JP6978689B2 - Magnetic simulation program, magnetic simulation method, and magnetic simulation device - Google Patents

Description

The present invention relates to a magnetic simulation program, a magnetic simulation method, and a magnetic simulation apparatus.

As a simulation technique in the field of electromagnetic fields, there is micromagnetics simulation in which the micromagnetization state of a magnetic material (magnetic material) such as a permanent magnet is numerically calculated on a computer. In micromagnetics simulation, a computer divides a magnetic material into minute elements (mesh) in the simulation space and arranges micromagnetization for each mesh. The computer then calculates the time-series changes in each micromagnetization.

In the analysis of magnetic materials, steady states often provide important information about magnetic properties. The steady state of a magnetic material is a state of magnetization that minimizes the magnetic energy of a predefined system. Therefore, if the micromagnetization state that minimizes the magnetic energy of the system can be obtained, the steady state of the magnetic material can be reproduced. The method of finding the state of micromagnetization that minimizes the total energy of the magnetic material in this way is called the energy minimization method.

One of the energy minimization methods used in micromagnetics simulation is the Nonlinear Conjugate Gradient Method (NCG Method).

In micromagnetics simulation, how to divide the mesh of magnetic material greatly affects the calculation time and calculation accuracy. The tendency is that the coarser the mesh, the smaller the total number of meshes, and as a result, the shorter the time required for the calculation, but the calculation result deviates from the true value. On the contrary, the finer the mesh, the larger the total number of meshes and the longer the time required for the calculation, but the calculation result approaches the true value. When actually performing the simulation, the mesh size is made as large as possible within the range where the calculation result does not deviate from the true value.

The mesh size does not have to be uniform within the model. By reducing the mesh size only in a part of the area of interest and increasing the mesh size in other areas, it is possible to reduce the total number of meshes and speed up the calculation. A model having such a dense mesh size is referred to as a non-uniform mesh model below.

As a technique for analyzing magnetization, for example, there is a magnetic material simulation device that reduces the amount of calculation for micromagnetics simulation using the nonlinear conjugate gradient method. In addition, in order to realize high-speed and high-precision magnetic field analysis, the magnetic field state of the particles is calculated by numerically solving the equation of motion that describes the relationship that the virtual particles in the elements of the Boronoi polyhedron shape should satisfy for each virtual particle. There is an analyzer to do.

Japanese Unexamined Patent Publication No. 2017-084081 Japanese Unexamined Patent Publication No. 2012-128490

In the NCG method, the calculation of a predetermined physical quantity is repeatedly executed until the convergence test is satisfied. Therefore, in order to speed up the micromagnetics simulation using the NCG method, it is important to reduce the number of iterations of the physical quantity calculation. However, when the magnetic material represented by the non-uniform mesh model is calculated by micromagnetics simulation using the NCG method, the number of iterations of the physical quantity calculation is more than doubled as compared with the case of using the uniform mesh. As a result, even if the non-uniform model is adopted, the simulation speed cannot be sufficiently increased due to the increase in the number of iterations of the physical quantity calculation.

In one aspect, the present case aims to speed up the processing of micromagnetics simulation.

One proposal provides a magnetization simulation program that causes a computer to perform the following processes.
The computer is based on magnetic material data showing a magnetic material whose structure is represented by a non-uniform mesh model containing multiple elements with non-uniform volume, and external magnetic field data showing the magnetic field in the space where the magnetic material is placed. , Calculate a gradient vector showing the gradient of magnetic energy in each of the plurality of elements. Next, for each of the plurality of elements, the computer calculates a direction vector indicating the search direction of the state that minimizes the magnetic energy, based on the reciprocal of the volume of the element and the gradient vector. Further, the computer calculates the magnetization vector of each of the plurality of elements that minimizes the magnetic energy by changing the magnetization vector indicating the magnetization state of each of the plurality of elements in the direction indicated by the direction vector. Then, the computer repeatedly executes the calculation of the gradient vector, the calculation of the direction vector, and the calculation of the magnetization vector until the convergence condition is satisfied.

According to one aspect, it is possible to speed up the processing of the micromagnetics simulation.

It is a figure which shows the functional configuration example of the magnetization simulation apparatus which concerns on 1st Embodiment. It is a figure which shows an example of the hardware of the computer used for the micromagnetics simulation. It is a block diagram which shows the function for a micromagnetics simulation. It is a figure which shows an example of mesh structure data. It is a schematic diagram which shows the magnetic material in which the magnetization of each mesh is defined. It is a figure which shows an example of the arrangement used for the micromagnetics simulation. It is a figure which shows an example of the storage method of the vector data in an array. It is a flowchart which shows an example of the processing procedure of a micromagnetics simulation. It is a flowchart which shows an example of the procedure of the preconditioner matrix creation process. It is a flowchart which shows an example of the procedure of a direction vector calculation process. It is a figure which shows the verification example of the micromagnetics simulation. It is a figure which shows an example of the magnetization curve.

Hereinafter, the present embodiment will be described with reference to the drawings. It should be noted that each embodiment can be implemented by combining a plurality of embodiments within a consistent range.
[First Embodiment]
First, the first embodiment will be described. The first embodiment is a magnetization simulation device that efficiently performs micromagnetics simulation using a non-uniform mesh model.

FIG. 1 is a diagram showing a functional configuration example of the magnetization simulation device according to the first embodiment. The magnetization simulation device 10 has a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the magnetization simulation device 10. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the magnetization simulation device 10. The magnetization simulation device 10 realizes a magnetization simulation method for efficiently performing micromagnetics simulation using a non-uniform mesh model by using the storage unit 11 and the processing unit 12. For example, the magnetization simulation device 10 realizes a magnetization simulation method by executing a magnetization simulation program in the processing unit 12 that describes a procedure for efficiently performing a micromagnetics simulation using a non-uniform mesh model. ..

The magnetization simulation device 10 executes, for example, micromagnetics simulation by the NCG method. Here, the micromagnetics simulation will be described in detail.

Micromagnetics simulation is a method of theoretical calculation of magnetic materials. The magnetization simulation device 10 defines a magnetic material in the simulation space, and divides the magnetic material into minute elements (sometimes called a mesh). Each mesh has, for example, a tetrahedral or octahedral three-dimensional structure. Also, the volume of each mesh is non-uniform. That is, the magnetic material is represented by the non-uniform mesh model 1 by being divided into a plurality of meshes.

The magnetization simulation device 10 executes a micromagnetics simulation using the non-uniform mesh model 1. For example, the magnetization simulation device 10 stores energy definition information indicating the _{magnetic energy E total, which is the total energy of the system.} The magnetic energy E _total is expressed by the following equation.

Here, E _ani is anisotropic energy, E _exc is exchange energy, E _appl is Zeeman energy, and E _static is static magnetic field energy. Anisotropic energy, exchange energy, Zeeman energy, and static magnetic field energy are expressed by the following equations, respectively.

Here, m is a unit magnetization vector. The unit magnetization vector is a vector obtained by dividing the magnetization vector indicating the magnetization of each mesh by the saturation magnetization. m _x is the x component of the unit magnetization vector. m _y is the y component of the unit magnetization vector. m _z is the z component of the unit magnetization vector. K _U is the magnetic anisotropy constant. k is a magnetic anisotropy vector. A is an exchange coupling constant. M _s is saturation magnetization. H _appl is an external magnetic field. φ is the static magnetic field potential. H _static is a static magnetic field vector. The static magnetic field potential φ can be obtained from the following relational expression.

The magnetization simulation device 10 obtains the state of micromagnetization that minimizes the magnetic energy represented by the equations (1) to (7) by micromagnetics simulation. When executing the micromagnetics simulation, the data input by the user as an execution condition is the non-uniform mesh model 1 including a plurality of elements having a non-uniform volume, and the initial magnetization vector in each element in the non-uniform mesh model 1. The state and the external magnetic field data 11b. Anisotropy vector k included formula (2) to Formula (7), the magnetic anisotropy constant K _U, exchange coupling constant A, as a physical property value of the saturation magnetization M _s is analyzed of the magnetic material, pre magnetic It can be set in the body data 11a. The external magnetic field data 11b includes the value of the _{external magnetic field H appl.} Then, the magnetization simulation device 10 outputs data showing the state of the magnetization vector in each mesh so as to minimize the magnetic energy by, for example, executing a micromagnetics simulation by the NCG method.

The magnetization simulation device 10 executes a micromagnetics simulation using the non-uniform mesh model 1 using the reciprocal of the volume of each mesh in order to reduce the number of processing iterations. For example, the storage unit 11 of the magnetization simulation device 10 contains magnetic data 11a showing a magnetic material whose structure is represented by a non-uniform mesh model 1 including a plurality of elements having a non-uniform volume, and a space in which the magnetic material is placed. The external magnetic field data 11b indicating the magnetic field is stored.

The processing unit 12 executes a micromagnetics simulation by the NCG method based on the magnetic material data 11a including the initial state of the magnetization vector in each element in the non-uniform mesh model 1 and the external magnetic field data 11b.

First, the processing unit 12 calculates a gradient vector indicating the gradient of the magnetic energy in each of the plurality of elements based on the magnetic material data 11a and the external magnetic field data 11b. The magnetic energy is represented by the above-mentioned equations (1) to (7).

Next, the processing unit 12 calculates, for each of the plurality of elements, a direction vector indicating the search direction of the state that minimizes the magnetic energy, based on the reciprocal of the volume of the elements and the gradient vector. For example, the processing unit 12 first calculates the volume of each element based on the structure of the non-uniform mesh model 1 shown in the magnetic data 11a. Then, the processing unit 12 calculates the direction vector based on the result of multiplying the gradient vector by the reciprocal of the volume of the element to the power of γ (γ is a positive real number).

The processing unit 12 may generate in advance a pre-processing matrix including a value to be multiplied by a component of the gradient vector. For example, the processing unit 12 generates a diagonal matrix having the reciprocal of the volume of each of the plurality of elements as diagonal elements as a preprocessing matrix. The processing unit 12 stores the generated preprocessing matrix in, for example, a memory. Then, the processing unit 12 calculates the direction vector of each of the plurality of elements using the pre-processing matrix.

When the calculation of the direction vector for each element is completed, the processing unit 12 changes the magnetization vector indicating the magnetization state of each of the plurality of elements in the direction indicated by the direction vector, thereby minimizing the magnetic energy of each of the plurality of elements. Calculate the magnetization vector of. In the calculation of the magnetization vector once, the direction of change of the magnetization vector is limited by the direction vector. Therefore, if the magnetization vector is changed in another direction, there may be a magnetization state (magnetization vector for each of a plurality of elements) that further reduces the magnetic energy.

Therefore, the processing unit 12 repeatedly executes the calculation of the gradient vector, the calculation of the direction vector, and the calculation of the magnetization vector until the convergence condition is satisfied. The convergence condition is, for example, a condition that the difference (residual) between the last calculated magnetization vector and the previously calculated magnetization vector is within a predetermined value. That is, when the magnetization vector converges to a certain value, the processing unit 12 exits the loop processing.

When the convergence condition is satisfied, the processing unit 12 outputs information indicating the magnetization state of the magnetic material. For example, the processing unit 12 outputs the magnetization vector of each element calculated last as the magnetization state of the magnetic material according to the external magnetic field data 11b.

In this way, by executing the micromagnetics simulation using the reciprocal of the volume of each mesh, it is possible to reduce the number of repetitions of the calculation process of physical quantities such as gradient vector, direction vector, and magnetization vector, and the processing efficiency is improved. Can be planned.

That is, when the cyclomagnetics simulation by the NCG method is calculated using the non-uniform mesh model 1 without using the reciprocal of the volume of each mesh, the number of repetitions of the physical quantity calculation process is doubled as compared with the case where the uniform mesh is used. It will increase more than that. The cause of this is considered as follows.

When the magnetic material is represented by a non-uniform mesh model, the volume of each mesh becomes non-uniform. Further, each component of the gradient vector calculated by the NCG method is expressed in a form proportional to the product of the effective magnetic field and the volume of the mesh. Therefore, the non-uniform mesh size causes the magnitude of the component of the gradient vector to vary. For example, if the effective magnetic fields of two components of a certain gradient vector are equal and the mesh size ratio is 10,000, the ratio of the two components is 10,000. As described above, the non-uniform mesh model tends to have a much larger variation in the magnitude of the gradient vector component than the uniform mesh model. If the variation of each component of the gradient vector is large, it is easily affected by an error during optimization, and the direction of the direction vector indicating the search direction of the minimum value of magnetic energy deviates from the direction in which the minimum value exists. As a result, the search path for the minimum value of magnetic energy becomes zigzag, and energy minimization becomes slow. Due to such circumstances, it can be considered that the convergence of the NCG method deteriorates, the number of iterations of the physical quantity calculation process increases, and the calculation time becomes long.

As described above, the large variation of each component of the gradient vector due to the non-uniformity of the mesh is the cause of the deterioration of the convergence. Then, if the variation of each component of the gradient vector can be suppressed, it is considered that the convergence is improved. Suppression of variation in each component of the gradient vector can be realized by executing the following preprocessing. That is, when the magnetization simulation device 10 obtains the minimum energy state of the magnetic material by using the NCG method, a preconditioner using the reciprocal of the volume of the mesh is prepared in advance, and this preconditioner is used when calculating the direction vector. use. By using a preconditioner that suppresses variations in the size of each component of the gradient vector, it can be expected that convergence will occur with the same number of iterations as a uniform mesh. For example, it is conceivable to diagonally scale the preconditioner matrix as a diagonal matrix. Each component of such a diagonal matrix should have a value of about 0.3 to 1.0 of the inverse of each mesh volume.

In this way, when calculating the direction vector, the reciprocal of the volume of the mesh is used to suppress the variation of the gradient vector due to the non-uniform mesh size, so that the orientation of the direction vector is optimized. To. By optimizing the orientation of the direction vector, it is possible to reach the minimum value of magnetic energy with a small number of iterations. As a result, the processing efficiency can be improved.

[Second Embodiment]
Next, the second embodiment will be described. The second embodiment embodies a computer-based micromagnetics simulation.

FIG. 2 is a diagram showing an example of computer hardware used for micromagnetics simulation. In the computer 100, the entire device is controlled by the processor 101. A memory 102 and a plurality of peripheral devices are connected to the processor 101 via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a CPU (Central Processing Unit), an MPU (Micro Processing Unit), or a DSP (Digital Signal Processor). At least a part of the functions realized by the processor 101 executing a program may be realized by an electronic circuit such as an ASIC (Application Specific Integrated Circuit) or a PLD (Programmable Logic Device).

The memory 102 is used as the main storage device of the computer 100. At least a part of an OS (Operating System) program or an application program to be executed by the processor 101 is temporarily stored in the memory 102. Further, various data used for processing by the processor 101 are stored in the memory 102. As the memory 102, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

Peripheral devices connected to the bus 109 include a storage device 103, a graphic processing device 104, an input interface 105, an optical drive device 106, a device connection interface 107, and a network interface 108.

The storage device 103 electrically or magnetically writes and reads data to and from the built-in recording medium. The storage device 103 is used as an auxiliary storage device for a computer. The storage device 103 stores an OS program, an application program, and various data. As the storage device 103, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive) can be used.

A monitor 21 is connected to the graphic processing device 104. The graphic processing device 104 causes the image to be displayed on the screen of the monitor 21 according to the instruction from the processor 101. The monitor 21 includes a display device using an organic EL (Electro Luminescence), a liquid crystal display device, and the like.

A keyboard 22 and a mouse 23 are connected to the input interface 105. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. The mouse 23 is an example of a pointing device, and other pointing devices can also be used. Other pointing devices include touch panels, tablets, touchpads, trackballs and the like.

The optical drive device 106 reads the data recorded on the optical disk 24 by using a laser beam or the like. The optical disk 24 is a portable recording medium on which data is recorded so that it can be read by reflection of light. The optical disk 24 includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (ReWritable), and the like.

The device connection interface 107 is a communication interface for connecting peripheral devices to the computer 100. For example, a memory device 25 or a memory reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a communication function with the device connection interface 107. The memory reader / writer 26 is a device that writes data to the memory card 27 or reads data from the memory card 27. The memory card 27 is a card-type recording medium.

The network interface 108 is connected to the network 20. The network interface 108 transmits / receives data to / from another computer or communication device via the network 20.

The computer 100 can realize the processing function of the second embodiment by the hardware configuration as described above. The magnetization simulation device 10 shown in the first embodiment can also be realized by the same hardware as the computer 100 shown in FIG.

The computer 100 realizes the processing function of the second embodiment, for example, by executing a program recorded on a computer-readable recording medium. A program describing the processing content to be executed by the computer 100 can be recorded on various recording media. For example, a program to be executed by the computer 100 can be stored in the storage device 103. The processor 101 loads at least a part of the program in the storage device 103 into the memory 102 and executes the program. Further, the program to be executed by the computer 100 can be recorded on a portable recording medium such as an optical disk 24, a memory device 25, and a memory card 27. The program stored in the portable recording medium can be executed after being installed in the storage device 103 by control from the processor 101, for example. The processor 101 can also read and execute the program directly from the portable recording medium.

Such a computer 100 performs a micromagnetics simulation by the NCG method using a non-uniform mesh.
FIG. 3 is a block diagram showing a function for micromagnetics simulation. The computer 100 has a storage unit 110, a preconditioner matrix creation unit 120, and a simulation unit 130 for micromagnetics simulation.

The storage unit 110 stores the magnetic material data 111 and the external magnetic field data 112. The magnetic material data 111 includes mesh structure data 111a and characteristic data 111b. The mesh structure data 111a is data showing the position and shape of each mesh when the magnetic material is divided into a plurality of meshes having a non-uniform size. The characteristic data 111b is data relating to the properties of the magnetic material. For example, the characteristic data 111b, the unit magnetization vector m, anisotropy vector k, the magnetic anisotropy constant K _U, exchange coupling constant A, and the like saturation magnetization M _s. The external magnetic field data 112 is data representing a magnetic field (external magnetic field H _appl ) in the space where the magnetic material is placed.

The pre-processing matrix creation unit 120 performs the pre-processing operation of the NCG method and creates a matrix (pre-processing matrix) for enhancing the convergence by the NCG method. For example, the preconditioner matrix creation unit 120 sets a value corresponding to the volume of each mesh of the mesh model as an element of the preconditioner matrix.

The simulation unit 130 executes micromagnetics simulation by the NCG method using the preconditioner matrix, and calculates the magnetization vector for each mesh of the mesh model. Since the NCG method is used, the simulation unit 130 repeatedly executes the calculation of the magnetization vector for each mesh until a predetermined convergence condition is satisfied. Then, when the convergence condition is satisfied, the simulation unit 130 outputs the last calculated magnetization vector for each mesh.

FIG. 4 is a diagram showing an example of mesh structure data. The storage unit 110 stores mesh structure data 111a representing the non-uniform mesh model 31 of the magnetic material. The non-uniform mesh model 31 has a reduced number of meshes as compared with the uniform mesh model 30 having a uniform size. The mesh structure data 111a includes, for example, mesh data 111d and node data 111e. In the mesh data 111d, an identifier (node number) of a node of the mesh is set in association with an identifier (mesh number) of each mesh included in the non-uniform mesh model 31. If the mesh is a tetrahedron, the mesh has four nodes. If the mesh is a hexahedron, the mesh has eight nodes. In the node data 111e, the coordinate values of the nodes in the three-dimensional space are set in association with the node numbers of the nodes included in the non-uniform mesh model 31.

The non-uniform mesh model 31 shown in the mesh structure data 111a represents a magnetic material divided into a plurality of meshes. The unit magnetization vector included in the characteristic data 111b represents the initial state of magnetization (micromagnetization) for each mesh.

FIG. 5 is a schematic diagram showing a magnetic material in which the magnetization of each mesh is defined. As shown in FIG. 5, when the magnetic material 40 is divided into a plurality of meshes 41, the strength and direction of magnetization in each mesh are defined by the magnetization vector. Then, the computer 100 calculates the behavior of the micromagnetization when the magnetic material 40 is placed in the space where the external magnetic field shown in the external magnetic field data 112 exists by the micromagnetics simulation by the NCG method. Specifically, the computer 100 calculates the state of micromagnetization that minimizes the magnetic energy represented by the equations (1) to (7). At this time, the computer 100 executes an efficient simulation process in which the number of repetitions of the physical quantity calculation process is small by using the preconditioner according to the reciprocal of the volume of each mesh.

The computer 100 manages the intermediate data generated in the processing process of the micromagnetics simulation on the memory 102 by using an array.
FIG. 6 is a diagram showing an example of an array used for a micromagnetics simulation. For example, when the preconditioner matrix creation unit 120 creates the preconditioner matrix Q based on the magnetic data 111, the elements of the preconditioner matrix Q are stored in the matrix element array Q'. The simulation unit 130 extracts the value of the element from the matrix element array Q'and calculates the physical quantity. For example, in the first physical quantity calculation, the simulation unit 130 calculates a gradient vector, a direction vector, and a magnetization vector for each mesh based on the magnetic material data 111, the external magnetic field data 112, and the matrix element array Q'. .. The simulation unit 130 stores the calculated physical quantity for each mesh in the array in the output data array group 51. The output data array group 51 includes a gradient vector array g ¹ , a direction vector array d ¹ , and a magnetization vector array m ¹ .

When the first physical quantity calculation is completed, the simulation unit 130 copies the values of each array in the output data array group 51 to the array provided as the input data array group 52. The input data array group 52 includes a gradient vector array g ² , a direction vector array d ² , and a magnetization vector array m ² .

The simulation unit 130 reads data from each of the matrix element array Q'and the array in the input data array group 52, and performs the second and subsequent physical quantity calculations. Then, the simulation unit 130 stores the physical quantity for each mesh calculated in the second and subsequent physical quantity calculations in the array in the output data array group 51.

In this way, by managing the intermediate data using the array, the micromagnetics simulation can be efficiently executed. When the vector value is stored in the array, the simulation unit 130 stores each component of the vector value in the x-axis, y-axis, and z-axis directions as one element of the array. Therefore, when the number of meshes is N, the number of elements in each array is 3N.

FIG. 7 is a diagram showing an example of a method of storing vector data in an array. Physical quantities calculated for each mesh of the non-uniform mesh model 31 include a magnetization vector, a gradient vector, and a direction vector. The structural data of each mesh includes the coordinates of the nodes constituting the mesh.

In the array, each value for each component of the vector is stored as an element of the array. For example, when the element numbers in the array are numbers in ascending order from "1", the x value of the first mesh is stored in the first element of the array. The y value of the first mesh is stored in the second element of the array. The z-value of the first mesh is stored in the third element of the array. Then, the x value of the second mesh is stored in the fourth element of the array.

When the values for each component of each vector are stored in the array in this way, the vector data related to the i-th mesh is the 3 (i-1) + 1st element to the 3 (i-1) + 3rd of each array. It is stored in the three elements up to. For example, the magnetization vector of the i-th mesh is set in the three elements from the 3 (i-1) + 1st to the 3rd (i-1) + 3rd ^{of the magnetization vector arrays m 1} and m ^{2, respectively.} gradient vector of i-th mesh, gradient vector sequence g ^1, g ² respectively 3 (i-1) +1 th 3 (i-1) is set to three elements of up to +3 th. The direction vector of the i-th mesh is set in the three elements from the 3 (i-1) + 1st to the 3rd (i-1) + 3rd, respectively ^{, of the direction vector arrays d 1} and d ^2.

Hereinafter, the processing procedure of the micromagnetics simulation by the NCG method will be described in detail.
FIG. 8 is a flowchart showing an example of the processing procedure of the micromagnetics simulation. Hereinafter, the process shown in FIG. 8 will be described along with the step numbers.

[Step S101] The preconditioner matrix creation unit 120 accepts the input of the initial value of the magnetization vector data indicating the magnetization vector for each mesh, and stores ^{the components in each axial direction of the magnetization vector for each mesh in the magnetization vector array m 2.} do.

[Step S102] The preconditioner matrix creation unit 120 creates a matrix element array Q'representing diagonal components of the preconditioner matrix Q based on the parameter γ and the mesh structure data 111a. The preconditioner matrix is, for example, the following diagonal matrix.

Here, γ is a parameter specified in advance by the user and is constant during the simulation. The value of γ is a positive real number, and for example, a value in the range of 0.3 to 1.0 is set as the value of γ. N is the number of meshes.

If the i and j components of the _{preconditioner} Q are written as Q ij, the values of each component of the preconditioner Q can be expressed as follows.

i and j are integers from 1 to N, respectively. s and t are integers taking 0 to 2 respectively. δ _ij and δ _st are Kronecker deltas. V _i is the volume of the element of element number i. The preconditioner matrix creation unit 120 calculates the volume of the mesh from the coordinate values of the nodes of each mesh shown in the mesh structure data 111a. Then, the preconditioner matrix creating unit 120 calculates the value of the component of the preconditioner matrix Q by the equation (9) based on the calculated volume of each mesh, and stores it in the memory 102. For example, the preconditioner matrix creation unit 120 stores each component of Q as an array. In that case, the preconditioner matrix creation unit 120 defines the following matrix element array Q'with 3N elements, and stores three diagonal components of the preconditioner matrix creation unit 120 in the array.

Details of the preconditioner matrix creation process for storing values in such a matrix element array Q'will be described later (see FIG. 9).
When the preconditioner Q is created, the simulation unit 130 executes a micromagnetics simulation by the NCG method. In the micromagnetics simulation, the simulation unit 130 calculates the physical quantity in the processes of steps S103 to S105.

[Step S103] The simulation unit 130 ^{calculates a gradient vector for each mesh based on the magnetization vector array m 2} , and stores the components of the gradient vector in the gradient vector array g ^1. For example, when the magnetization vector of the i-th mesh shown in magnetization vector sequence m ² was m _i, the gradient vector g _i of the mesh is "g _i = -∂E _total / ∂m _i".

[Step S104] The simulation unit 130 calculates a direction vector for each mesh using the preprocessing matrix Q based on ^{the gradient vector arrays g 1} and g ² and the direction vector array d ^{2, and directs the components of the direction vector.} Store in the vector array d ^1. The values calculated in the previous physical quantity calculation process are stored in the gradient vector array g ² and the direction vector array d ^2. In the case of the first physical quantity calculation process, the gradient vector array g ² and the direction vector array d ² have not been calculated. Therefore, in the first physical quantity calculation process, the simulation unit 130 calculates the direction vector for each mesh by the ^{gradient vector array g 1 and the matrix element array Q'.}

^{For example, in the case of the first physical quantity calculation, the simulation unit 130 is a column vector (gradient vector array g 1} ) in which the values (x value, y value, z value) of the elements of the gradient vector of each of the plurality of meshes are arranged in one column. Is multiplied by "-Q" from the left. The elements of the column vector obtained as a result of the multiplication represent the elements of the direction vector of each of the plurality of meshes. When the gradient vector array g ¹ is regarded as the column vector of the gradient vector, the column vector of the direction vector is "−Qg ¹ ".

Further, in the case of the calculation of the physical quantity from the second time onward, the simulation unit 130 calculates the correction coefficient β by the following equation (11). In equation (11), each array is regarded as a vector having elements of the array.

Here, v = g ^{1 −} g ² . (Array a, array b) in the equation (11) is an inner product operation of the vector represented by the array a and the vector represented by the array b.
Then, the simulation unit 130 multiplies the gradient vector (gradient vector array g ¹ ) calculated in step S103 by “−Q” from the left. Further, the simulation unit 130 uses the direction vector (direction vector array d ² ) calculated in the previous physical quantity calculation as a column vector, and multiplies the column vector by “β” from the left. ^{Then, the simulation unit 130 sets the total “−Qg 1} + βd ² ” of the multiplication result of “−Q” on the gradient vector and the multiplication result of “β” on the direction vector as the direction vector.

The simulation unit 130 stores the calculated direction vector for each mesh in the direction vector array d ¹ . The details of the direction vector calculation process will be described later (see FIG. 10).
[Step S105] The simulation unit 130 calculates the magnetization vector for each mesh by line search (direct search) processing based on ^{the direction vector array d 1} and the magnetization vector array m ^{2. For example, the simulation unit 130 changes the magnetization vector (magnetization vector array m 2} ) of each mesh obtained in the previous physical quantity calculation in the direction of the direction vector (direction vector array d ¹ ) of each mesh, and magnetic energy E. Search for the magnetization state that minimizes the _total. The simulation unit 130 uses the magnetization vector of each mesh that minimizes _{the magnetic energy E total as} the calculation result of the magnetization vector in the search in the direction indicated by the direction vector. Then, the simulation unit 130 updates the value of each element of the ^{magnetization vector array m 1} with the magnetization vector newly calculated for each mesh.

[Step S106] The simulation unit 130 determines whether or not the convergence condition is satisfied. For example, the simulation unit 130 ^{determines whether or not the residual | m 1 −} m ² | of the magnetization vector is equal to or less than the specified value. Further, the simulation unit 130 may use the average value or the maximum value of the magnitude of the difference vector between the magnetization vector before rotation and the magnetization vector after rotation for each mesh as the residual. If the residual is equal to or less than the specified value, the simulation unit 130 determines that the convergence condition is satisfied. When the convergence condition is satisfied, the simulation unit 130 advances the process to step S108. If the convergence condition is not satisfied, the simulation unit 130 advances the process to step S107.

[Step S107] The simulation unit 130 copies the gradient vector, the direction vector, and the magnetization vector calculated in steps S103 to S105 as data for the next loop processing. Specifically, the simulation unit 130 copies ^{the value of each element in the magnetization vector array m 1} to each element in the magnetization vector array m ² . Further, the simulation unit 130 copies ^{the value of each element in the gradient vector array g 1} to each element in the gradient vector array g ² . Further, the simulation unit 130 copies ^{the value of each element in the direction vector array d 1} to each element in the direction vector array d ² . After that, the simulation unit 130 advances the process to step S103 and starts the next physical quantity calculation process.

[Step S108] When the convergence condition is satisfied, the simulation unit 130 writes out the last calculated magnetization vector for each mesh to a file. For example, the simulation unit 130 ^{writes the value of each element of the magnetization vector array m 1 to} a file on the memory 102 in association with the mesh number of the mesh corresponding to the element. Then, the simulation unit 130 stores the file in, for example, the storage device 103.

In such a procedure, the micromagnetics simulation by the NCG method is executed.
Next, the preconditioner matrix creation process will be described in detail.

FIG. 9 is a flowchart showing an example of the procedure of the preconditioner matrix creation process. Hereinafter, the process shown in FIG. 9 will be described along with the step numbers.
[Step S111] The pre-processing matrix creation unit 120 repeats the processing of steps S112 to S115 until the variable i changes from 1 to N.

[Step S112] The preconditioner matrix creating unit 120 calculates the volume of the i-th mesh. For example, the preconditioner creating unit 120 calculates the volume of the mesh based on the coordinate values of the nodes of the i-th mesh shown in the mesh structure data 111a in the magnetic data 111.

[Step S113] The preconditioner matrix creation unit 120 stores the volume of the i-th mesh in the −γ power in the 3 (i-1) + 1st element of the matrix element array Q'.
[Step S114] The preconditioner matrix creation unit 120 stores the volume of the i-th mesh in the −γ power in the 3 (i-1) + second element of the matrix element array Q'.

[Step S115] The preconditioner matrix creation unit 120 stores the volume of the i-th mesh in the −γ power in the 3 (i-1) + 3rd element of the matrix element array Q'.
[Step S116] The preconditioner matrix creation unit 120 ends the preconditioner matrix creation process if the value of the variable i is N, and adds 1 to the value of the variable i if the value of the variable i is less than N. The processing of steps S112 to S115 is performed.

As a result of such a preconditioner matrix creation process, a matrix element array Q'stored diagonal components of the preconditioner matrix Q is output. For example, the pre-processing matrix creation unit 120 stores the matrix element array Q'in the memory 102 as a processing result.

Next, the calculation process of the direction vector using the matrix element array Q'will be described in detail.
FIG. 10 is a flowchart showing an example of the procedure of the direction vector calculation process. Hereinafter, the process shown in FIG. 10 will be described along with the step numbers.

[Step S121] The simulation unit 130 determines whether or not it is the first physical quantity calculation process. If it is the first physical quantity calculation process, the simulation unit 130 advances the process to step S122. Further, the simulation unit 130 advances the process to step S125 if it is the second and subsequent physical quantity calculation processes.

[Step S122] The simulation unit 130 repeats the process of step S123 until the variable i changes from 1 to 3N.
[Step S123] The simulation unit 130 ^{multiplies the value of the i-th element of the gradient vector array g 1} and the value of the i-th element of Q by "-1", and the i-th element of the direction vector array d ¹ Store in.

[Step S124] If the value of the variable i is 3N, the simulation unit 130 ends the direction vector calculation process, and if the value of the variable i is less than 3N, 1 is added to the value of the variable i, and step S123 Process.

[Step S125] The simulation unit 130 calculates the correction coefficient β and stores the calculation result in the memory 102.
[Step S126] The simulation unit 130 repeats the process of step S127 until the variable i changes from 1 to 3N.

[Step S127] The simulation unit 130 sets the i-th element of the gradient vector array g ^{1 and} the i-th element of the matrix element array Q'from ^{the product of the i-th element of the direction vector array d 2 and the correction coefficient β.} Subtract the product of. Then, the simulation unit 130 stores the subtraction result in the i-th element of the ^{direction vector array d 1.}

[Step S128] If the value of the variable i is 3N, the simulation unit 130 ends the direction vector calculation process, and if the value of the variable i is less than 3N, 1 is added to the value of the variable i, and step S127. Process.

In this way, the direction vector is calculated, and as a result of the processing, the direction vector array d ¹ is stored in the memory 102. In the calculation of the direction vector, the influence of the difference in volume between the meshes is suppressed by using the preconditioner Q including the reciprocal of the volume of each mesh. As a result, the increase in the number of iterations of physical quantity calculation due to the adoption of the non-uniform mesh model is suppressed.

Here, the verification result of the difference in the number of iterations of the physical quantity calculation process between the case where the preconditioner Q is used and the case where the preconditioner Q is not used will be described.
FIG. 11 is a diagram showing a verification example of a micromagnetics simulation. FIG. 11 shows the case where the preconditioner Q based on the reciprocal of the volume is used and the case where the preconditioner Q based on the reciprocal of the volume is used and not used for the number of iterations and the calculation time required for the calculation in which the uniformly magnetized magnetic material is relaxed to a stable state. The measurement results for each case are shown. In the micromagnetics simulation using the preconditioner Q, γ = 1.0.

The non-uniform mesh model 31 used for the verification has about 11 million meshes. The saturation magnetization of the magnetic material shown in this non-uniform mesh model 31 is 1.61T. The exchange coupling constant is 1.0 × 10 ^-11 J / m. The anisotropy constant is 4.50 × 10 ⁶ J / m ³ .

When the micromagnetics simulation was executed without using the preconditioner Q under such conditions, the convergence condition was satisfied with the number of iterations being 219 and the calculation time being 1172 seconds. On the other hand, when the micromagnetics simulation was executed using the preconditioner Q based on the reciprocal of the volume, the number of iterations was 67 and the calculation time was 388 seconds, and the convergence condition was satisfied.

In this example, by using the preconditioner Q, the number of iterations is reduced by about 0.3 times, and the calculation time is increased by about 0.33 times. In this way, the use of the preconditioner Q enables faster micromagnetics simulation.

By such micromagnetics simulation, the magnetic properties of a magnetic material used for, for example, a magnetic memory can be analyzed by computer simulation. For example, the magnetization curve of a magnetic material can be obtained by repeatedly executing a micromagnetics simulation while changing the strength of an external magnetic field.

FIG. 12 is a diagram showing an example of a magnetization curve. In FIG. 12, the vertical axis represents the magnetization [T] and the horizontal axis represents the external magnetic field [A / m]. FIG. 12 shows a magnetization curve 60 obtained by gradually increasing the external magnetic field and obtaining the magnetization of the magnetic material in each external magnetic field. The magnetization curve 60 shows how the magnetization of the magnetic material is reversed in a certain external magnetic field. For example, when the computer 100 displays the magnetization curve 60 on the monitor 21, the user can obtain the characteristics of the magnetic material such as the external magnetic field for stabilizing the magnetization of the magnetic material in a predetermined direction and the strength of the magnetization in the stable state. Can be grasped.

Although the embodiment has been illustrated above, the configuration of each part shown in the embodiment can be replaced with another having the same function. Further, any other components or processes may be added. Further, any two or more configurations (features) of the above-described embodiments may be combined.

1 Non-uniform mesh model 10 Magnetization simulation device 11 Storage unit 11a Magnetic material data 11b External magnetic field data 12 Processing unit

Claims (5)

On the computer
The above is based on magnetic material data showing a magnetic material whose structure is represented by a non-uniform mesh model containing a plurality of elements having a non-uniform volume and external magnetic field data showing a magnetic field in the space in which the magnetic material is placed. Calculate a gradient vector showing the gradient of magnetic energy in each of the multiple elements.
For each of the plurality of elements, a direction vector indicating a search direction for a state that minimizes magnetic energy is calculated based on the reciprocal of the volume of the element and the gradient vector.
By changing the magnetization vector indicating the magnetization state of each of the plurality of elements in the direction indicated by the direction vector, the magnetization vector of each of the plurality of elements that minimizes the magnetic energy is calculated.
The calculation of the gradient vector, the calculation of the direction vector, and the calculation of the magnetization vector are repeatedly executed until the convergence condition is satisfied.
A magnetization simulation program that executes the process. In the calculation of the direction vector, the direction vector is calculated based on the result of multiplying the gradient vector of each of the plurality of elements by the reciprocal of the volume of the element to the γ power (γ is a positive real number).
The magnetization simulation program according to claim 1. On the computer,
A process of generating a diagonal matrix whose diagonal elements are diagonal elements corresponding to the reciprocal of the volume of each of the plurality of elements is executed.
In the calculation of the direction vector, the preconditioner matrix is used to calculate the direction vector for each of the plurality of elements.
The magnetization simulation program according to claim 1 or 2. The computer
The above is based on magnetic material data showing a magnetic material whose structure is represented by a non-uniform mesh model containing a plurality of elements having a non-uniform volume and external magnetic field data showing a magnetic field in the space in which the magnetic material is placed. Calculate a gradient vector showing the gradient of magnetic energy in each of the multiple elements.
For each of the plurality of elements, a direction vector indicating a search direction for a state that minimizes magnetic energy is calculated based on the reciprocal of the volume of the element and the gradient vector.
By changing the magnetization vector indicating the magnetization state of each of the plurality of elements in the direction indicated by the direction vector, the magnetization vector of each of the plurality of elements that minimizes the magnetic energy is calculated.
The calculation of the gradient vector, the calculation of the direction vector, and the calculation of the magnetization vector are repeatedly executed until the convergence condition is satisfied.
Magnetization simulation method. A storage unit that stores magnetic material data indicating a magnetic material whose structure is represented by a non-uniform mesh model containing a plurality of elements having a non-uniform volume, and external magnetic field data indicating a magnetic field in the space in which the magnetic material is placed. When,
Based on the magnetic material data and the external magnetic field data, a gradient vector showing the gradient of the magnetic energy in each of the plurality of elements is calculated, and for each of the plurality of elements, the inverse of the volume of the element and the gradient vector. Based on the above, a direction vector indicating a search direction for a state that minimizes magnetic energy is calculated, and the magnetization vector indicating the magnetization state of each of the plurality of elements is changed in the direction indicated by the direction vector to obtain the magnetism. A processing unit that repeatedly calculates the magnetization vector of each of the plurality of elements that minimizes the target energy, and repeatedly executes the calculation of the gradient vector, the calculation of the direction vector, and the calculation of the magnetization vector until the convergence condition is satisfied. When,
Magnetization simulation device with.

Images