JPH08137831A - Analyzing method for field and analyzing method for trajectory of charged particle - Google Patents

Abstract

PURPOSE: To provide a field analyzing method which can shorten the analysis time which required a long period of time in the conventional method. CONSTITUTION: Boundary element method calculation over the entire region is performed (201). Then the potential ϕ at on the boundary of a sub region and the derivative (q) is its normal-direction are calculated from values of the whole region (202). Thus, the region is divided into sub regions and the boundary provided for the division is calculated. To calculate the electric field at a specific position, the sub region that the position belongs to is selected (204). The selection can easily be done from the coordinate values of the point to be found. When an electric field is found, not the values of the whole region, but the value of the sub region is used (205). Namely, when the point to be found is in the sub region, the electric field is found only through the integration along the boundary of the sub region. The region of integration required for the electric field calculation is reduced to almost 1/4 of that of the conventional example, so the calculation time of the electric field calculation is reduced to a 1/4.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing a field by a boundary element method using a computer.

[0002]

2. Description of the Related Art There are several methods for computer analysis of fields represented by partial differential equations such as electric fields, magnetic fields, and stress deformation. Among them, the finite element method is widely used because it can be easily applied to a system of various media.
However, since the potential distribution in the element is expressed by a function of a polynomial with a low degree, the expression capability of the potential distribution is limited. Also, the accuracy of the field, which is the spatial differential of the potential, is generally lower than the accuracy of the potential. Therefore, it is not suitable for the problem that the field value at an arbitrary point requires high accuracy.

On the other hand, the boundary element method is suitable for analyzing a field in a uniform medium region and has an ability to express the field distribution with high accuracy.

As an example in which the analysis of the electric field is required, an example of obtaining an electron orbit is shown in FIG. In the figure, reference numeral 1002
Electrodes 1006 each give a predetermined electric potential. An electric field is concentrated on the tip 1007 of the electrode 1002, and the electrons emitted from this are caused to move on an orbit as indicated by reference numeral 1008 by the effect of the electric field generated in the region 1009 and a magnetic field (not shown). As a method for obtaining the trajectory of charged particles in an electromagnetic field, the following method has been generally used.

(A) Area 1009 (electrode surface 1002-
1006 and the area surrounded by the virtual boundary 1001)
The electric field inside is analyzed. (However, the magnetic field is separately analyzed, and only the electric field will be described here.) (B) The trajectory of the particle is obtained using the equation of motion of the charged particle.

Here, the case where the boundary element method is used to analyze the electric field will be described in detail. FIG. 11 shows a conventional process. Reference numeral 1101 indicates a process of analyzing the entire analysis region by the boundary element method. The boundary element method deals only with quantities on the boundary. There are two types of quantities to be considered here, namely, the electric potential φ and the normal direction differential quantity q with respect to the boundary surface thereof.

As shown in the example of FIG. 10, if the distributions of φ and q at the boundaries 1001 to 1006 of the analysis region 1009 are known, the potential φ and the electric field vector E at an arbitrary position in the region 1009 can be obtained. By the way, in FIG. 10, the potential φ is known at the boundaries 1002 to 1006 of the electrode surfaces, but q is unknown. On the other hand, although the electric potential φ is unknown at the virtual boundary 1001, q can be treated as almost zero. Therefore, in the boundary element method, first, known quantities of φ and q on the boundary are set (1102 in FIG. 11). Next, unknown φ and q are obtained using the relationship between the boundaries (1103).

At this point, the distributions of φ and q on the boundary of the analysis area are all known. Therefore, if a position is designated, the electric field at that position can be analyzed. Next, the process of obtaining the electron trajectory from the equation of motion of charged particles will be described.

First, one particle whose trajectory is to be obtained is determined, and its initial condition is set (1104). The initial conditions include the position and initial velocity of particles at the time of starting movement.

Next, the value of the electric field at the position of the particle is represented by φ on all boundaries (1001 to 1006) of the analysis region in FIG.
And the distribution of q (1105 in FIG. 11). this is,
The integration is performed on the boundaries 1001 to 1006 of FIG.

Next, using the value of the electric field and the magnetic field whose description is omitted here, the position and velocity of the particle after a predetermined minute time Δt are obtained by the equation of motion (110 in FIG. 11).
6). Hereinafter, steps 1105 and 1106 of FIG. 11 are repeated until the particles reach the final position (1107).

After obtaining one particle, 1104 to 1107 in FIG. 11 are repeated for the next particle. After obtaining all particles (1108), the process of obtaining orbits is ended (1109).

The problem here is the time required for the process of obtaining. In the process of FIG. 11, it takes time for the process 1101 by the boundary element method and the process of obtaining the electric field 1105. Since the process 1106 of obtaining the locus by the equation of motion uses the ordinary differential equation, it is much faster than the former two processes. Comparing 1101 and 1105, 11
Since 01 takes more time, 1105 has a larger number of times, so overall, the time taken for the step 1105 of obtaining the electric field determines the time taken for obtaining the entire orbit.

In the step 1105 of obtaining the electric field, a step of integrating the function on the boundaries 1001 to 1006 of FIG. 10 is performed. If this is repeated about 10,000 times for one particle and further for a plurality of particles, it takes a lot of time even if a high-speed computer is used, which is a practical problem.

Now, a method for obtaining the magnetic field, which has not been described above, will be described.

FIG. 12 shows a magnetic field generator used for converging electron trajectories. In the figure, the coil 1 is attached to the magnetic core 1201.
202 (a cross section is shown in the figure) is wound.
α and β indicate lines of symmetry. With respect to this line of symmetry, the magnetic core 1201 and the coil 1202 exist in a ring shape. When a current is passed through the coil, a magnetic field is generated as indicated by reference numeral 1204. Since the gap 1203 is formed in the magnetic core, the magnetic field leaks in the vicinity of the symmetry line α-β and a force can be generated in the direction of converging the charged particles passing near the symmetry line. In order to control the trajectory of the charged particles as desired, it is necessary to properly control the distribution of the magnetic field generated by the magnetic field generator. From a design point of view, the shape, material, coil shape, and current value of the magnetic core 1201 of the magnetic field generator must be determined. Therefore, it is necessary to predict the relationship between these design factors and particle trajectories in design. The most powerful means of making this prediction is to perform numerical simulations. Numerical simulation is roughly divided into two processes.

1. Given the specifications of the magnetic field generator, find the distribution of the magnetic field generated.

2. Solving the equation of motion of particles using the above magnetic field distribution, the trajectory is obtained.

Among these, there are several methods for obtaining the magnetic field distribution, but the finite element method is suitable. The reason for this is that the system of the magnetic device is formed of a plurality of media (magnetic material and air), and the magnetic core has a magnetic non-linear system. Further, the shape of the magnetic core is generally complicated. The finite element method is suitable for systems with such complicated conditions. On the other hand, the boundary element method is difficult to analyze except for a homogeneous medium and is not practical.

FIG. 13 shows an analysis region when the system of the magnetic field generator is analyzed by the finite element method. Reference numeral 1301
Indicates the analysis area. Reference numeral 1302 indicates an air portion. Other reference numerals indicate the same as those in FIG. As described above, in the finite element method, a boundary is virtually set in order to make the analysis region finite, but if this boundary is sufficiently far from the intended place of analysis, the boundary condition is not exactly correct. However, the influence on the analysis accuracy is small. Therefore, if the analysis region is provided as shown in FIG. 13, the magnetic field can be obtained by the finite element method.

By the way, in the finite element method, the distribution of the solution in each element (region element, which is a surface element in the two-dimensional analysis and the volume element in the three-dimensional analysis) by a predetermined function (usually a polynomial function). However, this function cannot represent a general magnetic field distribution with high accuracy. Normally, the field is handled using the potential, but in this case, the magnetic field is given in the form of the spatial differentiation of the potential, so the expression capability of the magnetic field distribution is greatly reduced, and the accuracy of the magnetic field value is deteriorated. . On the other hand, when obtaining the trajectory of the charged particles, the accuracy of the obtained magnetic field has a great influence on the accuracy of the trajectory, so it is important to obtain the magnetic field distribution with high accuracy. Further, the region through which particles pass is often an extremely narrow region. For example, in FIG. 12, particles pass very near the symmetry line α-β. In order to obtain the magnetic field distribution in this narrow region with high accuracy, it is necessary to make the finite element division for obtaining the magnetic field fine so as to be commensurate with this, but it is not realistic because the time for obtaining is enormous. Also,
If the element is made fine in only one direction, the element shape becomes flat and the accuracy deteriorates.

As means for solving such a problem,
After obtaining the magnetic field by the finite element method, the boundary element method calculation is performed using the result. FIG. 14 is a diagram for explaining this. Reference numerals 1301, 1302, 120
1, 1202 shows the same thing as FIG. Reference numeral 1403
Is an area to be analyzed by the boundary element method, reference numerals 1401 and 1402
Is the boundary of the boundary element method area. Various methods can be used to set the boundary element method region, but here, the case where the boundary of the boundary element method region is made to coincide with the element boundary of the finite element mesh will be described. FIG. 15 is a diagram schematically showing this, and shows an element division diagram divided by primary triangle elements. Nodes 1501 to 15 located outside this element division
The boundary formed by 10 is made to coincide with the boundary of the boundary element method, and nodes 1501 to 1510 and sides 1531 of the finite element method are formed.
1540 is used as it is as a node and a boundary element (line element) of the boundary element method.

If the magnetic vector potential is used in the finite element method analysis, the value of the magnetic vector potential at the nodes 1501 to 1510 and the sides 1531 to 1 will be described.
The value B _n of the normal direction component of the average magnetic flux density at 540 is known. In the boundary element method, there are several kinds of methods depending on what is used as the unknown quantity, but here,
The case of using a magnetic scalar potential Ω that is easy to handle will be described. The magnetic scalar potential Ω is the magnetic field H _X , H
It is defined as follows for _Y and H _Z.

[0024]

[Equation 1]

Therefore, the magnetic field H _n in the normal direction on the sides 1531 to 1540 of FIG. 15 is given by the following equation.

[0026]

[Equation 2]

Now, as the boundary element, a 0-1 order element, that is, the magnetic scalar potential is a primary distribution on the boundary element, and its normal direction differential (in this case, the magnetic field normal direction component) is constant on the boundary element. Adopt elements that have values. In this way, the quantity handled by the boundary element method is the potential value Ω at the boundary node and the differential in the normal direction of the potential on the boundary element ∂Ω / ∂n (= −B _n / μ _o ). By the way, from the result of the finite element method analysis, the average magnetic flux density B on the side
_{Since n} is known, ∂Ω / ∂n is known. Therefore, in the boundary element method, an equation may be established with only Ω as an unknown number.

If Ω is obtained by the boundary element method, the distributions of Ω and ∂Ω / ∂n on the boundary element are all known, so that the potential at any point in the boundary element method region (1403 in FIG. 14). And the magnetic field can be determined by integrating a given function on the boundary element.

Since the solution distribution can be accurately expressed by the boundary element method, it is possible to analyze the potential and field with high accuracy.

In the boundary element method, the accuracy tends to be poor near the boundary, but the boundary 14 on the line of symmetry in FIG.
Since 02 does not need to have a boundary element due to the condition of symmetry, the accuracy of the magnetic field at the particle position passing near the symmetry line is high, and the accuracy is not deteriorated due to the existence of the boundary. Further, according to the boundary element method, it is possible to accurately obtain a fine magnetic field distribution in an extremely narrow area.

However, this method has a problem in calculation time. In order to obtain the magnetic field at one point, it is necessary to perform integration on all boundary elements. In addition, in order to obtain the trajectory of particles, it is necessary to analyze about 10,000 times for one particle. If this is performed for many particles, the time required to find the magnetic field becomes enormous, and a high-speed computer is required. Even if it was used, it could not be completed in a practical time.

[0032]

SUMMARY OF THE INVENTION As described above, an object of the present invention is to provide a field analysis method capable of shortening the time required for field analysis that has been time-consuming in the conventional analysis. To do.

[0033]

In order to achieve the above object, the invention according to claim 1 is a method for analyzing a field such as an electric field in an analysis region by a boundary element method. The process of creating the sub-region of, the process of analyzing the value on the boundary of this sub-region from the value of the original analysis region, and the value at the predetermined position in the sub-region using the value on the boundary of the sub-region It is a method of analyzing a field, which comprises a process of

According to a second aspect of the present invention, in the process of creating the partial area, the boundary of the partial area does not have a common portion with the boundary of the original analysis area.
This is the field analysis method described.

According to a third aspect of the present invention, in the process of creating the partial area, a part of the boundary formed by the partial area matches the boundary of the original analysis area. This is the field analysis method described.

The invention according to claim 4 is characterized in that, in the process of creating the partial area, the partial area has an overlapping portion with another adjacent partial area.
This is the field analysis method described.

A fifth aspect of the present invention is an orbital analysis method, wherein the orbit of a charged particle is obtained by using the field analysis method according to any one of the first to fourth aspects.

According to a sixth aspect of the present invention, there is provided a field analysis method, which comprises a first step of analyzing the inside of an analysis region using the finite element method and a first step of providing a boundary element method region inside the analysis region. The second process, the finite element on the boundary of the boundary element method region, the third process of obtaining an unknown boundary value by the boundary element method using the boundary as the boundary element, and the boundary element method region In the method for analyzing a field, which comprises a fourth step of obtaining the values of various quantities at a predetermined position in the boundary element method based on the boundary value of the boundary element method area, the second step is an analysis by the finite element method. The step of creating two or more boundary element method areas in the area and the fourth step include the boundary based on the boundary value of the boundary element method area having the values of various quantities at a predetermined position therein. What to do in the process of obtaining by the element method It is a field method of analysis which is characterized.

The invention according to claim 7 is the field analysis method according to claim 6, characterized in that the partial areas have areas overlapping between adjacent boundary element method areas.

The invention according to claim 8 is a trajectory analysis method characterized in that the trajectory of a charged particle is obtained by using the field analysis method according to claim 6 or 7.

The invention according to claim 9 is the analysis method according to any one of claims 1 to 8, which is performed by using a computer.

[0042]

According to the present invention, the calculation time can be shortened and the accuracy is not lowered.

[0043]

Embodiments of the present invention will be described below in detail with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of a computer system in which the present invention is executed. In FIG. 1, reference numeral 101 denotes a CPU, which controls the entire system. A keyboard 102 is used for system input together with a mouse 102a. A display device 103 is composed of a CRT, a liquid crystal, or the like. 104 is RO
M and 105 are RAMs, which constitute a storage device of the system,
Stores programs executed by the system and data used by the system. 106 is a hard disk device, 107
Is a floppy disk device and constitutes an external storage device used for the file system of the system. 108
Is a printer.

In the computer system shown in FIG. 1, the field analysis of the present invention is performed.

[First Embodiment] FIGS. 2 and 3 show a first embodiment of the present invention. FIG. 2 is a flow chart showing a procedure for field analysis of the present invention, and FIG. 3 is a flow chart of the present invention. It is a figure explaining the analysis method of a field.

Although FIG. 3 corresponds to FIG. 10 of the conventional example, the calculation area 1009 shown in FIG.
It is divided into 4 partial areas of 3. Therefore, FIG.
There are new boundaries 307-309 that did not exist. Boundaries 301-304 in FIG. 3 are equal to the corresponding boundaries in FIG. Further, reference numerals 321 to 325 denote portions of the boundaries 301 to 304 corresponding to the electrode surface.

Next, the calculation procedure in the embodiment of the present invention will be described with reference to FIG. Since the flow of the whole calculation is the same, the part different from the conventional boundary element method will be explained. First 3
Boundary element method calculation in the entire region including 10 to 313 is performed using the boundaries 301 to 304 (201 in FIG. 2).
This is the same as the conventional example. Next, new boundary 3
The potential φ and its normal direction differential value q on 07-309 are the values of the entire region (φ, q on the boundaries 301-304).
(202 in FIG. 2). In this way, dividing into the partial regions and calculating the boundaries provided for the division are different from the conventional boundary element method.

Next, in calculating the electric field at a predetermined position, first, the partial region to which the position belongs is selected (204 in FIG. 2). In the case of the example of FIG. 3, this can be easily performed from the coordinate values of the points to be obtained.

When the electric field is obtained, the value of the partial region is used instead of the value of the entire region (205 in FIG. 2). That is,
Conventionally, the integral calculation was performed on the boundaries of 301 to 304 in FIG. 3, but in the present embodiment, for example, the point to be obtained is the partial region 310.
, The electric field is obtained only by integration on the boundaries 301 and 307.

The rest of the procedure is the same as the above-mentioned conventional method.

In this embodiment, the integration area required for the electric field calculation is reduced to about 1/4 of that of the conventional example. Therefore, the calculation time required to calculate the electric field is reduced to 1/4, and as a result,
This has the effect of reducing the calculation time itself required for trajectory calculation to 1/4.

In this embodiment, the step 202 in FIG. 2 is added, but the number of calculations in 202 in FIG.
It is negligible compared to the number of calculations in 205 of FIG.

Further, in the present embodiment, the division into four partial areas is carried out, but a larger effect can be obtained by dividing into more partial areas.

FIG. 3 is a schematic diagram different from the actual scale for convenience of description, but since the ratio of the vertical width to the horizontal length is about 1: 100 in practice, the partial region shown this time is shown. It is extremely reasonable to make many partial regions of the above equation 4 or more.

[Second Embodiment] A second embodiment of the present invention is shown in FIG.

In this embodiment, four partial areas are created as in the first embodiment. However, these partial areas have overlapping portions 441 to 443 between adjacent partial areas. Different.

The first partial area comprises areas 410 and 441 and has boundaries 401, 421 and 432. The second partial area is composed of areas 441, 411 and 442, and has a boundary 43.
1, 421, 402, 422, 434. The third partial region includes regions 442, 412, 443 and has boundaries 433, 422, 403, 423, 436. Fourth
Boundaries 435, 42.
It has 3,404.

Next, the calculation procedure will be described. The calculation procedure is the same as in FIG. That is, at 202 in FIG.
Calculation is performed for 1 to 436. However, in FIG.
Since the method of selecting a partial area in the above is different from that in the first embodiment, this will be described with reference to FIG. FIG. 5 shows a connecting portion between the first partial area and the second partial area in FIG. Since the two partial areas overlap at the connecting part,
It is necessary to have a criterion to decide which one to select. In FIG. 5, the connecting portion formed by the reference numerals 511 and 512 is divided into two by a boundary 501 indicating a position near the center of the boundaries 431 and 432.
It is divided. The boundary 501 is merely provided as a reference for determining the position.

In the case where the particle position is on the left side of the boundary 501, that is, in the area of the connecting portion 511, the first partial area is selected and the boundary 50
On the right side of 2, that is, in the area of the connecting portion 512, the second partial area is selected.

The other calculation procedure is the same as that of the first embodiment.

In the boundary element method, the electric field calculation accuracy is generally poor near the boundary. That is, in the first embodiment, when particles pass near the boundaries 307 to 309 of FIG. 3, an error occurs in the trajectory calculation. But,
In the second embodiment, since it is not necessary to calculate the electric field in the vicinity of the boundaries 431 to 436, the error as in the first embodiment does not occur. That is, according to the second embodiment, the effect of shortening the calculation time can be obtained without lowering the accuracy of the trajectory calculation.

The length of the connecting portion (boundaries 431 and 432)
(Distance of) is more than twice the size of the boundary element created on the boundaries 431 and 432, and the selection reference boundary 5
By setting 01 near the center of both, it is possible to avoid an electric field calculation error near the boundary.

[Third Embodiment] FIG. 6 shows a third embodiment of the present invention.
Shown in Reference numerals 601 to 604 are electrodes, to which a predetermined potential is applied. At this time, the case where the electric field distribution in the area indicated by reference numeral 621 is calculated in detail is shown. As the calculation procedure, first, the boundary element method calculation indicated by 201 in FIG. 2 is performed. This is because the known potential φ is given to the boundaries 601 to 604 which are the electrode surfaces, and the normal direction differential q of the potential is given to the other boundaries 611 to 614 as zero, and the q at the boundaries 601 to 604 and the boundaries 611 to 614 are given. Is a calculation for obtaining φ of. Next, a boundary 622 surrounding the area 621 in which the electric field is to be calculated is created, and φ and q on this boundary are defined by the boundary 60.
1 to 604, 611 to 614 (20 in FIG. 2)
2). Then, the electric field at a point in the region 621 is
It is calculated by using φ and q on 2 and integrating on the boundary (205 in FIG. 2). In this case, the area 621
The electric field inside can be significantly shortened in calculation time as compared with the case where it is calculated using the boundaries 601 to 604 and 611 to 614. In the present embodiment, φ and q on the boundary 622 need to be calculated, which requires extra calculation time, but when the number of times the electric field is calculated in the region 621 is large, the boundaries 601 to 604 are required. , 611 to 614 can be used to reduce the calculation time as a whole.

Although the boundary 622 is shown as a quadrangle in FIG. 6, the shape of the boundary is not limited to the quadrangle. For example, the shape of the boundary may be a circle, a combination of straight lines and arcs, or a curved line. In the boundary element method, the accuracy tends to be poor in the vicinity of the corner, so that the boundary having such a shape has an advantage that the calculation accuracy is good.

[Fourth Embodiment] An embodiment in which a magnetic field is analyzed by the finite element method using the boundary element method will be described.

In FIG. 7, reference numerals 1301, 1302,
1201 and 1202 show the same thing as FIG.
Reference numerals 701 to 703 are boundary element method regions, respectively, and
Boundary element method area 701 of
Have 4. The second boundary element method region 702 has a boundary 71
It has 7,712,718,715. The third boundary element method region 703 has 718, 713, and 716. The boundaries 711 to 718 of the boundary element method region are made to coincide with the element division boundaries of the finite element method. Hereinafter, the process of performing the boundary element method calculation using the values obtained by the finite element method is the same as that in the case of FIG. However, in the fourth embodiment, since there are three boundary element method regions, the difference is that it is necessary to perform each of the three regions.

When the potential Ω on the boundaries 711 to 718 (or the boundaries 714 to 716 are excluded) and its differential value in the normal direction ∂Ω / ∂n are obtained in this way, the value of the magnetic field at an arbitrary point is as follows. To ask.

1. The boundary element method area in which the point to be obtained exists is discriminated and selected from 701 to 703. This can be easily done from the coordinate values of the points.

2. The magnetic field at that point is obtained using only the information of the boundary element method area including that point. According to the fourth embodiment, the integral region required for calculating the magnetic field is reduced to about 1/3. That is, in the conventional example, the boundaries of 711 to 716 are integration regions, but in the fourth embodiment, for example, in the first boundary element method region, only 711, 714, and 717 are required. If the integration area decreases, the amount of calculation decreases in proportion to it.

In the fourth embodiment, the first boundary element method calculation is performed three times and the number of times increases, but the scale of each boundary element method calculation decreases, so that the calculation amount also decreases in that process, which causes a problem. Absent. Normally, the amount of magnetic field calculation during orbit calculation is dominant, so the total calculation time decreases in inverse proportion to the number of boundary element method regions.

Further, in this embodiment, the case where the number of the boundary element method regions is three is shown for ease of explanation, but in actuality, the region through which charged particles pass, that is, 1403 in FIG. 14 is 1: 100. Since it is extremely long and narrow, it is reasonable to set the number of boundary element method regions to 10 or more, and in that case, the calculation time can be shortened to 1/10 or less.

[Fifth Embodiment] FIG. 8 shows a fifth embodiment.

Reference numerals 1301, 1302, 1201, 12
02 is the same as FIG. 14 and FIG. 7. Reference numerals 811 to 824
Indicates a boundary, and reference numerals 801 to 805 indicate regions. In the fifth embodiment, there are three boundary element method areas, and adjacent boundary element method areas have overlapping areas 802 and 804. That is, the first boundary element method area is composed of areas 801, 802 and has boundaries 811, 812, 822, 816, 817. The second boundary element method area includes areas 802 to 804, and boundaries 812 to 814, 817 to 819, 821, 8
Has 24. The third boundary element method area is the areas 804 and 80.
5 boundaries, boundaries 814, 815, 819, 820, 8
Have 23. All the boundaries 811 to 824 coincide with the finite element boundaries. The boundary element method calculation for obtaining the potential on the boundary element is performed for each of the three boundary element method regions as in the case of the first embodiment.

The magnetic field at an arbitrary point is as follows.

1. Select the boundary element method region to be used to find the point.

When the point is included in only one boundary element area, the boundary element method area is selected.

If the point is within the overlapping area, the position is used for the determination.

This will be described with reference to FIG. FIG. 9 shows FIG.
Part 1 of is expanded. If it is in the area 801, the first boundary element method area is selected, and if it is in the area 803, the second boundary element method area is selected.

When the point exists in the overlap area 802, if the point is on the left side of the line 901, the first boundary element method area, and if it is on the right side of the line 901, the second overlap is established. Select the element method area. Line 901 is border 82
Provided near the center of 1 and 822.

2. When the boundary element method area is determined, the magnetic field is obtained using only the information of the boundary element method area.

The fifth embodiment has the following advantages as compared with the fourth embodiment. That is, in the fourth embodiment, when particles are located near the boundary 717 or 718 shown in FIG. 7, the accuracy of the magnetic field calculation by the boundary element method becomes poor, but in the fifth embodiment, the magnetic field is generated near the boundary. Since the calculation is avoided, the calculation accuracy does not decrease.
On the other hand, the effect of shortening the calculation time is almost the same as that of the fourth embodiment.

A method of providing the overlapping portion will be described. Normal,
When the field is calculated by the boundary element method, if an appropriate method is used, the error is sufficiently small if it is separated from the boundary by the size of the boundary element or more. Therefore, the width of the overlap region (eg, the boundary 821)
And 822)) is more than twice the size of the boundary element,
An area selection determination boundary such as 901 in FIG. 9 may be set in the middle.

The embodiment described above is implemented by a program in the computer system shown in FIG.
This program is stored in the hard disk 106 or ROM 10.
4, stored and stored in the RAM 105, the CPU 10
It is executed in 1.

Although all of the embodiments described above relate to the electric field and the magnetic field, the method according to the present invention can be similarly applied to the analysis of fields other than the electric field and the magnetic field such as stress deformation.

The present invention also includes a two-dimensional analysis, an axisymmetric analysis,
Although it can be applied and effective for any of the three-dimensional analysis, the time-saving effect is the greatest in the three-dimensional analysis.

[0087]

As described above, according to the present invention, the following effects can be obtained.

1. The calculation time required for field analysis can be shortened.

2. The accuracy is not reduced.

Boundary element calculation is performed using the finite element analysis result, and the calculation time for obtaining various quantities such as the potential and the field is significantly shortened, and highly accurate calculation can be executed within the practical time. Has the effect of enabling.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a system for carrying out the present invention.

FIG. 2 is a flowchart for determining a particle trajectory using field analysis according to the present invention.

FIG. 3 is a diagram illustrating obtaining an electric field according to the present invention.

FIG. 4 is a diagram for explaining obtaining another electric field according to the present invention.

FIG. 5 is a partially enlarged view of FIG.

FIG. 6 is a diagram illustrating obtaining an electric field according to the present invention.

FIG. 7 is a diagram illustrating obtaining a magnetic field according to the present invention.

FIG. 8 is a diagram for explaining obtaining another magnetic field according to the present invention.

9 is a partially enlarged view of FIG.

FIG. 10 is a diagram for explaining obtaining a conventional electric field.

FIG. 11 is a flowchart for obtaining a particle trajectory using conventional field analysis.

FIG. 12 is a diagram showing a magnetic field generator used for converging electron trajectories.

FIG. 13 is a diagram for explaining obtaining a conventional magnetic field.

FIG. 14 is a diagram illustrating obtaining a conventional magnetic field.

FIG. 15 is a diagram for explaining obtaining a conventional magnetic field.

[Explanation of symbols]

 101 CPU 102 Keyboard 102a Mouse 103 Display Device 104 ROM 105 RAM 106 Hard Disk Device 107 Floppy Disk Device 108 Printer 321 to 325 Electrode 601 to 604 Electrode 1201 Magnetic Core 1202 Coil

Claims (9)

[Claims] 1. A method for analyzing a field such as an electric field in an analysis region by the boundary element method, wherein a process of creating one or more partial regions in the analysis region and a value on the boundary of the partial regions are also included. And a process of analyzing the value at a predetermined position in the partial region by using a value on the boundary of the partial region. 2. In the process of creating the partial area,
2. The field analysis method according to claim 1, wherein the boundary of the partial area does not have a common portion with the boundary of the original analysis area. 3. In the process of creating the partial area,
2. The field analysis method according to claim 1, wherein a part of the boundary formed by the partial areas matches the boundary of the original analysis area. 4. In the process of creating the partial area,
The field analysis method according to any one of claims 1 to 3, wherein the partial region has an overlapping portion with another adjacent partial region. 5. A trajectory analysis method, wherein the trajectory of a charged particle is obtained by using the field analysis method according to any one of claims 1 to 4. 6. A field analysis method, comprising a first process of analyzing the inside of an analysis region using a finite element method, a second process of providing a boundary element method region inside the analysis region, and a boundary. The finite element on the boundary of the element method region is used as the boundary element, and the third process of obtaining an unknown boundary value by the boundary element method using the values obtained by the finite element method, In a method of analyzing a field, which comprises a fourth step of obtaining a quantity value by a boundary element method based on a boundary value of a boundary element method area, the second step comprises two or more in an analysis area by the finite element method Of the boundary element method region, and the fourth step is a step of obtaining values of various quantities at a predetermined position by the boundary element method based on the boundary value of the boundary element method region having the position inside thereof. Field solutions characterized by doing Analysis method. 7. The field analysis method according to claim 6, wherein the partial areas have areas overlapping between adjacent boundary element method areas. 8. A trajectory analysis method, characterized in that a trajectory of a charged particle is obtained by using the field analysis method according to claim 6. 9. The method according to claim 1, which is performed by using a computer.
The analysis method according to any one of items.