embodiment, the same processing procedure as in the third embodiment (FIG. 6) is used. The acceleration coefficient is reset in step S28 of the fifth embodiment as follows.

That is, ωn = ω + Δω, where 0 ≦ | (N−N0) /N|≦0.075 Δ
ω = (0.15-2 × | (N−N0) / N |) × (2-
ω) 0.075 <| (N−N0) /N|≦0.15, Δω = 0.15−2 × | (N−N0) / N | 0.15 <| (N−N0) / When N |, Δω =
If -0.15 ωn ≥ 1.999, then ωn = 1.999 ωn <1.0, then ωn = 1.0 where N: number of unknowns whose solution value has increased in this iterative process N0: previous time The number of unknowns for which the solution value has increased by the iterative processing of ω: The current acceleration coefficient value ωn: The reset acceleration coefficient value Δω: The acceleration coefficient is reset based on the change amount of the acceleration coefficient.

Since the acceleration coefficient is reset as described above, the following effects are produced as compared with the above-described third and fourth embodiments.

That is, when the acceleration coefficient is far from the optimum value, the correction width of the acceleration coefficient is set large, so that the acceleration coefficient can be brought close to the optimum value quickly. In the vicinity of the optimum value, the amount of change in the acceleration coefficient is small, so the convergence process is not disturbed by fluctuations in the acceleration coefficient near the optimum value. In the third and fourth embodiments described above, since the amount of change in the acceleration coefficient is a fixed amount, only a discrete value can be set, and beauty adjustment cannot be performed. Therefore, in some cases, the convergence factor is sensitive to the value of the acceleration coefficient, and the acceleration coefficient may not be correctly set to the optimum value for the problem that the range of the optimum value of the acceleration coefficient is narrow. However, in the fifth embodiment, since the range of change of the acceleration coefficient can be continuously different values, it is possible to set the acceleration coefficient to a value closer to the optimum value. When the acceleration coefficient is close to 2.0, the increment amount of the acceleration coefficient is made small, so that it is possible to prevent the convergence process from being disturbed due to the acceleration coefficient becoming too large. Further, in general, the closer the optimum value of the acceleration coefficient is to 2.0, the narrower the range of the optimum value is. However, in the present embodiment, the acceleration coefficient can be corrected with a finer step in the vicinity of 2.0, which is more accurate. It is possible to make various settings. Has the effect.

As described above, in the fifth embodiment, the third embodiment is used.
Further, as compared with the fourth embodiment, more reliable convergence is realized and the convergence speed is faster.

Needless to say, various modifications can be made as the method of resetting the acceleration coefficient.

As described above, Embodiments 3 to 5 above
According to the method, the value of the acceleration coefficient can be modified according to the change in the number of unknowns in which the value of the solution increases in the iterative method, so that the optimum acceleration coefficient is set for any problem. Therefore, the convergence speed is improved. It can be applied regardless of the type of iterative method. It can be applied regardless of the nature of the equation. The procedure for obtaining the optimum acceleration factor is simple and the calculation time required for it is extremely short. The effect is obtained.

The present invention may be applied to a system composed of a plurality of devices or an apparatus composed of a single device. Further, it goes without saying that the present invention can also be applied to a case where it is achieved by supplying a program that causes a system or an apparatus to execute the processing defined by the present invention.

[0077]

As described above, according to the present invention, it is possible to accelerate the solution convergence speed in the iterative process of analysis processing and shorten the calculation time.

[0078]

[Brief description of drawings]

FIG. 1 is a block diagram illustrating a schematic control configuration of a structural analysis device according to a first embodiment.

FIG. 2 is a flowchart showing a procedure of structural analysis of Example 1.

FIG. 3 is a diagram showing an example of a state in which an analysis area is divided into partial structures.

FIG. 4 is a diagram for explaining the effect of the first embodiment.

FIG. 5 is a diagram showing numerical values of the convergence tendency shown in FIGS. 11 and 4.

FIG. 6 is a flowchart showing a structural analysis procedure of Example 3;

FIG. 7 is a diagram showing the relationship between the number of iterations of processing according to the third embodiment and the correction amount of a solution.

FIG. 8 is a diagram showing the relationship between the number of times the process is repeated and the correction amount of the solution when the acceleration coefficient α is fixed to 1.0.

FIG. 9 is a diagram showing an error of an approximate solution after 30 times of iterative processing.

FIG. 10 is a diagram showing a ratio of an approximate solution having an increased value in an iterative process.

FIG. 11 is a diagram showing an example of the relationship between the number of iterations and the solution convergence by a general substructure method.

[Explanation of symbols]

 1 CPU 2 ROM 3 RAM 4 External Storage Device 5 Input Unit 6 Display Unit 7 System Bus

Claims (14)

[Claims] 1. A structural analysis method for generating an approximate solution to a given analysis condition for a region to be analyzed and performing a numerical analysis, comprising an input step of setting and inputting an acceleration coefficient and an approximate solution, and the analysis target. For each of the partial regions obtained by dividing the region into a plurality of regions, a generating step that independently generates an approximate solution based on the analysis conditions and the set approximate solution, and the approximation generated in the generating step. The method further comprises an updating step of further updating the solution in the convergence direction of the solution based on the acceleration coefficient input in the input step, and a setting step of newly setting the value obtained by the updating step as an approximate solution, The structural analysis method, wherein the generation step, the update step, and the setting step are repeated until the values converge to a predetermined range. 2. In the setting step, V ⁽ⁿ⁾ = V ^(n-1) + α (v ⁽ⁿ⁾ -V ^(n-1) ), where v ⁽ⁿ⁾ is an approximate solution obtained in this calculation. 2. The structural analysis method according to claim 1, wherein V ^(n-1) is a previously set value, V ⁽ⁿ⁾ is a newly set value, and α is a newly set approximate solution by an acceleration coefficient. 3. The acceleration coefficient α is 1.0 ≦ α <2.0.
The structure analysis method according to claim 2, wherein the structure analysis method is in the range. 4. The structural analysis method according to claim 1, wherein in the updating step, an acceleration coefficient set independently for each of the partial regions is used. 5. A structural analysis device for generating an approximate solution to a given analysis condition for a region to be analyzed and performing a numerical analysis, the input means performing setting input of an acceleration coefficient and an approximate solution, and the analysis target. For each of the partial areas obtained by dividing the area into a plurality of areas, generating means for independently generating an approximate solution based on the analysis condition and the set approximate solution, and the approximation generated by the generating means. The updating means for updating the solution in the direction of convergence of the solution based on the acceleration coefficient input by the input means, and the setting means for setting the value obtained by the updating means as a new approximate solution, A structural analysis apparatus, characterized in that the processing by the generating means, the updating means and the setting means is repeated until it converges within a predetermined range. 6. The structural analysis apparatus according to claim 5, wherein the updating means uses an acceleration coefficient set independently for each of the partial regions. 7. A structural analysis method for generating an approximate solution to a given analysis condition for a region to be analyzed and performing a numerical analysis, wherein a new approximate solution in the region is obtained based on the first approximate solution and the analysis condition. And a setting step of updating the approximate solution generated in the generating step in the convergence direction based on the set acceleration coefficient and setting this as a second approximate solution, the second approximate solution A first updating step of updating the acceleration coefficient based on a change amount with respect to the first approximate solution; and a second updating step of updating the first approximate solution with the second approximate solution, the generating step, A structural analysis method comprising repeating a setting step, a first updating step and a second updating step until an approximate solution converges within a predetermined range. 8. The first updating step includes a counting step of counting the number of solutions having a value increased from the solution of the first approximate solution among the solution values of the second approximate solution, and the counting. 8. A coefficient updating step of updating the acceleration coefficient based on the counting result of the step.
Structural analysis method described in. 9. The coefficient updating step in the first updating step increases the acceleration coefficient by a predetermined amount when the number of solutions whose values have increased as a result of the coefficient of the coefficient step is a predetermined number or less, and increases the value. 9. The structural analysis method according to claim 8, wherein the acceleration coefficient is decreased by a predetermined amount when the number of the solved solutions is larger than the predetermined number. 10. The coefficient updating step of the first updating step increases the acceleration coefficient by a predetermined amount when the number of solutions whose values have increased as a result of the coefficient of the coefficient step is smaller than a first predetermined number. , The acceleration coefficient is decreased by a predetermined amount when the number of solutions whose value is increased is larger than a second predetermined number, and the second predetermined number is larger than the first predetermined number and the value is increased. 9. The structural analysis method according to claim 8, wherein the acceleration coefficient is not increased / decreased when the number of is between the first and second predetermined numbers. 11. The coefficient updating step in the first updating step determines increase / decrease of the acceleration coefficient according to the number of solutions with increased values obtained by the coefficient step, and based on the number of solutions with increased values. The structural analysis method according to claim 8, wherein the amount of increase or decrease is set and the acceleration coefficient is updated. 12. The generating step is characterized in that the region is divided into a plurality of partial regions, and a new approximate solution in the region is generated for each partial region based on a first approximate solution and analysis conditions. The structure analysis method according to claim 7. 13. A structural analysis device for generating an approximate solution to a given analysis condition for a region to be analyzed and performing a numerical analysis, wherein a new approximate solution in the region is obtained based on the first approximate solution and the analysis condition. Generating means for generating, the setting means for updating the approximate solution generated by the generating means in the convergence direction based on the set acceleration coefficient, and setting this as the second approximate solution, the second approximate solution A first updating unit that updates the acceleration coefficient based on a change amount with respect to the first approximate solution; and a second updating unit that updates the first approximate solution with the second approximate solution; A structural analysis device characterized in that the setting means, the first updating means and the second updating means are repeated until the approximate solution converges to a predetermined range. 14. The counting means for counting the number of solutions having a value increased from the solution of the first approximate solution among the solution values of the second approximate solution, the first updating means; 14. The structural analysis device according to claim 13, further comprising a coefficient updating unit that updates the acceleration coefficient based on a counting result of the unit.