JP2021131766A - Magnetic field analysis method, magnetic field analysis device, and program - Google Patents

Abstract

To provide a magnetic field analysis method capable of shortening a calculation time of iterative calculation for obtaining a magnetic field using an iteration method.SOLUTION: One time step of an iterative calculation, which calculates a magnetic field of an evaluation point inside each of a plurality of polyhedral elements representing an analysis model by iteration method, includes: obtaining a second magnetic field vector representing a magnetic field of each of a plurality of evaluation points after one time step on the basis of a first magnetic field vector representing a current magnetic field of each of the evaluation points; obtaining a magnetic field change vector representing a change in the magnetic field from the first magnetic field vector to the second magnetic field vector; and setting a vector, which is obtained by adding a vector obtained by increasing the size of the magnetic field change vector obtained in the current time step without changing its direction to the first magnetic field vector, as a first magnetic field vector used in the next time step when an angle formed by a magnetic field change vector obtained in a current time step and a magnetic field change vector obtained in an immediately preceding time step is less than 90°.SELECTED DRAWING: Figure 3

Description

The present invention relates to a magnetic field analysis method, a magnetic field analyzer, and a program.

Simulation based on the transfer group molecular dynamics method, which is a development of the molecular dynamics method to handle macroscale systems, as a method for exploring the phenomena of material science in general using a computer based on classical mechanics and quantum mechanics. Is known (see, for example, Patent Document 1). Since the particle method such as the molecular dynamics method can handle not only static phenomena but also dynamic phenomena such as flow, it is attracting attention as an alternative simulation method to the finite element method that mainly analyzes static phenomena. Has been done. For example, by applying a magnetic moment to each particle and calculating a magnetic physical quantity using an exact solution based on the spherical symmetry of each particle, it is possible to obtain relatively accurate simulation results at high speed. The bead method has been proposed (see, for example, Patent Document 2).

In the above-mentioned magnetic bead method, an object is divided into a plurality of elements, each element is regarded as a spherical particle, and a magnetic field is calculated using an exact solution based on spherical symmetry. At this time, if the object is to be filled with a plurality of particles, a gap is generated between the particles, so that an error due to the gap or the spherical particles may occur. In order to improve the calculation accuracy, a method has been proposed in which an object can be divided by polyhedral elements such as a cube without gaps and the calculation time can be shortened (see, for example, Patent Document 3).

Japanese Unexamined Patent Publication No. 2009-37334 JP-A-2015-111401 JP-A-2017-194884

In magnetic field analysis using the magnetic bead method, the iterative method is generally used. In the iterative method used in the magnetic bead method, magnetization is applied to each particle of the magnetic field analysis model, and the equation of motion that converges the magnetic field at the evaluation point in each particle to the optimum solution is numerically iteratively calculated and solved. It is desired to reduce the calculation time of this iterative calculation.

An object of the present invention is to provide a magnetic field analysis method, a magnetic field analyzer, and a program capable of shortening the calculation time of the iterative calculation for obtaining a magnetic field by using an iterative method.

According to one aspect of the invention
This is a magnetic field analysis method for calculating the magnetic field of the evaluation points inside each of the plurality of polyhedral elements of the analysis model divided into a plurality of polyhedral elements by the iterative method.
One time step of iterative calculation is
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. A magnetic field analysis method is provided that includes a procedure of adding a vector whose magnitude has been increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step.

According to another aspect of the invention
A magnetic field analyzer having a magnetic field calculation unit that calculates the magnetic field of the evaluation point inside each of the plurality of polyhedral elements by an iterative method of an analysis model divided into a plurality of polyhedral elements.
The magnetic field calculation unit is used in one time step of the iterative calculation.
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. Provided is a magnetic field analyzer that executes a procedure of adding a vector whose magnitude has been increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step.

According to yet another aspect of the invention.
A program that causes a computer to execute a procedure of calculating the magnetic field of the evaluation point inside each of the plurality of polyhedral elements by the iterative method of the analysis model divided into a plurality of polyhedral elements.
In one time step of iterative calculation
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. A program is provided that causes a computer to execute a procedure of adding a vector whose magnitude has been increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step.

By setting the vector obtained by adding the vector whose magnitude is increased to the first magnetic field vector as the first magnetic field vector to be used in the next time step without changing the direction of the magnetic field change vector obtained in the current time step. It is possible to shorten the calculation time of the iterative calculation.

FIG. 1 is a block diagram of a magnetic field analyzer according to this embodiment. FIG. 2A is a schematic diagram of a state in which a magnetic material to be analyzed arranged in a virtual space is divided into a plurality of voxels, and FIG. 2B is a schematic diagram showing a plurality of evaluation points arranged in one voxel. It is a figure. FIG. 3 is a flowchart showing a magnetic field analysis method according to an embodiment. FIG. 4 is a schematic diagram showing the relationship between the i-th voxel and the j-th voxel. FIG. 5 is a schematic diagram showing various magnetic field vectors obtained in one time step of the iterative calculation in the magnetic field vector space. FIG. 6 is a schematic diagram showing various magnetic field vectors obtained in one time step of the iterative calculation in the magnetic field vector space. FIG. 7 is a perspective view of the analysis model. 8A and 8B are graphs showing changes in the magnetic field of a voxel on the virtual time axis. FIG. 9 is a graph showing changes in the virtual time axis between the provisional magnetic field vector and the second magnetic field vector as a result of performing the magnetic field analysis without applying the multi-time step method in step S15 of FIG. FIG. 10 is a graph showing the results of magnetic field analysis by a method according to an example, a method in which the FIRE method is applied and the multi-step method is not applied, and a method in which neither the FIRE method nor the multi-step method is applied.

FIG. 1 is a block diagram of the magnetic field analyzer 30 according to this embodiment. The magnetic field analysis device 30 according to the present embodiment includes a processing device 20, a storage device 25, an input device 28, and an output device 29. The processing device 20 includes an analysis information acquisition unit 21, a voxel division unit 22, a magnetic field calculation unit 23, and an output control unit 24.

Each block shown in FIG. 1 can be realized by an element such as a central processing unit (CPU) of a computer or a mechanical device in terms of hardware, and can be realized by a computer program or the like in terms of software. .. FIG. 1 shows a functional block realized by cooperation of hardware and software. Therefore, these functional blocks can be realized in various aspects by a combination of hardware and software.

The processing device 20 is connected to the input device 28 and the output device 29. The input device 28 receives input of commands and data from a user related to the processing executed by the processing device 20. As the input device 28, for example, a keyboard or mouse that inputs by the user, a communication device that inputs via a network such as the Internet, a reading device that inputs from a recording medium such as a CD or DVD, or the like is used. Can be done. The output device 29 outputs the analysis result under the control of the processing device 20. As the output device 29, for example, a display device for displaying an image, a communication device for transmitting data via a network such as the Internet, a writing device for recording data on a recording medium such as a CD or DVD, or the like can be used.

The analysis information acquisition unit 21 acquires magnetic field analysis information via the input device 28. The magnetic field analysis information includes various information necessary for the magnetic field analysis. For example, information that defines the shape and physical property values of the analysis object defined in the virtual space, information that divides the analysis object into boxels, information that defines the external magnetic field, and parameters that should be defined for analysis. Values etc. are included.

The function of the voxel dividing unit 22 will be described with reference to FIGS. 2A and 2B.
FIG. 2A is a schematic view of a state in which a magnetic material to be analyzed arranged in a virtual space is divided into a plurality of voxels 40, and FIG. 2B is a plurality of evaluation points 41 arranged in one voxel 40. It is a schematic diagram which shows.

As shown in FIG. 2A, the voxel dividing unit 22 divides the magnetic material arranged in the virtual space into a plurality of voxels 40 based on the magnetic field analysis information. In FIG. 2A, the distribution of voxels 40 is represented two-dimensionally, but in reality, the magnetic material has a three-dimensional shape, and a plurality of voxels 40 are arranged in a three-dimensional space. Further, in FIG. 2A, one voxel 40 is represented by a square, but when expanded three-dimensionally, the voxel 40 becomes a regular hexahedron. The voxel 40 may be a polyhedron other than a regular hexahedron. For example, the voxels 40 may be arranged by dividing the magnetic material into Voronoi diagrams. The voxel dividing unit 22 assigns each of the voxels 40 a voxel identifier (voxel ID) for identifying one voxel. A serial number i starting from 1 is used as the voxel identifier.

The voxel dividing unit 22 further arranges a plurality of evaluation points 41 inside each of the voxels 40 as shown in FIG. 2B. The evaluation point 41 is arranged, for example, at the midpoint of the perpendicular line drawn from the center of gravity of the voxel 40 to each surface. The number of evaluation points 41 arranged inside one voxel 40 is equal to the number of planes constituting the surface of the polyhedron voxel 40. For example, six evaluation points 41 are arranged inside the regular hexahedron voxel 40. The reason why a plurality of evaluation points 41 are arranged in one voxel 40 is to keep the magnetic field analysis accuracy high.

The voxel dividing unit 22 assigns an evaluation point identifier (evaluation point ID) to a plurality of evaluation points 41 arranged inside each of the voxels 40. A serial number p starting from 1 is used as the evaluation point identifier. One of the plurality of evaluation points 41 is specified by a pair of a voxel identifier and an evaluation point identifier.

The magnetic field calculation unit 23 applies magnetization to each of the plurality of evaluation points 41, and calculates the magnetic field generated at each evaluation point 41. As shown in FIG. 2B, the magnetization vector assigned to the p-th evaluation point 41 (i, p) inside the i-th voxel 40 (i) is referred to as _Mip. The evaluation points 41 (i, p) the unit normal vector of the outward surface corresponding to the denoted as n _ip. The procedure performed by the magnetic field calculation unit 23 will be described later with reference to FIGS. 3 to 6.

The output control unit 24 outputs the analysis result, for example, the calculation result of the magnetic field for each evaluation point 41 stored in the storage device 25 to the output device 29.

FIG. 3 is a flowchart showing a magnetic field analysis method according to an embodiment.
First, the analysis information acquisition unit 21 (FIG. 1) acquires the analysis conditions, and the voxel division unit 22 (FIG. 1) divides the magnetic material to be analyzed into a plurality of voxels 40 (FIG. 2A) (step S11). Further, the voxel dividing unit 22 arranges a plurality of evaluation points 41 (FIG. 2B) inside each of the plurality of voxels 40 (step S11).

Next, the magnetic field calculation unit 23 (FIG. 1) repeats the calculation of the magnetic field for one time step from step S12 to step S16 for each of the evaluation points 41 until the calculation for all the evaluation points 41 is completed ( Steps S17 and S18). The calculation of the magnetic field for one time step for all the evaluation points 41 is repeated until the calculation result of the magnetic field converges (steps S19 and S20). When the calculation result of the magnetic field converges, the analysis is completed and the analysis result is output to the output device 29 (FIG. 1) (step S21).

Before explaining the processing from step S12 to step S16, a method of calculating the magnetic field by the iterative method will be described.

ここで、Ｈ_ｉｐは、ｉ番目のボクセル４０（ｉ）内のｐ番目の評価点４１（ｉ，ｐ）（図２Ｂ）に付与されている磁場ベクトルである。α_ｉｐは、評価点４１（ｉ，ｐ）の磁場を時間発展させるときに用いる仮想質量である。λ_ｉはラグランジュの未定乗数である。γは人工的に付与された減衰定数である。 In the iterative method, the equation of motion that converges the magnetic field to the optimum solution is numerically solved. This equation of motion is expressed by the following equation.

Here, _Hip is a magnetic field vector applied to the p-th evaluation point 41 (i, p) (FIG. 2B) in the i-th voxel 40 (i). α _ip is a virtual mass used when the magnetic field at the evaluation point 41 (i, p) is time-evolved. λ _i is the Lagrange multiplier. γ is an artificially assigned attenuation constant.

The magnetic field vector H ( _rip ) is a magnetic field generated at the position of the evaluation point 41 (i, p) by the magnetization in the magnetic body and the external magnetic field. _{The magnetic field vector H (rip} ) on the right side of the equation (1) will be described with reference to FIG.

FIG. 4 is a schematic diagram showing the relationship between the i-th voxel 40 (i) and the j-th voxel 40 (j). _{Magnetization M jq} is given to the q-th evaluation point 41 (j, q) of the j-th voxel 40 (j). When the magnetic susceptibility of a magnetic material is expressed as χ, the magnetization M _jq is expressed by the following equation by the magnetic field H _jq.

ここで、ΔＳ_ｊｑ及びｎ_ｊｑは、それぞれボクセル４０（ｊ）の評価点４１（ｊ，ｑ）に対応する表面の面積及び外側を向く単位法線ベクトルである。Ｈ_{ｅｘｔ，ｉｐ}は、評価点４１（ｉ，ｐ）の位置における外部磁場を表す磁場ベクトルである。ｑに関するシグマは、ｊ番目のボクセル４０（ｊ）内のすべての評価点４１（ｊ、ｑ）についての和をとることを意味する。ｊに関するシグマは、すべてのボクセル４０（ｊ）についての和をとることを意味する。 The position vector of the evaluation point 41 (i, p) _{is referred to as r ip,} and the position vector of the evaluation point 41 (j, q) is referred to _{as r jq.} A magnetic field is generated at the position of the evaluation point 41 (i, p) by _{the magnetization M jq of the} evaluation point 41 (j, q). _{The magnetic field H (rip} ) generated at the evaluation points 41 (i, p) by the magnetization applied to all the evaluation points 41 in the magnetic body is expressed by the following equation.

Here, ΔS _jq and n _jq are the area of the surface corresponding to the evaluation point 41 (j, q) of the voxel 40 (j) and the unit normal vector facing outward, respectively. H _{ext, ip} is a magnetic field vector representing an external magnetic field at the position of evaluation point 41 (i, p). The sigma with respect to q means to take the sum of all the evaluation points 41 (j, q) in the j-th voxel 40 (j). Sigma with respect to j means to take the sum for all voxels 40 (j).

ここで、式（４）の右辺のｐに関するシグマは、ｉ番目のボクセル４０（ｉ）内のすべての評価点４１について和をとることを意味する。 The right side of C _{i (M p)} of the formula (1) is the i th volume integral of the divergence of the magnetization vector in the interior of the voxel 40 (i), and replaced with a surface integral by Gauss divergence theorem, the following It is expressed by the formula of.

Here, the sigma regarding p on the right side of the equation (4) means that all the evaluation points 41 in the i-th voxel 40 (i) are summed.

Next, the physical meaning of the equation (1) will be described.
The left side of the equation (1) corresponds to an acceleration term representing the acceleration of the change in the magnetic field H. The first term on the right side corresponds to the spring force, the second term corresponds to the external force, and the fourth term corresponds to the damping term. The third term on the right side is a binding term that represents the binding condition of the equation of motion. The equation of motion shown in equation (1) is subject to a binding condition that the divergence of magnetization is zero inside each of the voxels 40 by the third term on the right side. When the calculation result of the magnetic field is converged, the acceleration term, the attenuation term, and the constraint term become zero. In this state, the magnetic field _Hip at the evaluation point 41 (i, p) becomes equal to the magnetic field generated at the position of the evaluation point 41 (i, p) due to the magnetization applied to the evaluation point in the magnetic body.

In the iterative method, the equation of motion of Eq. (1) is numerically iteratively calculated with a certain virtual time step width, and the time change of the _{magnetic field Hip is obtained for each evaluation point 41.} At this time, _{the calculation result of the magnetic field Hip} converges to the optimum value with the passage of time. The SHAKE method (JM Thyssen "computational physics") is known as a method for solving equations of motion with binding conditions. In the SHAKE method, the equation of motion is first solved without imposing a binding condition, and then the binding condition is added. In the method according to the examples described below, the SHAKE method is applied.

Next, the procedure from step S12 to step S16 shown in FIG. 3 will be described. In the description of this procedure, reference will be made to FIGS. 5 and 6 as necessary.
5 and 6 are schematic diagrams showing various magnetic field vectors obtained in one time step of the iterative calculation in the magnetic field vector space.

_{First, the first magnetic field vector H1 ip} (n) at the evaluation point 41 (i, p) at the end of the nth time step (current time) without imposing the binding condition of the equation of motion of the equation (1), and the current time. The provisional magnetic field vector HT ip ( _{provisional magnetic field vector HT ip,} which is a magnetic field vector obtained by developing the magnetic field generated at the evaluation points 41 (i, p) by one time step based on the _{magnetization vector M jq} given to each evaluation point 41 in Calculate n + 1). Hereinafter, the calculation method of the provisional magnetic field vector HT _ip (n + 1) will be described.

ここで、δｔは仮想時間の刻み幅であり、Ｆ_ｉｐ（ｎ）は以下の式で定義される。

式（５）〜（７）を用いて、第１磁場ベクトルＨ１_ｉｐ（ｎ）を１タイムステップ分だけ時間発展させた暫定磁場ベクトルＨＴ_ｉｐ（ｎ＋１）を求めることができる。 The following equation is obtained by discretizing the equation of motion (1), which does not impose a binding condition, by the leapfrog method.

Here, .DELTA.t is the step size of the virtual time, F _{ip (n)} is defined by the following equation.

Using equations (5) to (7), it is possible to obtain _{the provisional magnetic field vector HT ip (n + 1) obtained by evolving the first magnetic field vector H1 ip} (n) by one time step.

After obtaining the provisional magnetic field vector HT _{ip (n + 1), the provisional magnetic field vector HT ip} (n + 1) is updated until the binding condition of the equation of motion (1) is satisfied, and the magnetic field satisfying the binding condition (second magnetic field vector H2 _ip (second magnetic field vector H2 ip). Find n + 1)).

ここで、式（８）の右辺の暫定磁場ベクトルＨＴ_ｉｐ（ｎ＋１）は反復計算による更新前のベクトルを表し、左辺の暫定磁場ベクトルＨＴ_ｉｐ（ｎ＋１）は反復計算による更新後のベクトルを表す。式（９）の右辺の磁化ベクトルＭＴ_ｑ（ｎ＋１）は、暫定磁場ベクトルに磁化率χを乗じたものである。 The second magnetic field vector H2 _ip (n + 1) can be obtained by iteratively calculating the following equation until the calculation results converge.

_{Here, the provisional magnetic field vector HT ip} (n + 1) on the right side of the equation (8) represents the vector before the update by the iterative calculation, and the provisional magnetic field vector HT _ip (n + 1) on the left side represents the vector after the update by the iterative calculation. _{The magnetization vector MT q} (n + 1) on the right side of equation (9) is the provisional magnetic field vector multiplied by the magnetic susceptibility χ.

Equation (8), the provisional magnetic field vector _{HT ip} convergence value of the temporary magnetic field vector _{HT ip} obtained by iterative calculation until convergence is equivalent to the second magnetic field vector _H2 ip (n + 1).

When the second magnetic field vector H2 _ip (n + 1) is obtained, the magnetic field calculation unit 23 (FIG. 1) determines the rate of change of the magnetic _{field from the second magnetic field vector H2 ip} (n + 1) to the first magnetic field vector H1 _{ip (n).} Calculate (step S14). The rate of change of the magnetic field is expressed by the following equation.

Subsequently, the multi-time step method is applied _{to calculate the first magnetic field vector H1 ip} (n + 1) in the next time step (step S15). The calculation in step S15 will be described with reference to FIGS. 5 and 6.

２つの速度ベクトルのなす角度が９０°未満の場合、内積Ｑは正の値をとる。図５は、内積Ｑが正の場合を示している。２つの速度ベクトルのなす角度が９０°より大きい場合、内積Ｑは負の値をとる。図６は、内積Ｑが負の場合を示している。２つの速度ベクトルのなす角度が９０°に等しい場合、内積Ｑはゼロになる。 First, the inner product Q of the velocity vector of the change of the magnetic field obtained most recently and the velocity vector of the change of the magnetic field obtained in the previous time step is calculated. The inner product Q is expressed by the following equation.

If the angle between the two velocity vectors is less than 90 °, the inner product Q takes a positive value. FIG. 5 shows a case where the inner product Q is positive. If the angle between the two velocity vectors is greater than 90 °, the inner product Q takes a negative value. FIG. 6 shows a case where the inner product Q is negative. If the angles formed by the two velocity vectors are equal to 90 °, the inner product Q becomes zero.

The vector obtained by multiplying the velocity vector of the magnetic field change by the step width δt of the virtual time is the _{amount of change of the vector from the first magnetic field vector H1 ip} (n) to the second magnetic field vector H2 _ip (n + 1) (hereinafter, the magnetic field change vector). It corresponds to.). Instead of equation (11), the inner product of the current magnetic field change vector and the magnetic field change vector obtained in the immediately preceding time step may be calculated. The angle formed by the two velocity vectors of the magnetic field change is equal to the angle formed by the two magnetic field change vectors.

ここで、ｆはマルチステップ法で適用される伸長短縮係数である。 Based on the following equation, the first magnetic field vector H1 _ip (n + 1) used in the next time step is calculated.

Here, f is an extension / shortening coefficient applied by the multi-step method.

As shown in FIG. 5, when the angle between the current velocity vector of the magnetic field change and the velocity vector of the magnetic field change obtained in the immediately preceding time step is less than 90 °, the elongation shortening coefficient f is made larger than 1. At this time, the vector obtained by adding the vector whose magnitude is increased without changing the direction of the magnetic field change vector obtained in the current time step to the first magnetic field vector H1 _{ip (n) is used in the next time step.} It is set as the magnetic field vector H1 _ip (n + 1).

As shown in FIG. 6, when the angle between the current velocity vector of the magnetic field change and the velocity vector of the magnetic field change obtained in the immediately preceding time step is larger than 90 °, the elongation shortening coefficient f is made smaller than 1. At this time, the vector obtained by adding the vector whose magnitude is reduced without changing the direction of the magnetic field change vector obtained in the current time step to the first magnetic field vector H1 _{ip (n) is used in the next time step.} It is set as the magnetic field vector H1 _ip (n + 1).

When the first magnetic field vector H1 _ip (n + 1) to be used in the next time step is obtained, the FIRE method (fast inertial relaxation engine) for shortening the calculation time is applied (step S16). The FIRE method is described in Erik Bitzek, Pekka Koskinen, Franz Gahler, Michael Moseler, and Peter Gumbsch, “Structural Relaxation Made Simple”, Physical Review Letters, 97, 170201 (2006).

Next, the FIRE method will be briefly described. When the inner product of the velocity vector of the change in the magnetic field and the acceleration vector is positive or zero, the virtual mass α _ip is made smaller than the current value. On the contrary, when the inner product of the velocity vector and the acceleration vector of the magnetic field is negative, the virtual mass α _ip is made larger than the current value. Hereinafter, the physical meaning of changing the virtual mass will be described.

When the inner product of the velocity vector of the magnetic field and the acceleration vector is positive or zero, the angle formed by the velocity vector and the acceleration vector is 90 ° or less. At this time, it is considered that the calculation result of the magnetic field is approaching the convergence value. In this case, if the virtual mass α _ip is reduced, the amount of change in the magnetic field becomes large, and the calculation result of the magnetic field approaches the convergence value faster. When the inner product of the velocity vector and the acceleration vector of the magnetic field is negative, the angle formed by the velocity vector and the acceleration vector is larger than 90 °. At this time, it is considered that the calculation result of the magnetic field is far from the convergence value. In this case, when the virtual mass α _ip is increased, the amount of change in the magnetic field becomes smaller, and the speed at which the calculation result of the magnetic field moves away from the convergence value becomes slower.

Next, the excellent effect of the above embodiment will be described.
In the above embodiment, since the FIRE method is applied in step S16 shown in FIG. 3, the convergence of the calculation result of the magnetic field can be accelerated. As a result, the calculation time can be shortened.

As shown in FIG. 5, when the angle between the magnetic field change velocity vector obtained in the current time step and the magnetic field change velocity vector obtained in the immediately preceding time step is less than 90 °, the magnetic field calculation result is obtained. Is considered to be approaching the convergence value. At this time, by making the extension / shortening coefficient f of the equation (12) larger than 1, the calculation result of the magnetic field can be brought closer to the convergence value more quickly. As a result, the calculation time can be shortened.

As shown in FIG. 6, when the angle between the magnetic field change velocity vector obtained in the current time step and the magnetic field change velocity vector obtained in the immediately preceding time step is larger than 90 °, the magnetic field calculation result is It is unknown whether it is approaching the convergence value. At this time, by setting the extension / shortening coefficient f of the equation (12) to less than 1, it is possible to prevent the calculation result of the magnetic field from deviating significantly from the convergence value. As a result, the calculation time can be shortened.

Next, with reference to FIGS. 7 to 10, the results of magnetic field analysis performed to confirm the excellent effects of the above examples will be described.

FIG. 7 is a perspective view of an analysis model that is the target of magnetic field analysis. The shape of the magnetic material used as the analysis model was a cube with a side length of 10 mm. It is assumed that this magnetic material is made of a linear magnetic material whose magnetization is proportional to the magnetic field. A spatially uniform external magnetic field _ext parallel to one ridge of the analytical model was given to the analytical model. The magnitude of the external magnetic field _{ext was 0.1 T.}

First, the magnetic field analysis was performed without applying the multi-time step method of step S15 in FIG. In this magnetic field analysis, the elongation / shortening coefficient f shown in FIGS. 5 and 6 is always 1. That is, the second magnetic field vector H2 _ip (n + 1) is set as the first magnetic field vector H1 _ip (n + 1) to be used in the next time step.

8A and 8B are graphs showing changes in the magnetic field of one voxel 40 (FIG. 2A) on the virtual time axis. The horizontal axis represents the number of time steps, and the vertical axis represents the magnitude of magnetization in the unit "A / m". FIG. 8B is an enlarged view of the vicinity of the origin on the horizontal axis of FIG. 8A. For comparison, the results of the analysis performed in step S16 of FIG. 3 without applying the FIRE method are shown by broken lines.

It can be seen that when the FIRE method is applied, the magnitude of magnetization approaches the convergence value faster than when the FIRE method is not applied. From this analysis result, it was confirmed that the excellent effect that the calculation time can be shortened can be obtained by applying the FIRE method.

However, from the graph shown in FIG. 8A, after the vibration in the initial stage of analysis has subsided, the change in the magnetization calculation result is gradual until the magnetization calculation result converges, and a huge time step is required for convergence. It can be read that it is done. Hereinafter, with reference to FIG. 9, the reason why an enormous time step is spent until the calculation result of magnetization converges after the vibration has subsided will be described.

FIG. 9 is a graph showing changes in the virtual time axis between _{the provisional magnetic field vector HT ip} and the second magnetic field vector H2 _{ip as} a result of performing the magnetic field analysis in step S15 of FIG. 3 without applying the multi-time step method. Since the multi-time step method is not applied, the second magnetic field vector H2 _ip is set as the first magnetic field vector H1 _{ip in the next time step.}

Since the contribution from the external magnetic field and other boxels 40 is dominant in the initial stage of the analysis in which the magnitude of magnetization changes rapidly, the provisional magnetic field vector HT _ip obtained in step S12 (FIG. 3) is the first magnetic field. It changes significantly from the vector H1 _ip. With respect to this change, the change _{from the provisional magnetic field vector HT ip} to the second magnetic field vector H2 _ip is relatively small. Therefore, the amount of change from the provisional magnetic field vector HT _ip to the second magnetic field vector H2 _ip has a small effect on the speed of convergence of the magnetic field.

On the other hand, when the change in the magnetic field becomes gradual, the _{amount of change from the first magnetic field vector H1 ip} to the provisional magnetic field vector HT _ip and the amount of change _{from the provisional magnetic field vector HT ip} to the second magnetic field vector H2 _ip are almost the same. It will be the same size. Therefore, the provisional magnetic field vector HT _ip (n), which is significantly changed from the first magnetic field vector H1 _ip (n-1), imposes the binding condition of the motion equation (1) and calculates the magnetic field to obtain the second magnetic field. The vector H2 _ip (n) is returned to the vicinity of the original first magnetic field vector H1 _ip (n-1). As a result, the amount of change in the magnetic field in one time step is extremely small.

When the virtual mass is reduced by applying the FIRE method in step S16 (FIG. 3), the amount of change in the magnetic _{field from the first magnetic field vector H1 ip} (n-1) to the provisional magnetic field vector HT _{ip (n) becomes large.} The direction of this change deviates from the original direction of change in the time zone when the change of the magnetic field becomes gradual. Therefore, the effect of applying the FIRE method is low in the time zone when the change of the magnetic field becomes gradual.

In the above embodiment, the magnetic field change vector is stretched by making the elongation shortening coefficient f larger than 1 as shown in FIG. 5 in the time zone when the change of the magnetic field becomes gradual, and is used in the next time step. 1 The magnetic field vector H1 _ip (n + 1) is obtained. Therefore, the calculation result of the magnetic field can be brought closer to the convergence value more quickly.

FIG. 10 shows a method according to an embodiment in which both the FIRE method and the multi-time step method are applied, a method in which the FIRE method is applied and the multi-step method is not applied, and a method in which neither the FIRE method nor the multi-step method is applied. , It is a graph which shows the result of having performed the magnetic field analysis. The horizontal axis represents the number of time steps, and the vertical axis represents the magnitude of magnetization of one voxel 40 in the unit "A / m". When the angle between the current magnetic field change vector and the magnetic field change vector in the immediately preceding time step is less than 90 °, the elongation shortening coefficient f is set to 1.1. Further, when the angle formed by the two magnetic field change vectors is 90 ° or more, the elongation shortening coefficient f is set to 0.9.

By applying the FIRE method, it can be seen that the calculation result of the magnetic field approaches the convergence value faster. Furthermore, by applying the multi-time step method, it can be seen that the calculation result of the magnetic field approaches the convergence value faster. From the analysis results shown in FIG. 10, the excellent effect of this example that the calculation time can be shortened was confirmed.

Next, the value of the elongation / shortening coefficient f will be described. If the elongation / shortening coefficient f is made too large, the calculation becomes unstable and the calculation result tends to diverge. In order to stabilize the iterative calculation, it is preferable that the elongation reduction coefficient f is less than 2. When the angle between the current magnetization change vector and the magnetic field change vector in the immediately preceding time step is 90 °, the elongation shortening coefficient f may be 1 or less than 1.

Next, a modified example of the above embodiment will be described.
In the above embodiment, the FIRE method was applied in step S16 (FIG. 3), but it is not always necessary to apply the FIRE method. By applying only the multi-time step method, the calculation result of the magnetic field can be brought closer to the convergence value faster in the time zone when the change of the calculation result of the magnetic field becomes gradual.

The value of the expansion / shortening coefficient f of the equation (12) may be input by the user from the input device 28 (FIG. 1). When the angle between the current magnetic field change vector and the magnetic field change vector in the immediately preceding time step is 90 ° or more, the value of the elongation shortening coefficient f may be set to 1.

In the above embodiment, the evaluation point 41 is arranged at the midpoint of the perpendicular line drawn from the center of gravity of the voxel 40 (FIG. 2B) to each surface. The position of the evaluation point may be another position in the voxel. For example, the evaluation point 41 may be arranged at a position closer to the surface than the midpoint of the perpendicular line drawn from the center of gravity of the voxel 40 to each surface.

Further, in the above embodiment, the magnetic material to be analyzed is divided into a plurality of regular hexahedral voxels 40, but it may be divided into a plurality of polyhedral elements having other shapes. Further, the number of faces of the plurality of divided polyhedral elements does not have to be the same among all the polyhedral elements. The number of evaluation points 41 may not be the same as the number of faces of the polyhedral element including the evaluation points 41, may be less than the number of faces, or may be larger than the number of faces.

The present invention is not limited to the above examples. For example, it will be obvious to those skilled in the art that various changes, improvements, combinations, etc. are possible.

20 Processing device 21 Analysis information acquisition unit 22 Voxel division unit 23 Magnetic field calculation unit 24 Output control unit 25 Storage device 28 Input device 29 Output device 30 Magnetic field analysis device 40 Voxel 41 Evaluation points

Claims (7)

This is a magnetic field analysis method for calculating the magnetic field of the evaluation points inside each of the plurality of polyhedral elements of the analysis model divided into a plurality of polyhedral elements by the iterative method.
One time step of iterative calculation is
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. A magnetic field analysis method including a procedure of adding a vector whose magnitude is increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step. When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is larger than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. The magnetic field analysis method according to claim 1, further comprising a procedure of setting a vector obtained by adding a vector reduced in magnitude to the first magnetic field vector without changing it as the first magnetic field vector to be used in the next time step. In the procedure for obtaining the second magnetic field vector, the equation of motion that converges the magnetic fields applied to the plurality of evaluation points to the optimum solution is numerically solved.
The magnetic field analysis method according to claim 1 or 2, wherein the FIRE method for changing the parameter corresponding to the mass of the equation of motion is applied after obtaining the second magnetic field vector and before executing the next time step. The equation of motion includes a binding term that represents a binding condition that the divergence of the magnetization vector inside each of the plurality of polyhedral elements is zero.
In the procedure for obtaining the second magnetic field vector,
Using the first magnetic field vector at the present time, the equation of motion is numerically solved under the condition that the binding condition is not imposed, and the provisional magnetic field vector is obtained.
The magnetic field analysis method according to claim 3, wherein the provisional magnetic field vector is updated by an iterative method to obtain the second magnetic field vector until the binding condition is satisfied. Further, it includes a procedure for acquiring information for increasing the magnetic field change vector.
The magnetic field analysis method according to any one of claims 1 to 4, wherein the magnitude of the magnetic field change vector is increased based on the acquired information in the procedure for setting the first magnetic field vector to be used in the next time step. .. A magnetic field analyzer having a magnetic field calculation unit that calculates the magnetic field of the evaluation point inside each of the plurality of polyhedral elements by an iterative method of an analysis model divided into a plurality of polyhedral elements.
The magnetic field calculation unit is used in one time step of the iterative calculation.
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. A magnetic field analyzer that executes a procedure of adding a vector whose magnitude has been increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step. A program that causes a computer to execute a procedure of calculating the magnetic field of the evaluation point inside each of the plurality of polyhedral elements by the iterative method of the analysis model divided into a plurality of polyhedral elements.
In one time step of iterative calculation
A procedure for obtaining a second magnetic field vector representing each magnetic field of the plurality of evaluation points after one time step elapses based on a first magnetic field vector representing the current magnetic field of each of the plurality of evaluation points.
A procedure for obtaining a magnetic field change vector, which is a vector representing a change in a magnetic field from the first magnetic field vector to the second magnetic field vector, and
When the angle between the magnetic field change vector obtained in the current time step and the magnetic field change vector obtained in the immediately preceding time step is less than 90 °, the direction of the magnetic field change vector obtained in the current time step is determined. A program that causes a computer to execute a procedure of adding a vector whose magnitude has been increased without changing it to the first magnetic field vector and setting the vector as the first magnetic field vector to be used in the next time step.

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