JP2010072711A - High speed magnetic field analyzing method, high speed magnetic field analyzing program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for accelerating the speed of the transient analysis of a non-linear magnetic field. <P>SOLUTION: This high speed magnetic field analyzing method for performing the transient analysis of a non-linear magnetic field by using a finite element method includes: a process for reading an input data file in which a first convergence decision value in the iterative solution method of a matrix equation used in a first time step, a second convergence decision value related with a non-linear magnetic field solution used in the first time step, and a third convergence decision value related with simple iterative calculation used in a second and succeeding time steps are described; a process for removing a magnetic field itself by using the iterative solution of the matrix equation, the first convergence decision value and the second convergence decision value in the first time step; and a process for obtaining the amount of the fluctuation of the magnetic field from the time step by using the simple iterative calculation and the third convergence decision value in the second and succeeding time steps, wherein magnetic resistivity expressed by 3×3 tensile is used for simple iterative calculation in the second and succeeding time steps. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a magnetic field analysis method, a magnetic field analysis program, and a recording medium on which the magnetic field analysis program is recorded.

  As a typical conventional nonlinear magnetic field analysis method, there is an analysis method by a finite element method. An iterative solution method by an ICCG method (a conjugate gradient method with incomplete Cholesky decomposition pretreatment) or a Newton-Raphson method that sequentially corrects magnetic permeability is used. Some methods are used in combination. This method is shown in Non-Patent Document 1, for example.

“Finite Element Method of Electrical Engineering” by Takayoshi Nakata and Norio Takahashi, Morikita Publishing, 1986

  As a general method for magnetic field analysis by the finite element method, when described by the A method using the magnetic vector potential A, the basic equation of the quasi-static field in which the influence of the displacement current can be ignored is

It becomes. Here, ν is the magnetic resistivity (reciprocal of magnetic permeability), σ is the conductivity, J ₀ is the current density vector of the coil, and M ₀ is the residual magnetic flux density vector of the magnet. Regarding the magnet, for convenience, it was _{H = ν (B-M 0} ). B is a magnetic flux density vector, and H is a magnetic field vector.

  Since the magnetic resistivity ν depends on the field, the equation (1) is non-linear, and the solution is usually obtained using the Newton-Raphson method. That is, the equation (1) is discretized, and the solution of the finally obtained matrix equation is obtained by the iterative method in consideration of the boundary condition. In the Newton-Raphson method, the correction terms of the solution are sequentially obtained until then. The calculation is advanced by adding a correction term to the solution obtained in.

  However, even if this correction term is added, the residual (the error when substituting approximate solutions) for the matrix equation is not very small and the convergence of the solution is poor. Yes. For this reason, nonlinear magnetic field analysis, especially transient nonlinear magnetic field analysis in a rotating machine is difficult.

  In order to solve the above problems, the high-speed magnetic field analysis method according to the present invention has the following characteristics.

  A high-speed magnetic field analysis method for performing a transient analysis of a nonlinear magnetic field by performing arithmetic processing in a plurality of time steps using a finite element method by an arithmetic device, wherein a matrix equation for magnetic field analysis used in a first time step The first convergence judgment value in the iterative solution, the second convergence judgment value for the nonlinear magnetic field analysis used in the first time step, and the simple iteration calculation in the nonlinear magnetic field analysis used in at least one time step after the second time step. A process for reading each input information from an input data file describing the convergence judgment value of 3 and a mesh data file in the analysis space including the analysis target, and an iterative solution of the matrix equation in the first time step, Using the convergence determination value of 1 and the second convergence determination value, the magnetic field itself is In the process and at least one time step after the second time step, a simple iterative calculation in the nonlinear magnetic field analysis and the third convergence determination value are used to determine the amount of magnetic field variation from the previous time step. And a magnetic resistivity represented by a 3 × 3 tensor is used for the simple iterative calculation in the nonlinear magnetic field analysis in at least one time step after the second time step.

  Further, the magnetic field itself is obtained from the magnetic vector potential, and the fluctuation amount of the magnetic field from the previous time step is obtained from the fluctuation amount of the magnetic vector potential from the previous time step.

  Furthermore, the high-speed magnetic field analysis program according to the present invention for solving the above-described problems is characterized by coding a series of processes in the above-described high-speed magnetic field analysis method.

  A recording medium according to the present invention for solving the above-described problems is a computer-readable recording medium on which the above high-speed magnetic field analysis program is recorded.

  According to the high-speed magnetic field analysis method according to the present invention, the transient analysis of the nonlinear magnetic field of the system including the magnetic material can be performed several times faster than the analysis by the conventional Newton-Raphson method.

  Examples of the present invention will be described in detail below. In this embodiment, the finite element method is used as a magnetic field analysis method for solving a transient nonlinear magnetic field. Moreover, the symbol used by Formula (1) is used.

  In Example 1, a high-speed magnetic field analysis method according to the present invention will be described. This high-speed magnetic field analysis method obtains a magnetic field for each time step.

  First, in the first time step, Equation (1) is discretized using the magnetic vector potential A as an unknown, and the magnetic field is obtained by a general finite element method.

  In at least one arbitrary time step after the second time step, only ΔA that is the amount of fluctuation of the magnetic vector potential A from the previous time step is solved by a simple iteration method. In this embodiment, it is assumed that only ΔA is solved by the simple iteration method at all time steps after the second time step. The present invention is not limited to this, and it is possible to solve only ΔA by a simple iterative method at one or a plurality of arbitrary time steps as long as they are after the second time step. The equation for solving ΔA after the second time step is

It is. Here, H ₀ is the magnetic field vector in the previous time step, and Δt is the time step width. Further, ν is a differential magnetic resistivity tensor, which is an amount represented by a 3 × 3 tensor defined by the equations (3) and (4).

ν ′ is the differential magnetic resistivity, which is a value defined by the gradient of two points (Bm ₀ , Hm ₀ ) at the previous time step and (Bm, Hm) at the current time step in the magnetization curve. That is,
ν ′ = (Hm−Hm ₀ ) / (Bm−Bm ₀ )
It is expressed. Here, Bm means the magnitude of magnetic flux density, and Hm means the magnitude of magnetic field strength.

In this high-speed magnetic field analysis method, the differential magnetic resistivity tensor ν represented by this 3 × 3 tensor is used.

  In the magnetic field analysis, the convergence determination value is used to determine whether or not the calculated value has converged. In this embodiment, the first convergence determination value in the iterative solution of the matrix equation used in the first time step, the second convergence determination value related to the nonlinear magnetic field analysis used in the first time step, and the nonlinearity used in the second time step and thereafter. A third convergence determination value for simple iterative calculation in magnetic field analysis is used. These convergence determination values are described in the input data file and are input as input data.

  Here, the magnetic field analysis process 10 in the first time step will be described with reference to FIG. In the magnetic field analysis of the first time step, the magnetic vector potential A itself is solved, but the same method as the conventional magnetic field analysis method can be used.

  First, as pre-processing for magnetic field analysis at the first time step, in step 101, input data necessary for analysis such as the above-described three convergence determination values, analysis space mesh data, analysis condition data such as boundary conditions and physical property values, and the like. Enter. As an input method, for example, a file describing these input data is read.

  From step 102, the magnetic field analysis of the first time step starts. In step 102, a matrix equation for calculating the magnetic vector potential A is created based on the input data.

  In step 103, the matrix equation created in step 102 is solved by an iterative method to calculate A. The first convergence determination value is used for the convergence determination at this time. For example, the convergence is determined when the relative residual of the matrix equation related to A is equal to or less than the convergence determination value.

  In step 104, a matrix equation for calculating the correction amount δA of A is created.

  In step 105, the matrix equation created in step 104 is solved by an iterative method to calculate δA. The first convergence determination value is also used for the convergence determination at this time. For example, the convergence is determined when the relative residual of the matrix equation relating to δA is equal to or less than the convergence determination value.

  In step 106, δA obtained in step 105 is added to A obtained in step 103, and A is updated.

  In step 107, the second convergence determination value is used to determine whether or not A obtained by the nonlinear magnetic field analysis by the above iterative solution has converged. For example, the convergence is determined when the relative residual of the matrix equation related to A is equal to or less than the convergence determination value.

  If not converged, the process returns to step 104, and the above-described nonlinear magnetic field analysis by the iterative solution is repeated until convergence.

  When A converges at step 107, the process proceeds to the magnetic field analysis process 20 after the second time step.

  Next, the magnetic field analysis process 20 after the second time step will be described with reference to FIG. After the second time step, only ΔA, which is the fluctuation amount of the magnetic vector potential A from the previous time step, is solved by the simple iteration method.

  After completion of the magnetic field analysis process 10 in the first time step, in step 11, the differential magnetic resistivity ν 'is set to the same value as in the previous time step.

In step 12, the differential magnetic resistivity tensor ν is calculated according to equation (3).

  In step 13, the fluctuation amount ΔA of the magnetic vector potential is obtained by the finite element method. Here, ΔA can be obtained by the same method as in the magnetic field analysis process 10 in the first time step.

  In step 14, the fluctuation amount ΔB of the magnetic flux density is obtained from ΔA obtained as ΔB = rotΔA.

  In step 15, it is determined whether ΔB obtained in step 14 has converged by using the third convergence determination value. That is, if the difference between ΔB obtained and ΔB obtained in the previous calculation is within the third convergence determination value, it is determined that ΔB has converged.

If not converged, the process returns to step 16 to update the differential magnetic resistivity ν ′ and repeat the above processing until it converges. That is, step 12 recalculates the differential magnetic resistivity tensor ν , step 13 ΔA, step 14 ΔB, and step 15 determines convergence.

  When ΔB converges in step 15, the process proceeds to the next time step, and returns to step 11 to obtain ΔB. At this time, in order to speed up the convergence of the solution in the simple iterative method when solving for ΔA, after the third time step, the solution regarding the magnetic field fluctuation amount in the previous time step such as the differential magnetic resistivity ν ′ is the initial solution. Set to.

  As described above, the transient analysis of the nonlinear magnetic field can be performed by obtaining ΔB at each time step.

  In the present embodiment, by using the equation (2), even when the magnetic field is rotating, the magnetic flux density vector B and the magnetic field vector H are always maintained in a parallel state and equivalent to the equation (1). Analysis becomes possible.

  In this embodiment, three convergence determination values are input as input data. However, the convergence determination value for the iterative calculation of the matrix equation after the second time step (step 13) is the fourth convergence determination value separately from that at the first time step. The convergence determination value may be set. In this case, the total number of convergence determination values to be input is four.

  In the linear magnetic field analysis in which the magnetic permeability of the magnetic material is kept constant over time, the transient magnetic field analysis method according to this embodiment is used to perform a transient analysis with a constant rate of change of the coil current. Then, since the fluctuation amount of the field is obtained after the second step, the fluctuation amount of the coil current after the third step is the same as that of the second step. Therefore, ΔA, which is the amount of field fluctuation, becomes the same solution after the second step, so that the number of iterations in the iterative solution of the matrix after the third step is only one. In this case, since the fluctuation amount of the coil current is not changed, the current time step may be processed as the same solution as the previous time step without performing the calculation itself. Thus, in the linear magnetic field analysis in which the magnetic permeability of the magnetic material is made constant over time, when the transient analysis is made with the change rate of the coil current made constant, the solutions after the second step are the same. Is nothing but solving field fluctuations.

  According to this embodiment, there is an effect that a convergent solution can be obtained at a higher speed than the conventional nonlinear analysis method that solves the magnetic field itself.

  Example 2 will be described with reference to FIG. Example 2 is an example in which the high-speed magnetic field analysis method of Example 1 is applied to magnetic field analysis of a rotating machine. The analysis target includes a rotor and a stator, and FIG. 2 is a part of a mesh diagram of a space including them. The rotor is rotated at each time step.

  The analysis space is divided into a rotor space 31 including the rotor 21 and a stator space 32 including the stator 22, and the boundary 23 between the rotor space 31 and the stator space 32 has an angular width Δθ in the rotation direction. Divide the mesh into equal intervals. The angle width Δθ can be determined in advance and input as input data. In the example of FIG. 2, the parts other than the boundary 23 are also divided into meshes at equal intervals. However, only the part of the boundary 23 may be divided into meshes at equal intervals in the rotation direction.

  For this analysis model, the rotor space 31 and the stator space 32 are not deformed, and the rotor space 31 is rotated while rotating the rotor space 31 by an angular width Δθ or an integral multiple thereof while maintaining mesh consistency. Analyze the machine. In the example of FIG. 2, an example in which the angular width Δθ is rotated is shown.

  For such a calculation system, the magnetic field calculation is performed by the high-speed magnetic field analysis method described in the first embodiment. That is, in the first time step, Equation (1) is discretized and calculated by the finite element method with the magnetic vector potential A as an unknown. After the second time step, only ΔA, which is a fluctuation amount from the previous time step of the magnetic vector potential A, is calculated by the finite element method by discretizing the equation (2).

  When the rotation speed of the rotor changes, if the time step width is made constant, the rotation angle for each time step in the rotor space 31 deviates from an integer multiple of Δθ, and the mesh shape is distorted. In order to prevent this, in this embodiment, the time step width Δt is changed in accordance with the change in the rotational speed of the rotor, and the rotor mesh always matches the stator mesh when the next time step is started. Thus, the rotor space is rotated by an angular width Δθ or an integral multiple thereof. In this way, even in a system in which the rotation speed changes, mismatching between the rotor mesh and the stator mesh can be prevented. Therefore, the analysis can be performed without distorting the mesh shape and without accompanying a sudden change in the mesh shape due to the rotation, so that a highly accurate analysis can be performed.

  Example 3 is an example in which the high-speed magnetic field analysis method of Example 1 is applied to magnetic field analysis in a laminated structure in which electromagnetic steel sheets are stacked.

For such a layered structure system, the magnetic field analysis becomes possible by replacing the differential magnetic resistivity tensor ν shown in Equation (3) with ν expressed by Equation (5). This ν is a differential magnetic resistivity tensor in consideration of the anisotropy of magnetoresistance due to the laminated structure, and is an amount represented by a 3 × 3 tensor. However, in this case, it is assumed that no eddy current is generated.

Various amounts appearing in the equation of the differential magnetic resistivity tensor ν shown in the equation (5) are shown in the equations (6) to (10).

Here, α is a space factor of the electrical steel sheet, and typically has a value of about 0.95 to 0.98. N _// represents the magnetic resistivity in the stacking direction, and _N⊥ represents the magnetic resistivity in the direction perpendicular to the stacking direction. Ν ₀ is the magnetic resistivity of air (vacuum).

  According to the present embodiment, the magnetic field analysis considering the anisotropy of the magnetoresistance due to the laminated structure can be calculated at high speed after the second step.

Example 4 is an example in which the side element finite element method is used to solve the magnetic field. In this case, the fluctuation amount ΔA for each time step of the magnetic vector potential A is expressed by the equation (11) using the unknown variable Δa _j set for the side j of the element (mesh) and the side element basis function N _j for the side j. It can be expressed as

When weighting N _j is applied to both sides of equation (2) and integration is performed in the analysis space, a discretization equation represented by equation (12) is obtained.

  This embodiment is extremely effective for solving an analysis space in which an insulating layer having a thin thickness g is sandwiched between two magnetic bodies, for example. In this case, when the thin insulating layer is modeled as an infinitely thin gap element, the spatial integral term of the first term on the left side in the discretization formula of Equation (12) is the surface area of the surface of the thin insulating layer as shown in Equation (13). It can be expressed as a term.

  Thus, by performing the area portion without performing the space integration (volume integration), even when there is a thin insulating layer, no flat element is generated, so that the convergence of the solution can be prevented from deteriorating.

  Example 5 will be described with reference to FIG. In this embodiment, the magnetic body 41 and the coil 42 exist in the analysis space 50, and the magnetic field generated by the coil current is analyzed. FIG. 3 is a mesh diagram of the analysis space 50.

If the amount of fluctuation of the magnetic vector potential due to the bio-Saval field due to the coil current at each time step is _denoted by ΔA _c , the amount of fluctuation ΔA of each time step of the magnetic vector potential can be written as ΔA = ΔA _r + ΔA _c . Here, the bio-Savart field refers to a field induced by a coil current in an air region where only the coil current exists. The magnetic vector potential ΔA is the total potential. .DELTA.A _r is the amount of change of each time step of the deformation potential, and deformation potential, in the analysis space 50, a potential obtained by subtracting the magnetic vector potential by Biot-Savart field from the total potential.

As shown in FIG. 3, 2 potential fluctuation amount of the field of the analysis space 50, the total potential region 51 is a region expressed by .DELTA.A, use both deformation potential region 52, and .DELTA.A a .DELTA.A _r expressed in .DELTA.A _r The boundary layer 53 is divided into regions. The total potential region 51 and the deformation potential region 52 are overlapped by a two-potential boundary layer 53, and the two-potential boundary layer 53 is a region having a width corresponding to one mesh layer. A magnetic body 41 exists in the total potential region 51, and a coil 42 exists in the deformation potential region 52.

  In the air region of the total potential region 51, ΔA satisfies Equation 14, and in the air region of the deformation potential region 52, ΔAr satisfies Equation (15).

  When formulas (14) and (15) are discretized, formulas (16) and (17) are obtained, respectively.

Less than,

.

  FIG. 4 shows a part of the analysis space 50 shown in FIG. 3 where the two-potential boundary layer 53 is in contact with the potential region 51 and the deformation potential region 52. . As shown in FIG. 4, in the two-potential boundary layer 53, a side j1 and a side j2 are set on the sides of each mesh. The side j1 is a side in contact with the total potential region 51 of the two-potential boundary layer 53, and the side j2 is a side other than the side j1 of the two-potential boundary layer 53, that is, a side not in contact with the total potential region 51.

  Expressions (16) and (17) can be transformed into Expressions (19) and (20) using j1 and j2.

Furthermore, when Δa _j1 and Δa _j2 are collectively expressed as an unknown variable Δx _j , Equation (19) and Equation (20) become Equation (21) and Equation (22).

Δa ^c _j1 and Δa ^c _j2 on the right side are the projection components on the sides j1 and j2 of the fluctuation amount of the magnetic vector potential induced by the coil current in free space (a space obtained by removing all objects in the analysis space). This is the line integral above and can be easily calculated. And by solving the equation (22) Equation (21) is a simultaneous equation for the unknown variable [Delta] x _j, it is possible to determine the variation amount ΔA of the magnetic vector potential.

  According to the present embodiment, the coil mesh does not need to be formed in the analysis space and can be provided separately from the analysis space. Therefore, even when the coil shape is complicated or the coil moves, mesh creation and analysis are convenient. There is an advantage of becoming. Also in this embodiment, since the fluctuation amount of each time step of the magnetic vector potential is solved, the magnetic field analysis can be executed at high speed.

  Example 6 will be described with reference to FIG. FIG. 5 is a mesh diagram of a system in which a thin insulating layer 63 is sandwiched between the conductor 61 and the conductor 62.

  In the magnetic field analysis of such a system, the thin insulating layer 63 is not assigned an element by mesh division as shown in FIG. 5, and the node 70 is doubly set on the boundary surface between the conductor 61 and the conductor 62. To model. An electric scalar potential φ is set on each node 70. Note that the electric scalar potential φ at the node 70 other than the boundary surface where the thin insulating layer 63 exists among the nodes 70 of the conductor 61 and the conductor 62 can be set to zero.

  The basic formula of magnetic field analysis using this electric scalar potential φ is

It is. Furthermore, the equation for the field variation after the second time step is

It is. The electric scalar potential φ set on the boundary surface between the conductor 61 and the conductor 62 and its variation Δφ are solved by natural boundary conditions (values of φ and Δφ are not set).

  According to the present embodiment, even in the case of an analysis space where a thin insulating layer exists, the thin insulating layer is not modeled with a flat element, and thus there is an advantage that the solution convergence is good. In addition, since the fluctuation amount Δφ of the electric scalar potential φ is solved after the second time step, there is an advantage that the magnetic field analysis can be performed at high speed.

  An example of an analysis system that implements the first to sixth embodiments of the present invention is shown in FIG. This analysis system includes a computer 1, a display device 2, a storage medium 3, and an input device 4. In FIG. 6, the storage medium 3 is taken out of the computer 1 for the sake of clarity, but may be installed inside the computer 1. It is assumed that the computer 1 stores a program based on at least one of the above-described embodiments. The input device 4 is, for example, a keyboard or a mouse, and inputs the input data necessary for the analysis, such as at least three convergence determination values, mesh data in the analysis space, and analysis condition data described above, and data storing the input data. Used to specify file reading and writing, perform calculations, etc. After the input data is input, the computer 1 executes arithmetic processing such as reading of the input data and magnetic field calculation according to the stored program. The calculation result is displayed on the display device 2 and stored in the storage medium 3 as a data file. A part of the obtained calculation result may be displayed or stored. Since the analysis is performed while ticking the time step, the calculation proceeds while reusing the data stored in the storage medium 3.

The figure which shows the process of the magnetic field analysis after a 2nd time step. FIG. 6 is a mesh diagram of a space including the rotor and the stator according to the second embodiment. FIG. 10 is a mesh diagram of an analysis space including a magnetic body and a coil according to the fifth embodiment. FIG. 9 is a diagram illustrating symbols representing sides of a two-potential boundary layer in the fifth embodiment. The mesh figure of the system by which the thin insulating layer is pinched | interposed between the conductors of Example 6. FIG. The figure which shows an example of the analysis system which implement | achieves Examples 1-6. The figure which shows the process of the magnetic field analysis in a 1st time step.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Computer, 2 ... Display apparatus, 3 ... Storage medium, 4 ... Input device, 10 ... Magnetic field analysis process in 1st time step, 20 ... Magnetic field analysis process after 2nd time step, 21 ... Rotor, 22 ... Stator, 23 ... Boundary between rotor space and stator space, 31 ... Rotor space, 32 ... Stator space, 41 ... Magnetic body, 42 ... Coil, 50 ... Analysis space, 51 ... Total potential region, 52 ... Deformation potential region, 53 ... Two potential boundary layer, 61, 62 ... Conductor, 63 ... Thin insulating layer, 70 ... Node.

Claims (11)

A high-speed magnetic field analysis method for performing a transient analysis of a nonlinear magnetic field by performing arithmetic processing in a plurality of time steps using a finite element method by an arithmetic device,
The first convergence determination value in the iterative solution of the matrix equation for the magnetic field analysis used in the first time step, the second convergence determination value for the nonlinear magnetic field analysis used in the first time step, and at least one after the second time step A process of reading each input information from an input data file describing a third convergence judgment value regarding simple iterative calculation in nonlinear magnetic field analysis used in one time step, and a mesh data file of an analysis space including an analysis target;
A process of solving the magnetic field itself using an iterative solution of the matrix equation, the first convergence determination value, and the second convergence determination value in a first time step;
In at least one time step after the second time step, a simple iterative calculation in the non-linear magnetic field analysis and a process for obtaining a magnetic field fluctuation amount from the previous time step using the third convergence determination value. Have
Using a magnetic resistivity represented by a 3 × 3 tensor for the simple iterative calculation in the nonlinear magnetic field analysis in at least one time step after the second time step;
High-speed magnetic field analysis method characterized by   2. The high-speed magnetic field analysis method according to claim 1, wherein the magnetic field itself is obtained from a magnetic vector potential, and a fluctuation amount of the magnetic field from the previous time step is obtained from a fluctuation amount of the magnetic vector potential from the previous time step. analysis method.   2. The fast magnetic field analysis method according to claim 1, wherein at least one time step after the second time step is calculated based on a fluctuation amount of a magnetic vector potential and a fluctuation amount of an electric scalar potential from the previous time step. Fast magnetic field analysis method to find the amount of magnetic field fluctuation from In the high-speed magnetic field analysis method according to any one of claims 1 to 3,
When analyzing a rotating machine, the analysis space is divided into a rotor space including a rotor and a stator space including a stator,
The mesh data of this analysis space is divided into meshes at equal intervals with a predetermined angular width Δθ in the rotation direction at the boundary between the rotor space and the stator space.
A high-speed magnetic field analysis method for analyzing the rotor space by rotating the mesh in the rotor space by an angular width Δθ or an integral multiple thereof. In the high-speed magnetic field analysis method according to claim 4,
When analyzing to change the rotation speed of the rotor, the time step width is adjusted to the change in the rotation speed of the rotor so that the mesh of the rotor space and the mesh of the stator space are matched. Fast magnetic field analysis method to change. The high-speed magnetic field analysis method according to claim 1,
The magnetic resistivity is represented by a 3 × 3 tensor considering the anisotropy of the analysis space. The high-speed magnetic field analysis method according to claim 1,
When a thin insulating layer is included in the analysis space, the thin insulating layer is modeled by an infinitely thin gap element, and analysis is performed by solving an equation in which the space integral is replaced by the area by this modeling. Magnetic field analysis method. The high-speed magnetic field analysis method according to claim 3,
The analysis space includes two conductors and a thin insulating layer sandwiched between these conductors, and no element is assigned to the thin insulating layer, and nodes are set on the surface in a double manner. A high-speed magnetic field analysis method for analyzing an analysis space in which electric scalar potentials are set at these nodes. The high-speed magnetic field analysis method according to claim 1,
The analysis space includes a magnetic body and a coil,
The magnetic vector potential is defined as the total potential, and the potential obtained by subtracting the magnetic vector potential due to the bio-Savart field induced by the coil current in the air region of the analysis space from the total potential is defined as the deformation potential.
An area where the magnetic body is present and the total potential is an unknown variable, an area where the coil is present and the deformation potential is an unknown variable, and the two potentials of the total potential and the deformation potential are unknown variables. A high-speed magnetic field analysis method for analyzing an analysis space divided into two potential boundary layers.   A high-speed magnetic field analysis program coding a series of processes in the high-speed magnetic field analysis method according to any one of claims 1 to 9.   A computer-readable recording medium on which the high-speed magnetic field analysis program according to claim 10 is recorded.

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